FRM Level 1 Part 3

Question 1

chapter 1 bank
accounting
banking book

Answer 1

https://www.youtube.com/watch?v=G5rYrwCko2E

focus on loan

The banking book consists of assets and liabilities that are expected to be held until maturity.

the solution of the not mark to market: smoothing rule and rescheduling the debt

Question 2

trading book

Answer 2

All assets & liabilities

procession: marked to market and marked to model

The trading book (as its name implies) consists of assets and liabilities that are held to trade.

Question 3

the difference between banking book and trading book

Answer 3

Items in the trading book are subject to market risk capital calculations, whereas items in the banking book are subject to credit risk capital calculations.

Question 4

The Fundamental Review of the Trading Book mentioned______

Answer 4

earlier attempts to clarify the Basel Committee’s rules concerning whether an instrument should be in the banking book or the trading book.

Question 5

investment banking

How to raising debt / equity financing

Answer 5

1. originating
2. underwriting
3. Placing securities
   tips: Underwriting securities and Placing securities can be done by Road Show

Question 6

Originating securities includes______

Answer 6

private placement

Public offering

Question 7

Public offering involve_____

Answer 7

Best effort (as a broker)
Firm commitment (as a dealer)

tips: IPO
The advantage of using investment banks to handle an IPO is that they have the necessary expertise as well as relationships with potential investors. However, some issuers feel that they would prefer for the market to decide the right price for their company.

One way they can do this is through a Dutch auction. This is a procedure where all investors (not just clients of an investment bank) are invited to submit bids indicating how many shares they would like to purchase and at what price.

Question 8

Commercial banking face ______

Answer 8

market risk, credit risk and operational risk

Question 9

Capital requirement include _____

Answer 9

Regulatory capital and economic capital

Question 10

regulatory capital involves _____

Answer 10

Tier I: Equity and Tier II: Subordinated debt

Question 11

regulatory Capital ______(more or less) significant effect than economic capital

Answer 11

more

Question 12

deposit insurance for _________

Answer 12

depositors and banks

Question 13

To depositor, deposit insurance can______

Answer 13

1. maintain confidence in bank (by GOV)
2. against loss to a certain level
3. have disadvantage: moral hazard

Question 14

To bank, deposit insurance have disadvantage_____, and its solution is_______

Answer 14

Moral hazard, risk-based deposit insurance premiums

Question 15

what is deposit insurance?

Answer 15

To maintain confidence in the banking system, many countries have introduced deposit insurance. This typically provides a certain amount of protection to a depositor against losses arising from a bank failure.

Deposit insurance is a measure implemented in many countries to protect bank depositors, in full or in part, from losses caused by a bank’s inability to pay its debts when due. Deposit insurance systems are one component of a financial system safety net that promotes financial stability.

Question 16

what is regulatory Capital

Answer 16

Regulatory capital is the minimum capital that regulators require banks to keep.

Question 17

what is Economic capital

Answer 17

Economic capital is a bank’s own estimate of the capital it requires.

Question 18

what is the same area and different aspect between regulatory capital and economic capital

Answer 18

common area:
In both cases, capital can be thought of as funds that are available to absorb unexpected losses.

different aspect:
A com-mon objective in calculating economic capital is to maintain a high credit rating (as will be described in later chapters). Economic capital is allocated to a bank’s business units so that they can be compared using a return on allocated economic capital metric.

Question 19

The amount of capital that is necessary depends on:

Answer 19

the size of possible losses.

Question 20

Potential conflict mentions_______

Answer 20

advisor-seller problem, dump garbage, information leakage, research independent problem

Question 21

the solution for information leakage and research independent problem is______

Answer 21

Chinese Wall

Question 22

what is Chinese wall

Answer 22

Chinese wall is a business term describing an information barrier within an organization that was erected to prevent exchanges or communication that could lead to conflicts of interest. For example, a Chinese wall may be erected to separate and isolate people who make investments from those who are privy to confidential information that could improperly influence the investment decisions. Firms are generally required by law to safeguard insider information and ensure that improper trading does not occur.

For finance, A Chinese wall is most commonly employed in investment banks, between the corporate-advisory area and the brokering department in order to separate those giving corporate advice on takeovers from those advising clients about buying shares;[1] see #Research there. The “wall” is thrown up to prevent leaks of corporate inside information, which could influence the advice given to clients making investments, and allow staff to take advantage of facts that are not yet known to the general public.

For insurance, The term is used in property and casualty insurance to describe the separation of claim handling where both parties to a claim (e.g. an airport and an airline) have insurance policies with the same insurer. The claim handling process needs to be segregated within the organisation to avoid a conflict of interest.

Question 23

what is information leakage

Answer 23

1. Capital that exits an economy or system rather than remaining within the system is leakage.
2. Funds spent on taxes, deposited into savings, or used to buy imported goods will create leakage.
3. Export funds can result in leakage when those funds are invested in areas other than where the exports are produced

Information or data leakage occurs when internal information that should be held private or confidential is released to the public. This release of information can include the accidental or intentional disclosure of information, or a failure to secure the information, which leads to exposure.

Question 24

what is Originate-to-distribute model

Answer 24

Traditionally, banks have originated loans and kept them on their balance sheet. An alternative to this is what has become known as the originate-to-distribute model. Under this model, banks use their expertise to originate loans and then sell them (directly or indirectly) to investors.

Question 25

Originate-to-distribute arrangements have been used in the U.S. mortgage market for many years. The U.S. government has sponsored the creation of three entities:

Answer 25

1. Government National Mortgage Association (GNMA) or Ginnie Mae,
2. Federal National Mortgage Association (FNMA) or Fannie Mae, and
3. Federal Home Loan Mortgage Corporation (FHLMC) or Freddie Mac.

Question 26

The originate-to-distribute model played a role in the 2007–2008 crisis, because____

Answer 26

Banks relaxed their mortgage lending standards so that the quality of the mortgages being originated declined. Despite this decline in quality, however, banks still managed to securitize them. In fact, they re-securitized mortgages by creating tranches from tranches. As defaults on the mortgages grew higher, losses were experienced by tranche holders. Unsurprisingly, for a period after the crisis, the originate-to-distribute model could not be used because it was not trusted by investors.

Question 27

Process of the originate-to-distribute model _______

Answer 27

Originator provide loan for borrower and receive asset. Originator exchange cash by SPV. SPV receive investors’ Cash and output ABS to investor.

Question 28

what is ABS

Answer 28

An asset-backed security (ABS) is an investment security—a bond or note—which is collateralized by a pool of assets, such as loans, leases, credit card debt, royalties, or receivables. … For investors, asset-backed securities can be an alternative to corporate debt

Question 29

Securitized Asset from______

Answer 29

Student loans and Credit card receivable

Question 30

E.g. for SPV

Answer 30

House holder (Borrower) applies for bank's Mortgage and bank receives house holder's loan.
Bank sell loans to GNMA, FNMA, FHLMC (or other originators or lenders) and bank receive cash from them. GNMA, FNMA, FHLMC issues MBS to investor.

Question 31

what is MBS

Answer 31

A mortgage-backed security (MBS) is an investment similar to a bond that is made up of a bundle of home loans bought from the banks that issued them. Investors in MBS receive periodic payments similar to bond coupon payments. … An MBS may also be called a mortgage-related security or a mortgage pass-through.

Question 32

insurance companies and pension plans
category of insurance company

Life insurance: based on insurance term
it is divided into term life insurance and whole life insurance

term life insurance have two circumstance:

Answer 32

1. a predetermined number of years

2. Usage: use as mortgage funding

Question 33

a predetermined number of years have two situations:

Answer 33

Policyholder dies within term: face value amount of payment

Policyholder survives: get nothing

Question 34

whole life involve the following several features

Answer 34

1. protection for the life policyholder
2. higher premiums (payout is certain)
3. redeem early
4. Use it as collateral
5. surplus premiums in early years, later deficit
6. tax advantage

Question 35

Life insurance: based on surplus premium choice:
it is divided into variable life insurance, universal life insurance, variable-universal life insurance

variable life insurance mentions following three characteristics:

Answer 35

1. surplus premiums are invested in a fund chosen by policyholder
2. minimum payout on death is guaranteed
3. policyholder would receive more if fund perform well

Question 36

universal life insurance involves the following feature or options:

Answer 36

feature: Minimum payout on death is guaranteed

surplus premium payout invested in fixed income product

two options on policy holder:

1. Premium could be reduced down to a specified minimun, but only fixed payout could be received if policyholder dies
2. paying more premium, fixed more floating payout could be received if policyholder dies

Question 37

variable-universal life insurance have the following two features

Answer 37

1. after the scanning from insurance company, a number of alternative
2. it also can reduce the premium down to a specific without policy lapsing

Question 38

the following two kind of others insurances:

Answer 38

endowment life insurance and Group life insurance

Question 39

endowment life insurance have the following three features:

Answer 39

1. pays a lump sum (requires two situation: the policyholder dies or at the end of period)
2. payout can be with-profit
3. pure endowment (only if policyholder survive)

Question 40

Group life insurance have the following three features:

Answer 40

1. cover many people under a single policy
2. premium can be contributory and noncontributory
3. medical test is not necessary

Question 41

mortality table 的均衡保费思想：

Answer 41

PV 缴费 = PV 赔付

Question 42

Annuity contract (advantage: Tax deferral; feature: option might be embedded)

pension plan is divided into two plans:

Answer 42

Defined Benefit Plan:
features:
1. contribution and fund are managed in a pool
2. employee may receive on retirement is defined by the plan

Defined Contribution Plan:
features:
1. contribution are invested on behalf of the employee
2. investment alternatives are available to be chosen by the employee (Take the investment risk by themselves)
3. Independent account for each employee

Question 43

Health insurance:

Answer 43

Policy holder makes regular premium payment and payouts are triggered by event like body examinations etc.

Question 44

Non-life insurance companies:

Answer 44

Properties-casualty insurance:

1. property insurance
2. Casualty insurance

Ratios calculated by property-casualty insurers:
Loss ratio = payouts / premium earned (保险费的获取)
Expense Ratio = expenses / premiums earned
combined ratio = expense ratio + loss ratio
combined ratio after dividend = combined ratio + dividend
operating ratio = combined ratio after dividend - investment income (%)
= combined ratio + dividend - investment income

investment income (%) = investment income/premium

Question 45

regulation

Answer 45

Europe: central regulation

US:
state regulation
contribution have to be made after insolvency occurred in guaranty system

Question 46

capital requirements

Answer 46

life insurance company balance sheet: high liabilities and low equity——> high leverage

Question 47

property-casualty insurance company balance sheet:

Answer 47

Higher equity that life insurance companies because that short term insurance periods needs higher liquidity.

Question 48

risks faced by insurance companies

Answer 48

moral hazard: the policyholder behave differently with the existence of insurance than he would without the insurance

adverse selection: insurance company cannot distinguish between good and bad risks ——-longevity risk and mortality

other risk: investment performance risk, policy reverse shortfall risk, liquidity risk, credit risk, operational risk, business risk

Question 49

Mutual fund

Answer 49

3 main types of long-term funds:
bond funds
equity funds
hybrid funds

open-end fund: outstanding share change with buying or reminding at next NAV

close-end fund: fixed number of shares outstanding

Open-end funds can be categorized as follows:
• Money market funds, • Bond funds, and • Equity funds.

Equity funds are the most popular type of mutual funds. They can be subdivided into:
• Actively managed funds, and • Index funds.

ETF (Exchange-traded funds (ETFs) ): 开放式指数证券基金, 开放式基金的一种，交易和封闭式基金类似

NAV = (funds assets-funds liabilities)/total share outstanding

NAV could only be calculated after the close of the trading days (for open-end funds)

NAV could only be calculated continuously during the time of trading (close-end fund and ETFs)

Question 50

hedge funds

Answer 50

hedge fund strategies (7):
Long/short equity
dedicated short 
distressed securities 
merger/fixed income/convertible arbitrage
emerging markets 
Global Macro
managed future

Question 51

Funds from different clients are pooled, and the fund managers choose investments in accordance with stated invest-ment goals and risk appetites. There are several advantages to this approach:

Answer 51

• Fund managers may have more investment expertise than their clients.
• Transaction costs (as a percentage of the amount traded) are usually lower for large trades than for small trades.
• It is difficult for a small investor to be well diversified, but a large fund with billions of dollars should not have any difficulty in achieving diversification

Question 52

Despite these safeguards, there have been instances of undesirable behavior:

Answer 52

a) Late Trading. As mentioned, all trades to buy and sell shares in an open-end mutual fund are at 4 p.m., and thus trade instructions should reach a broker before 4 p.m.
b) Market Timing. Not all the assets of an open-end mutual fund trade actively. This may lead to the prices used to calculate NAV being stale (i.e., not reflecting recent information).
c) Front Running. If a trader working for a mutual fund (or any other type of fund) knows that the fund will execute a big trade that is likely to move the market, it is tempting for the trader to trade on his or her own account immediately before putting through the fund’s trade.
d) Directed Brokerage. This involves an informal arrangement between a mutual fund and a brokerage house. The unwritten agreement is that the mutual fund will use the brokerage house for its trades if the brokerage house recommends the mutual fund to its clients.

Question 53

While mutual funds and ETFs cater to the needs of small investors, hedge funds usually accept only large investments from wealthy private individuals or institutions. There are several other differences. The following are examples.

Answer 53

• A mutual fund or ETF allows investors to redeem their shares on any day. A hedge fund may have a lock-up period during which time funds cannot be withdrawn. Lock-up periods of one year are common.
• The NAV of a mutual fund or ETF must be calculated and reported at least once a day. In contrast, hedge funds have no such requirements, and their NAVs are reported much less frequently.
• Mutual funds and ETFs must disclose their investment strategies. Hedge funds generally follow proprietary strategies that they see as fundamental to their competitiveness and/or value proposition. They give prospective clients some information to explain their value proposition, but do not disclose everything. Furthermore, they are not obligated to stick to one strategy.
• Mutual funds and ETFs may be restricted in their use of leverage. A hedge fund is only restricted by the amount banks are willing to lend to it.
• Hedge funds charge an incentive fee as well as a management fee. A typical hedge fund fee is 2 plus 20%. This means that the investors are charged 2% of the value of their investment per year along with 20% of the profits (if these net profits are positive).11

Question 54

The descriptor hedge fund arises from the long-short strategies followed by many hedge funds.

Answer 54

This type of strategy involves taking long positions in stocks expected to provide good returns and short positions in stocks expected to provide poor returns. However, there are also hedge fund strategies that involve little to no hedging whatsoever

Question 55

hedge fund performance measurement bias

Answer 55

survivorship bias: overestimated return of industry
backfill bias: backfill only good strategies
stale price bias: underestimate volatility
self-selection bias: only good players choose to report

计算： management fee, incentive fee
Hedge funds charge an incentive fee as well as a management fee. A typical hedge fund fee is 2 plus 20%. This means that the investors are charged 2% of the value of their investment per year along with 20% of the profits (if these net profits are positive).

Question 56

A long-short fund’s performance should depend entirely on the fund manager’s ability to pick winners and losers (and not on what happens to the market as a whole) so long as:

Answer 56

• The value of the shares shorted equals the value of those bought, and
• Both the long and short portfolios have the same sensitivity to market movements.

Question 57

Dedicated Short

Answer 57

At any given time, it is reasonable to suppose that there are as many overvalued shares as undervalued shares. A dedicated short fund devotes its attention to picking overvalued stocks. Hedge funds using dedicated short strategies look for companies that are experiencing difficulties not recognized by the market. However, they are not hedged against the overall performance of the market. It is therefore not surprising that dedicated short strategies perform badly during bull markets.

Question 58

Distressed Debt

Answer 58

Some hedge funds specialize in trading distressed debt. They use their understanding of the bankruptcy process to find situations where they can take a big position in the debt and benefit from reorganization proposals.

Question 59

Merger Arbitrage

Answer 59

When a company announces that it is prepared to buy another company, there is usually some uncertainty about whether the acquisition will proceed. The share price of the target company usually increases, but not to the price being offered. A merger arbitrage hedge fund might consider that there is an 80% chance that the acquisition will be successful and that the acquisition price will be higher than the current price. Buying the target company’s shares could then be a good trade. If the offer on the table is a share-for-share exchange and the hedge fund expects an improvement in the terms before a deal is finally announced, it could buy the shares in the target company and sell shares in the acquiring company in a ratio that reflects the current offer.

It should be emphasized that merger arbitrage is not about trading on inside (non-public) information (which is illegal).16 It is about assessing the probability of a merger being successful and the likely final price (or exchange ratio in the case of a share-for-share exchange) at the time of the merger announcement.

Question 60

Convertible Arbitrage

Answer 60

Convertible bonds are bonds issued by a company that can be converted into a predetermined number of the company’s shares at a future time. Convertible arbitrage hedge funds use sophisticated models to value convertible bonds. They hedge the risks associated with the company’s share price, credit spreads, and interest rates. If the market price is currently different from the hedge fund’s model price, the strategy can be profitable if the market price converges to the model price.

Question 61

Fixed-Income Arbitrage

Answer 61

At any given time, some traded bonds are likely to be relatively expensive compared with other similar bonds, while others are relatively cheap. In a fixed-income arbitrage strategy, the hedge fund manager buys bonds that seem relatively cheap and shorts the ones that are relatively expensive. Typically, they use a lot of leverage to make the strategy worthwhile.

Question 62

Emerging Markets

Answer 62

Hedge funds that specialize in emerging markets attempt to gather information about little-known equity securities in developing countries. When they consider a security to be under-valued (overvalued), they buy (short) it in the local markets. An alternative is to use American Depositary Receipts (ADRs), which are certificates backed by shares of a foreign company and traded on an exchange in the U.S. Any discrepancies between ADR prices and local prices can give rise to arbitrage opportunities.
Hedge funds can also invest in emerging market sovereign debt. However, this is fraught with risks. Countries such as Russia, Argentina, Brazil, and Venezuela have defaulted multiple times (as will be discussed in Chapter 5 of Valuation and Risk Models).

Question 63

Global Macro

Answer 63

Global macro hedge funds use macroeconomic analysis to determine their trades. Specifically, they look for situations where markets are not in equilibrium using models based on factors such as exchange rates, interest rates, balance of payments, inflation rates, etc. Sometimes the results are spectacular: The Quantum Fund managed by George Soros made a profit of USD 1 billion in 1992 by betting that the British pound was overvalued. However, not all global macro trades are that successful, and economies can remain in disequilibrium for long periods of time.

Question 64

Managed Futures

Answer 64

Managed futures strategies attempt to predict future commodity prices and take positions that will be profitable if the predictions are correct. Several different models are used and trading rules are usually back-tested by seeing how well they would have performed if they had been used in the past. However, there is a danger in this. Back-testing does not differentiate between strategies with a fundamental understanding of the markets and strategies that were just lucky (and thus not necessarily bound to be successful in the future)

Question 65

Questions a prospective mutual fund investor might reasonably ask are as follows.

Answer 65

• On average, do actively managed mutual funds outperform the market?
• Do actively managed funds that outperform the market in one year have a high probability of doing so in the next year?

Question 66

the different between mutual fund and hedge fund

Answer 66

mutual fund hedge fund

NAV calculation Daily longer period

investment policy full disclosure not full disclosure

leverage limited use high leverage

redeemability redeemable Usually lock-up
at any time period exists

Question 67

derivatives

Answer 67

price undermined by underlying assets

Question 68

type of derivatives

Answer 68

forward commitment  (权利义务对等)
contingent claim

Question 69

forward commitment (权利义务对等)

Answer 69

Forward (OTC):

1. 买卖双方约定fixed price, identity, quantity
2. sign the contract, after certain time, expire

futures (exchange trade)：

1. standardize & trade on Exchange
2. Everything is settled:
   a. specified underlying
   b. Time to expiration
   c. delivery
   d. settlement conditions
   c. quantities
3. exchange: physical location or electronic system
4. liquidity provided by authorized market makers

SWAP(OTC, a.k.a: a series off-market forward):

1. interest rate swap:
   a. same currency
   b. fixed rate —— floating rate
2. currency sway:
   a. fixed — fixed
   b. fixed — floating
   c. floating — floating

Question 70

contingent claim

In finance, a contingent claim is a derivative whose future payoff depends on the value of another “ underlying ” asset, or more generally, that is dependent on the realization of some uncertain future event.

Answer 70

options (both OTC & exchange trade)

1. counterparty:
   a. Long call: right to buy
   b. Short call: obligation to sell
   c. Long put: right to sell
   d. short put: obligation to buy
2. Premium:
   c 表示看涨期权权费
   p 表示看跌期权权费
3. Strick / exercise price (K or X)

4. 能否提前行权
European Option(No)
American Option(Yes)

Question 71

Type of trader in financial derivatives market

Answer 71

hedger
speculator
Arbitrageurs

Question 72

function in financial derivatives

Answer 72

price discovery

Transfer price rick

Question 73

pricing in financial derivatives

Answer 73

law of one price

1. arbitrage: buy low sell high
2. replication: asset + derivatives = risk-free asset

Question 74

interest rate

risk-free rate

Answer 74

treasury rates
LIBOR
REPO rates

Question 75

spot rate (a.k.a. zero-coupon rate or zero rate)

Answer 75

spot rate valuation method

The spot rate is calculated by finding the discount rate that makes the present value (PV) of a zero-coupon bond equal to its price. These are based on future interest rate assumptions. So, spot rates can use different interest rates for different years until maturity.

Bootstrapping spot rate — bootstrapping

Bootstrapping spot rates using the par curve is a very important method that allows investors to derive zero coupon interest rates from the par rate curve. Bootstrapping the zero coupon yield curve is a step-by-step process that yields the spot rates in a sequential way.

Question 76

par yield

Forward rate

Answer 76

RF = (R2T2 - R2T2) / (T2 - T1)

= R2 + (R2 - R1)* T1/(T2 - T1)

Question 77

three theory of term structure

Answer 77

pure expectation theory

A theory that asserts that forward rates exclusively represent the expected future rates. In other words, the entire term structure reflects the market’s expectations of future short-term rates. For example, an increasing slope to the term structure implies increasing short-term interest rates

liquidity preference (premium) theory

Liquidity preference theory suggests that investors demand progressively higher premiums on medium and long-term securities as opposed to short-term securities.

market segmentation theory

Market segmentation theory states that long- and short-term interest rates are not related to each other because they have different investors.
Related to the market segmentation theory is the preferred habitat theory, which states that investors prefer to remain in their own bond maturity range due to guaranteed yields. Any shift to a different maturity range is perceived as risky.

Question 78

Forward rate agreement (FRA)

Answer 78

What Is a Forward Rate Agreement – FRA?

Forward rate agreements (FRA) are over-the-counter contracts between parties that determine the rate of interest to be paid on an agreed upon date in the future. An FRA is an agreement to exchange an interest rate commitment on a notional amount.

OTC
long position: borrow at the fixed rate
short position: lend at the fixed rate

value of long position:
= Principle x (Rreal - Rforward) x (T2 - T1) e^(-R2xT2)

Question 79

利率风险度量

duration

Answer 79

Macaulay duration
MacDur = the sum of (t x PVCFt) / the sum of (PVCFt)
perpetuity bond, MacDur = (1 +r)/r
The Macaulay duration is the weighted average term to maturity of the cash flows from a bond. The weight of each cash flow is determined by dividing the present value of the cash flow by the price. Macaulay duration is frequently used by portfolio managers who use an immunization strategy.

Macaulay Duration= the sum of [t = 1 to n] {(t x c)/(1 + y)^t + (n x M)/(1+y)^n}/current bond price

t=respective time period
C=periodic coupon payment
y=periodic yield
n=total number of periods
M=maturity value
Current Bond Price=present value of cash flows 

2. modified duration
   ModDur = MacDur / (1+r) r 是期间利率
   % delta price =~~ -ModDur x delta Yield
   Modified duration is a formula that expresses the measurable change in the value of a security in response to a change in interest rates. Modified duration follows the concept that interest rates and bond prices move in opposite directions. This formula is used to determine the effect that a 100-basis-point (1 percent) change in interest rates will have on the price of a bond.
   Modified Duration= Macauley Duration/ 1 + YTM/n
   Macauley Duration=weighted average term to
   maturity of the cash flows from a bond
   YTM=yield to maturity
   n=number of coupon periods per year
   ​
3. money duration / dollar duration:
   MoneyDur = Mod x Price(full)

money duration is called dollar duration. It is the approximate dollar change in a bond’s price for a 100 basis point change in yield. It is the approximate dollar change in a bond’s price for a 100 basis point change in yield.
The dollar duration measures the dollar change in a bond’s value to a change in the market interest rate. The dollar duration is used by professional bond fund managers as a way of approximating the portfolio’s interest rate risk. Dollar duration is one of the several different measurements of bond duration.
As duration measures the sensitivity of a bonds price in interest rate changes, dollar duration seeks to give these changes an actual dollar amount.

4. DVO1(a.k.a. PVBP):
   PVBP = (P_ - P+)/2 P_是YTM上升1bp的价格， P+ 是YPM 下降1bp的价格

Price value of a basis point (PVBP) is a measure used to describe how a basis point change in yield affects the price of a bond.
Price value of a basis point is also known as the value of a basis point (VBP), dollar value of a basis point (DVBP), or basis point value (BPV).

Question 80

convexity

Answer 80

Convexity is a measure of the curvature, or the degree of the curve, in the relationship between bond prices and bond yields. Convexity demonstrates how the duration of a bond changes as the interest rate changes. Portfolio managers will use convexity as a risk-management tool, to measure and manage the portfolio’s exposure to interest rate risk.

凸度是衡量债券价格和债券收益率之间关系的曲率或曲线的程度。 凸度说明了债券的期限如何随利率的变化而变化。 投资组合经理将使用凸度作为风险管理工具，以衡量和管理投资组合面临的利率风险。

KEY TAKEAWAYS
Convexity is a risk-management tool, used to measure and manage a portfolio’s exposure to market risk.
Convexity is a measure of the curvature in the relationship between bond prices and bond yields.
Convexity demonstrates how the duration of a bond changes as the interest rate changes.
If a bond’s duration increases as yields increase, the bond is said to have negative convexity.
If a bond’s duration rises and yields fall, the bond is said to have positive convexity.

Bond duration measures the change in a bond’s price when interest rates fluctuate. If the duration of a bond is high, it means the bond’s price will move to a greater degree in the opposite direction of interest rates. Conversely, when this figure is low the debt instrument will show less movement.

Typically, if market rates rise by 1%, a one-year maturity bond price should decline by an equal 1%. However, for bonds with long-dated maturities, the reaction increases. In other words, if rates rise by 1%, bond prices fall by 1% for each year of maturity. For example, if rates rise by 1%, the two-year bond price would fall 2%, the three-year bond price by 3%, and the 10-year price by 10%.

债券期限是衡量利率波动时债券价格的变化。 如果债券的期限很高，则意味着债券的价格将在与利率相反的方向上更大程度地波动。 相反，当该数字较低时，债务工具将显示较少的变动。

通常，如果市场利率上升1％，则一年期债券价格应下降相等的1％。 但是，对于期限长的债券，反应会增加。 换句话说，如果利率上升1％，则到期的每一年债券价格都会下降1％。 例如，如果利率上升1％，则两年期债券价格将下降2％，三年期债券价格将下降3％，十年期价格将下降10％。

% delta price full =~~ [-ModDur x delta] x [0.5 x Con x Yield^2]

Question 81

interest rate future

T-bill and T-bond

Answer 81

day count convention:
US. treasury bond: actual /actual
US. corporate and municipal bond: 30/360
US. money market instruments (Treasury bills: actual / 360)

A day-count convention is a standardized methodology for calculating the number of days between two dates.
The interest on most money market deposits and floating-rate notes is calculated on an actual/360 day-count convention while bonds and notes issued by the U.S. Treasury earn interest calculated on an actual/actual basis..
The fixed-rate leg of an interest rate swap and most fixed-rate bonds use either the 30/360 or 30/365 day-count convention while the floating-rate leg uses some variation of an actual/360 or 365 day-count convention.

30 / 360 - calculates the daily interest using a 360 day year and then multiplies that by 30 (standardized month)
30 / 365 - calculates the daily interest using a 365 day year and then multiplies that by 30 (standardized month)
actual / 360 - calculates the daily interest using a 360 day year and then multiplies that by actual number of days in each time period.
actual / 365 - calculates the daily interest using a 365 day year and then multiplies that by actual number of days in each time period.
actual / actual - calculates the daily interest using the actual number of days in the year and then multiplies that by actual actual number of days in each time period.

quotations for T-bill:
quoted price = 360/n * (100 - Y)
Y is cash price

Maturity (sometimes shown as “issue”): This is the date the bill will be redeemed and the investor paid the face value amount. For purposes of this example, assume the maturity date is 100 days in the future.
Bid: The bid represents the interest rate the buyer wants to be paid. Converting the bid into an actual price requires a bit of work. The process involves multiplying the bid (dropping the decimals) by the number of days until maturity and then dividing by 360 and then subtracting that number from 10,000.
4100/360=$1.11
$10,000-$1.11=$9,998.89
In this example, the buyer is willing to pay $9,998.89 for a bill that will be redeemed for $10,000 in 100 days.
Ask: The ask represents the interest rate the seller is willing to pay. The equation to determine the asking price is the same as that used to determine the bid. Simply replace the asking price with the bid price in the equation.
3100/360=$0.83
$10,000-$0.83=$9,999.17
In this example, the seller is willing to accept $9,999.17 for a bill that will be redeemed for $10,000 in 100 days.
Change: The change shows the difference from the prior bid. In this case, the prior bid was higher by 0.01 basis points.
Yield: The yield is the annualized rate of return if held until maturity based on the asking price. In this example, the yield is 0.03.

quotation for T-bond

a. dollars and thirty-seconds(32) of a dollar with a face value of $100
b. Full price = Clean price + Accrued interest
c. accrued interest: accrued interest = # of days from coupon to the settlement date / # of days in coupon period

A bond quote refers to the last price at which a bond traded.
Bond quotes are expressed as a percentage of par (face value) and converted to a point scale.
The par value is traditionally set at 100, which represents 100% of a bond’s $1,000 face value.
Bond quotes may also be expressed as fractions.

Question 82

T-bond future (physical delivery)

Answer 82

a. conversion factor
b. short position choose to delivery any government bond
c. face value is 100000 USD
d. cheapest-to-deliver bond
1. revenue for short position: QFP x CF + AI
2. cost for short position: QBP + AI
3. CTD is the on that minimizes: QBP - (QFP x CF)

QFP = quoted futures price/settlement price

CF = conversion factor

AI = accrued interest since the last coupon date on the bond delivered

Bond Conversion Factors
The bonds that can be delivered are standardized through a system of conversion factors calculated according to the rules of the exchange. The conversion factor is used to equalize coupon and accrued interest differences of all delivery bonds. The accrued interest is the interest that’s accumulated and yet to be paid.
债券转换因子
通过根据交换规则计算的转换因子系统，可以对可交割的债券进行标准化。 转换因子用于均衡所有交付债券的息票和应计利息差额。 应计利息是已累计但尚未支付的利息。

What Is Accrued Interest?
In accounting, accrued interest refers to the amount of interest that has been incurred, as of a specific date, on a loan or other financial obligation but has not yet been paid out. Accrued interest can either be in the form of accrued interest revenue, for the lender, or accrued interest expense, for the borrower.
什么是应计利息？
在会计中，应计利息是指截至特定日期已就贷款或其他财务义务产生但尚未支付的利息金额。 应计利息可以是贷方应计利息收入的形式，也可以是借款人应计利息费用的形式。

Accrued interest is a feature of accrual accounting, and it follows the guidelines of the revenue recognition and matching principles of accounting.
Accrued interest is booked at the end of an accounting period as an adjusting journal entry, which reverses the first day of the following period.
The amount of accrued interest to be recorded is the accumulated interest that has yet to be paid as of the end date of an accounting period.

What Does Cheapest to Deliver Mean?
The term cheapest to deliver (CTD) refers to the cheapest security that can be delivered in a futures contract to a long position to satisfy the contract specifications. It is relevant only for contracts that allow a variety of slightly different securities to be delivered. This is common in Treasury bond futures contracts, which typically specify that any treasury bond can be delivered so long as it is within a certain maturity range and has a certain coupon rate. The coupon rate is the rate of interest a bond issuer pays for the entire term of the security.

最便宜的交付意味着什么？
术语“最便宜的交割”（CTD）是指可以在期货合约中交割以满足合约规格的多头头寸的最便宜的证券。 它仅与允许交付各种略有不同的证券的合同有关。 这在国债期货合约中很常见，通常规定只要在一定期限内并且具有一定的票面利率，就可以交付任何国债。 息票利率是债券发行人在整个证券期限内支付的利率。

CTD = Current Bond Price – Settlement Price x Conversion Factor

Question 83

Eurodollar futures (cash settle)

Answer 83

maturity: 3 mouth (0.25 year)
value of one Eurodollar Futures contract:
Pt = 10000 x [100 - 0.25(100 - Z)] = 10000 x [100 - 0.25Ft]

short positions makes a profit when Forward rate increases

1 basis point up move in the futures quote with $25 change per contract

convexity adjustment
actual forward rate = forward rate implied by futures - 0.5 x sigma^1 x T1 x T2

LIBOR zero curve
Rforward = (R2T2 - R1T1) / (T2 - T1)
R2 = [Rforward x (T2 - T1) + R1T1] / T2

duration-based hedging
N = (P x Dp)/(F x Df)

Not to be confused with the euro/U.S. dollar (EUR/USD) currency pair or the euro currency, eurodollars are a type of U.S. dollar deposit held in a bank outside of the United States.
The name eurodollars stems from the fact that the term initially referred to dollar-denominated deposits largely held in European banks, but now dollar deposits are held in a variety of banks across the globe.
Eurodollars typically offer higher yields because they are not subject to U.S. bank regulation and therefore carry greater risk.
Eurodollar futures trade on the trading floor and electronically on the Chicago Mercantile Exchange.
不要与欧元/美国混淆 美元（EUR / USD）货币对或欧元货币，欧元是在美国以外的银行中持有的美元存款的一种。
欧洲美元之所以得名，是因为该术语最初指的是主要在欧洲银行中持有的以美元计价的存款，但现在美元存款则在全球的多家银行中持有。
欧洲美元通常会提供更高的收益率，因为它们不受美国银行监管的约束，因此风险更大。
欧洲美元期货在交易大厅和芝加哥商业交易所进行电子交易。

LIBOR and Eurodollars
The price of eurodollar futures reflects the interest rate offered on U.S. dollar-denominated deposits held in banks outside the United States. More specifically, the price reflects the market gauge of the 3-month U.S. dollar LIBOR (London Interbank Offered Rate) interest rate anticipated on the settlement date of the contract. LIBOR is a benchmark for short-term interest rates at which banks can borrow funds in the London interbank market. Eurodollar futures are a LIBOR-based derivative, reflecting the London Interbank Offered Rate for a 3-month $1 million offshore deposit.

Eurodollar futures prices are expressed numerically using 100 minus the implied 3-month U.S. dollar LIBOR interest rate. In this way, a eurodollar futures price of $96.00 reflects an implied settlement interest rate of 4%, or 100 minus 96. Price moves inverse to yield.

For example, if an investor buys one eurodollar futures contract at $96.00 and the price rises to $96.02, this corresponds to a lower implied settlement of LIBOR at 3.98%. The buyer of the futures contract will have made $50. (1 basis point, 0.01, is equal to $25 per contract, then a move of 0.02 equals a change of $50 per contract.)
LIBOR和欧洲美元
欧元兑美元期货的价格反映了在美国以外银行持有的以美元计价的存款所提供的利率。更具体地说，该价格反映了在合同结算日预期的3个月美元伦敦银行同业拆借利率（LIBOR）的市场价格。 LIBOR是银行可以在伦敦银行间市场借贷资金的短期利率基准。欧洲美元期货是一种基于伦敦银行同业拆借利率的衍生产品，反映了伦敦银行同业拆借利率，为期三个月的100万美元离岸存款。

欧洲美元期货价格以100减去隐含的3个月美元LIBOR利率的数字表示。这样，96.00美元的欧洲美元期货价格反映了4％（即100减去96）的隐含结算利率。价格与收益率成反比。

例如，如果投资者以96.00美元的价格购买一份欧元美元的期货合约，并且价格上涨至96.02美元，则对应于伦敦银行同业拆借利率的隐含结算价较低，为3.98％。期货合约的买主将获得$ 50。 （1个基点0.01，等于每张合约$ 25，然后移动0.02等于每张合约变动$ 50。​​）
Hedging with Eurodollar Futures
Eurodollar futures provide an effective means for companies and banks to secure an interest rate for money it plans to borrow or lend in the future. The eurodollar contract is used to hedge against yield curve changes over multiple years into the future.

For example, say a company knows in September that it will need to borrow $8 million in December to make a purchase. Recall that each eurodollar futures contract represents a $1 million time deposit with a three-month maturity. The company can hedge against an adverse move in interest rates during that three-month period by short selling eight December eurodollar futures contracts, representing the $8 million needed for the purchase.

The price of eurodollar futures reflects the anticipated London Interbank Offered Rate (LIBOR) at the time of settlement or, in this case, December. By short selling the December contract, the company profits from upward movement in interest rates, reflected in correspondingly lower December eurodollar futures prices.

Let’s assume that on Sept. 1, the December eurodollar futures contract price was exactly $96.00, implying an interest rate of 4.0%, and at the expiry in December, the final closing price is $95.00, reflecting a higher interest rate of 5.0%. If the company had sold eight December eurodollar contracts at $96.00 in September, it would have profited by 100 basis points (100 x $25 = $2,500) on eight contracts, equaling $20,000 ($2,500 x 8) when it covered the short position.

In this way, the company was able to offset the rise in interest rates, effectively locking in the anticipated LIBOR for December as it was reflected in the price of the December eurodollar contract at the time it made the short sale in September.

Question 84

SWAP

SWAP characteristics

Answer 84

OTC
Not trade in any organized secondary market 
largely unregulated 
default risk is a concern
most participant are large institutions
private agreements
difficult to alter or terminate

Question 85

Credit risk of SWAP

Answer 85

SWAP is an OTC derivative

1. one with positive payoff would face credit risk, and one with negative payoff may default

Question 86

type of SWAP

Answer 86

interest rate SWAP

currency swap

other type of swap:
equity swap
swaption 
commodity swap 
volatility sway

Question 87

interest rate swap

Answer 87

swap rate: fixed rate(固定端要支付的利率)

swap value:
zero at initiation, but usually non-zero after initiation (互换起始价值为零，期末不为零)
guiding principle (value of payer swap = value of “replicating” floating rate bond - value of “replicating” fixed rate bond)

plain vanilla  interest rate swap:
fixed rate payment  floating rate payments
notional amount is not exchange 
netting payment 
pay the difference 

floating rate bond valuation
reset to par on each settlement date (when interest rate adjust to market rates)
settlement date pull to par
on other date:
settlement date pull to par from principle (par)
coupon: based on LIBOR
1. Finding the next settlement date
2. on next settlement date, total value equal par plus coupon payment at the point
3. discount that value to current time point

Question 88

current swap

Answer 88

two parties
long a bond dominated in current X
short a bond dominated in current Y

value
different of value between two bond by current exchange rate transformation

national amount exchange(互换本金)

Question 89

8 commodity forward and futures

Risk involve with commodity spot transaction

Answer 89

price risk
transportation risk
delivery risk
credit risk

Question 90

basis risk

Answer 90

basis = Spot - forward
基差的方差 = var(s(t)-f(t)) = var(s(t)) + var(f(t)) - 2var(s(t))*var(f(t))*coe(sf)

Question 91

market depth

Answer 91

流动性越好，市场深度越深，反之亦然

Question 92

commodity pricing

Answer 92

Fo = So*e^(r - & + u)T
如果等式不成立，将出现套利机会

1. cash-and-carry arbitrage 
Fo > So*e^rT
at initiation:
borrow money so at risk free rate 
long the spot asset 
short the forward at Fo
at expiration:
settle the position at Fo by delivering the asset 
pay back so with risk-free interest 

Profit at expiration:
Fo - So*e^rT

2. reserve cash-and-carry arbitrage 
Fo < So*e^rT
at initiation:
borrow and short the spot asset
invest the proceed so at risk free rate 
Long the forward at Fo
at expiration:
settle the forward contract at Fo 
close the shot position by delivering the spot asset 
Profit at expiration:
So*e^rT - Fo

Question 93

Commodity market

Answer 93

commodity spread:
crush spread 压榨
crack spread 裂解
掌握计算
1. The crack spread is the contrast between a barrel of crude oil and the petroleum products refined from it. The “crack” is an industry term for breaking apart crude oil into the component finished products, including gases like propane, heating fuel, gasoline, light distillates, intermediate distillates, and heavy distillates.
2. A crush spread is used to hedge the margin between soybean futures and soybean oil and meal futures. With this strategy, a trader takes a long position on soybean futures and a short position on soybean oil and meal futures. The trader may also take the opposite side of this options spread.
3. The spark spread uses natural gas as the raw material component and electricity as the finished product. It is a standard metric for estimating the profitability of natural gas-fired electric generator. For coal, the difference is called the dark spread.

https://cloud.tencent.com/developer/article/1338695

commodity characteristic:
corn: seasonality
crude oil: long-term price less volatile
natural gas: regional, costly to store, seasonal
electricity: demand not constant, none storability
gold: gold mind is assume to operate, synthetic gold better

strip hedge & stark hedge:
risk faced by strip and stack hedge:
strip hedge: 
larger bid-ask spread
 stack hedge: Price risks

Question 94

9 Fundamental of Future Markets

Characteristic

Answer 94

asset 
contract size 
delivery months 
price option 
price limits and position limits

Question 95

subject of future market

Answer 95

clearing 
clearing house:
act as central counterparty 
manages margin accounts 
reduce credit risk
provide liquidity 

brokerage firms
traders

Question 96

mechanics of future markets

Answer 96

margin:
1. initial margin (must be deposited when contract is initiated)
2. maintenance margin (the minimum amount of equity that must be maintained in a margin account)
3. variation margin
variation margin = initial margin - margin account balance

Question 97

daily price limit

Answer 97

pros
increasing the stability 
decreasing the fluctuations 
supplying more time to analyze 
reducing the irrational trading 

cons
enhancing the time of value discovery

Question 98

types of order

Answer 98

market order
limit order
stop order / stop-loss order
stop-limit order

What Is an Order?

1. An order is a set of instructions to a broker to buy or sell an asset on a trader’s behalf.
2. There are multiple order types which will affect what price the investor buys or sells at, when they will buy or sell, or if their order will be filled or not.
3. Which order type to use depends on the trader’s outlook for the asset, whether they want to get in and out quickly, and/or how concerned they are about the price they get.

Here are some the basic order types:
1. A market order instructs the brokerage to complete the order at the next available price. Market orders have no specific price and are generally always executed unless there is no trading liquidity. Market orders are typically used if the trader wants in or out of a trade quickly and is not concerned about the price they get.
2. A limit buy order instructs the brokerage to buy a security at or below a specified price. Limit orders ensure that a buyer pays only a specific price to purchase a security. Limit orders can remain in effect until they are executed, expire, or are canceled.
3. A limit sell order instructs the broker to sell the asset at a price which is above the current price. For long positions, this order type is used to take profits when the price has moved higher after buying.
4. A sell stop order instructs the brokerage to sell if an asset reaches a specified price below the current price. A stop order can be a market order meaning it takes any price once triggered, or it can be a stop limit order where it can only execute within a certain price range (limit) after being triggered.
5. A buy stop order instructs the broker to buy an asset when it reaches a specified price above the current price.
6. A day order must be executed during the same trading day that the order is placed.
Good till canceled (GTC) orders remain in effect until they are filled or canceled.
7. If an order is not a day order or a good til canceled order, the trader typically sets an expiry for the order.
Immediate or cancel (IOC) means that the order only remain active for a very short period of time, such as several seconds.
8. An all or none (AON) order specifies that the entire size of the order be filled, an partial fills will not be accepted.
9. A fill or kill (FOK) order must be completed immediately and completely or not at all and combines an AON order with an IOC order.

Question 99

ways to terminate a futures contract

Answer 99

physical delivery
cash settlement
reverse trading
exchange for physicals

Closeout

This is the case where the futures trader closes out the futures contract even before the expiry. A trader who has a long position can take an equivalent short position in the same contract, and both the positions will be offset against each other. Similarly, a trader with a short position can take a long position in the same contract to closeout the position.

Delivery

On the settlement date, the short can settle the contract by delivering the underlying asset to the long. The contract is settled by delivery. This method is hardly used and constitutes not more than 1% of contract settlements.

In case of the physical delivery, the clearinghouse will select a counterparty for physical settlement (accept delivery) of the futures contract. Typically the counterparty selected will be the one with the oldest long position.

Cash Settlement

Cash settlement can be done only if the contract specifies so. The trader just leaves his position open and when the contract expires, his margin account will be marked-to market for P&L on the final day of the contract. This is the most commonly used method as the trader saves on the transaction costs of closing out the position.
只有在合同中明确规定，才可以进行现金结算。 交易者只是开仓，合约到期时，其保证金账户将在合约的最后一天被标记为损益表。 这是最常用的方法，因为交易者节省了平仓的交易成本。

Exchange for Physicals

A contract can also be terminated through an exchange of physicals. In this case, a trader finds another trader who has an opposite position in the same futures contract and delivers the underlying assets to him. This happens outside the exchange floor, and is called an ex-pit transaction. The traders will then inform the clearinghouse about the transaction.

Question 100

collateralization in the over-counter Market

Answer 100

significant credit (counterparty risk)
similar to the posting margin in the futures markets

Question 101

10 determination of forward and future price

Answer 101

asset
investment assets
consumption assets

Question 102

远期价格公式及变形

Answer 102

assumption:
no transaction cost 
same tax rate 
same risk-free rate 
arbitrage-opportunities

forward price with carrying cost and benefits
Fo = (So + or - I)*e^rT

forward price with a know dividend
Fo = (So )*e^(r-q)T

forward price with storage cost
Fo = (So + U)e^rT
Fo = (So )e^(r+u)T

forward price with storage cost and convenience yield
Fo = (So )*e^(r+u-y)T

forward foreign exchange rate
Fo = (So )*e^(r - rf)T
本币 - 外币

加成本减收益

Question 103

contango and backwardation

Answer 103

1. Contango is when the futures price is above the expected future spot price. A contango market is often confused with a normal futures curve.
2. Normal backwardation is when the futures price is below the expected future spot price. A normal backwardation market is often confused with an inverted futures curve.
3. A futures market is normal if futures prices are higher at longer maturities and inverted if futures prices are lower at distant maturities.

Contango
A contango market is often confused with a normal futures curve.

Normal Backwardation
A normal backwardation market—sometimes called simply backwardation—is confused with an inverted futures curve.

Question 104

delivery option

Answer 104

short position determines where, when, and what to deliver 
c > y: short position to deliver early 
c > y: short position to deliver early 
c: 持有成本
y: 便利收益

Question 105

11 hedging strategies using futures

Answer 105

hedging strategies
short hedge: short future
long hedge: long future

argument for & against hedging 
advantage: 
reduce price risk
disadvantage: 
less impact on the company
less profitability 

character of futures contracts
convergence of futures and spot prices
backwardation:
sport price > future price to sport price = future price
contango:
sport price < future price to sport price = future price

two results of hedging 
perfect hedging:
exactly offset any gains or losses from an existing investment position
without perfect hedging 
basis risk:
spot price - future price 
reasons:
different asset 
different maturity 
closing out before delivery month 
two kinds of imperfect hedging:
close hedging (different underlying)
stack and roll (facing rollover basis risk)

calculation
1. optimal hedge ratio
The optimal hedge ratio or minimum variance hedge ratio is a concept that defines the degree of correlation between an asset or liability and the financial product (normally a futures contract) purchased to hedge financial risks.

h* quantifies the systematic comovement between 2 asset, minimize the portfolio most, can be calculated based on the standard deviation of both the spot and future price and their correlation

h* = ps,f x std(s)/std(f)

hedge effectiveness
R^2 = p^2

optimal number of contract
amount of contracts
after having determined the optimal hedge ratio, the amount of futures contract (N) equals the hedging amount (Na) divided by the contract size of the future(Qf), multiplied by the optimal hedge ratio
N = (h*) x (Na/Qf)

stock index future
N* = beta x (P/A) 将beta对冲到零
(beta* - beta) x (P/A) 调整beta 到 beta*
negative result: sell 
positive result: buy 
beta is a systematic risks measurement

Question 106

12 foreign exchange risks

Answer 106

exposures:
positive net exposure
negative net exposure
净敞口 = （外汇资产 - 外汇负债）+ （外汇购买 - 外汇出售）

interest rate parity theorem (IRPT)
forward = spot[(1 + rDC)/(1 + rFC)]^T discrete rate
forward = spot x e^(rDC - rFC)T continuously compounded rates
meaning:
forward exchange rate determined by 1. spot exchange rate 2. interest rate differential between the two countries.

balance sheet hedging
on-balance-sheet hedging (利用资产负债表进行对冲)
off-balance-sheet hedging (利用金融工具对冲)

nominal rate (Rn) and real rate (Rr)
Rn = (1 + Rr)x(1 + inflation rate) -1
Rn is about equal to Rr + inflation rate

Question 107

13 introduction of options

Answer 107

based on exercise date 
European options (不可提前行权)
American options (可提前行权)

based on trading position
exchanged-traded options
OCT options

based on underlying assets:
1. financial options:
equity, fixed income, futures, foreign currency
2. commodity options

based on right or obligation

1. long call: right to buy
2. long put: right to sell
3. short call: obligation to sell
4. short put: obligation to buy
5. Call options allow the holder to buy the asset at a stated price within a specific timeframe.
6. Put options allow the holder to sell the asset at a stated price within a specific timeframe.

In options trading, what is the difference between a short call and a long call?
At the core level, a short call is the exact opposite of a long call. A “buying to open” a long call gives a trader the right, but not the obligation, to purchase shares of a stock at a predetermined price on a predetermined date.

On the other hand, “selling to open” a short call obligates a trader to sell shares of a stock at a predetermined price on a predetermined date, assuming the short call is in the money.

For every trader that buys a call option, there was theoretically another who sold that same call option.

在期权交易中，空头和多头有什么区别？
在核心级别，短电话与长电话完全相反。 “买入”多头买权赋予交易者权利，但没有义务在预定日期以预定价格购买股票。

另一方面，“卖空”卖空交易使交易者有义务在预定日期以预定价格出售股票，前提是卖空是在货币中。

从理论上讲，对于每个购买看涨期权的交易者，都有另一个卖出相同看涨期权的交易者。

the difference between ‘in the money’, ‘at the money’, ‘out the money’
期权里面的概念，分别对应in the money实值，at the money 平值， out the money虚值。代表着投资者在期权投资中的盈利、盈亏平衡和亏损三种状态。举例，对于一个股票看涨期权而言，行权价格是20元，对应市场价格有以下情况：如目前市场价格如果是20元，则投资者收益即为20-20=0，此时代表平值期权(at the money)。如果目前市场价格是25元，则投资者收益时25-20=5元，此时代表的是实值期权(in the money)。如果市场价格是15元，则投资者收益即为15-20=-5元，对应的就是虚值期权(out the money)。

terminology
strike price (行权价)
premium（期权价）
expiration date / maturity date (到期日)

standard product trading in CBOE

1. options on exchanged-traded funds
2. weeklys
3. binary option
4. credit event binary option (COOEs)
5. Doom options

A binary option is a financial exotic option in which the payoff is either some fixed monetary amount or nothing at all.[1][2] The two main types of binary options are the cash-or-nothing binary option and the asset-or-nothing binary option. The former pays some fixed amount of cash if the option expires in-the-money while the latter pays the value of the underlying security. They are also called all-or-nothing options, digital options (more common in forex/interest rate markets), and fixed return options (FROs)
二元期权是一种金融异国期权，其收益要么是某个固定的货币金额，要么完全没有。[1] [2] 二元期权的两种主要类型是无现金二元期权和无资产二元期权。 如果期权在价内到期，则前者支付一定的现金量，而后者则支付基础证券的价值。 它们也被称为“全有或全无”期权，数字期权（在外汇/利率市场中更为常见）和固定收益期权（FRO）

Credit Event Binary Options (CEBOs) are the CBOE’s translation of credit default swaps (CDS) to a regulated and centralized marketplace CEBOs pay a fixed amount if a credit event is confirmed in a reference entity. CEBOs expire worthless if no credit event is confirmed before expiration ‘Credit Event’: Bankruptcy Failure to pay
信用事件二元期权（CEBO）是CBOE将信用违约掉期（CDS）转换为受监管的集中化市场CEBO，如果参考实体中确认了信用事件，则支付固定金额。 如果未在“信用事件”到期之前确认任何信用事件，则CEBO会一文不值：破产无法付款

What Is Deep Out Of The Money?
An option is considered deep out of the money if its strike price is significantly above (for a call) or significantly below (for a put) the current price of the underlying asset. Typically, this means the strike price of the option must be more than a few strikes in the option chain away from the price of the underlying asset.

Out of the money options have no intrinsic value and trade on their time value. The deeper out of the money the option, the more exaggerated this becomes. Conversely, in the money options have both intrinsic value and time value.
如果期权的行使价显着高于标的资产的当前价格（看涨期权）或显着低于（看跌期权）当前价格，则该期权被认为是货币深度期权。 通常，这意味着期权的行使价必须大于期权链中远离基础资产价格的若干行使。

货币选择权没有内在价值，只能用其时间价值进行交易。 期权的钱越深，这种选择就越夸张。 相反，货币期权既具有内在价值，又具有时间价值。

Question 108

14 properties of stock options

six factors affecting options price

Answer 108

There are six factors that impact the value of an option:

S = current stock price
European call (EC): +
European put (EP): -
American call (AC): +
American put (AP): -

K = strike price of the option
European call (EC): -
European put (EP): +
American call (AC): -
American put (AP): +

T = time to expiration of the option
European call (EC): ?
European put (EP): ?
American call (AC): +
American put (AP): +

r = short-term risk-free interest rate 
European call (EC): +
European put (EP): -
American call (AC): +
American put (AP): -

D = present value of the dividend of the underlying stock
European call (EC): -
European put (EP): +
American call (AC): -
American put (AP): +

sigma = expected volatility of stock prices over T
European call (EC): +
European put (EP): +
American call (AC): +
American put (AP): +

https://analystprep.com/study-notes/frm/part-1/properties-of-stock-options/

Question 109

option value

Answer 109

in the money 
Call option: S > X
put option: S < X
at the money 
Call option: S = X
put option: S = X
out the money 
Call option: S < X
put option: S > X

profit (期权利润，扣除期权费) 
Long Call: Max(0, ST - X) - c0
Short Call = (profit long)
Long Call: Max(0, X-ST) - p0
Short Put = - (profit of short)

Question 110

upper and lower pricing bond

Answer 110

option proxy min value max value
European call c max(0, So - Xe^rT) So
American call C max(0, So - Xe^rT) So
European put p max(0, Xe^rT - So) Xe^T
American put P max(0, X - So) X

Question 111

put-call parity

Answer 111

p + S = c + Xe^-rT for European
p + S - D = c + Xe^-rT with dividend
s - X <= C - P <= S - Xe^-rT for American option

Question 112

American option

Answer 112

early exercise:
1. With dividend: Both American call and put option can be delivered early

2. Without dividend:
   American call never exercise early without dividend (American call options = European call options)
   American put options may need to exercise early(a. American put option > European put options; b. American put would be exercised when X-S is larger an interest rate is high);

Question 113

15 Trading Strategies involving option
covered call (short call, long stock)

Answer 113

St =X
short call C C - (St - X)
Long stock St -So St - So
合计 C + St - So C + X - So

Question 114

protective put (Long put, long stock)

Answer 114

St>=X St

Question 115

Spread strategy (用同种期权构成的策略，要么只用call，要么只用put)

Answer 115

page 32

Bull call spread (long one call at X1, shot one call at X2, X1

Question 116

butterfly spread:

Answer 116

1. By call
   long 1 call at X1, short 2 call at X2, long 1 call at X3, X1
2. By put
   long 1 put at X1, short 2 put at X2, long 1 put at X3, X1

Question 117

calendar spread

Answer 117

page 34

short one call at T1, long one call at T2 (T1 T2)

Calendar spread is a trading strategy for futures and options to minimize risk and cost by buying two contracts or options with the same strike price and different delivery dates.

日历价差是通过在相同的执行价格但交割月份不同的同时对同一基础资产输入多头和空头头寸而建立的期权或期货价差。 有时将其称为货到付款，市场内，时间或水平价差。

典型的期权交易包括具有近期到期日的期权（看涨或看跌）的出售，以及具有长期到期日的期权（看涨或看跌）的同时购买。 两种期权的类型相同，行使价格相同。

卖出近期看跌/看涨期权
购买长期看跌/看涨期权
最好但不要求隐含波动率低

Question 118

diagonal strategies

Answer 118

对角点差是通过同时在两个相同类型（两个看涨期权或两个看跌期权）的期权中建立多头和空头头寸而建立的期权策略，但是执行价格不同，到期日不同。 通常，这些结构的比率为1 x 1。

根据期权的结构，此策略可能看涨或看跌。

该策略被称为对角线价差，因为它结合了水平价差（也称为时间价差或日历价差）（代表到期日期的差异）与垂直价差或价格价差（其代表行使价的差异）。

水平，垂直和对角线价差是指每个选项在选项网格上的位置。 期权以行使价和到期日的矩阵形式列出。 因此，垂直传播策略中使用的期权都在同一垂直列中列出，并具有相同的到期日期。 横向点差策略中的期权使用相同的执行价格，但到期日期不同。 因此，这些选项在日历上水平排列。

对角价差中使用的期权具有不同的行使价和到期日，因此期权在报价网格上以对角线排列。

Question 119

box spread

Answer 119

it consist with a bear put spread and a bull call spread

Question 120

combination strategy (用不同期权构成的策略， 混合put，call & stock)

Answer 120

page 36
collar (short on call at X2, long put at X1, long 1 share X1 < X2)

long straddle (long one call, long one put)
赌波动，call和put行价权相同

strangle (long one call at X2, long one put at X1， X2>X1)
赌波动， 便宜

page 37
strip (long one call, long two put)
赌波动，投资者认为股价下跌可能性更大

strap （long two call, long one put）
赌波动，投资者认为股价上涨可能性更大

Question 121

interest rate cap and floor

Answer 121

利率上限是一种利率衍生工具，在这种利率衍生工具中，买方在利率超过商定的行使价的每个期间结束时收到付款。 上限的示例是协议，规定每个LIBOR利率超过2.5％的月份都将收到付款。

同样，利率下限是衍生合同，在该合同中，买方在利率低于商定的行使价的每个时期结束时收到付款。

上限和下限可以用来对冲利率波动。 例如，以贷款LIBOR利率支付的借款人可以通过购买2.5％的上限来保护自己免受利率上升的影响。 如果在给定期间的利率超过2.5％，则可以使用从衍生工具收取的款项来帮助支付该时期的利息，因此从借款人的角度来看，利息支付实际上被“限制”在2.5％以内。

long cap is looking like long call, the strike price is Cap strike

long floor is looking like long put, the strike price is floor strike

Question 122

exotic options

Answer 122

packages:
zero cost initially
example: bull, bear, butterfly

transformation of American options:
Bermuda options: early exercise may restricted to certain dates
initial lookout period: early exercise may be somehow restricted
warrants: strike price may change during the life of an option

volatility and variance swap
volatility swap
在金融中，波动掉期合约是针对给定基础资产在未来实现的波动率的远期合约。 波动掉期允许投资者直接交易资产的波动，就像交易价格指数一样。 到期时的收益等于
[std(realised) - Kvol] x Nvol
std(realised): is the annualised realised volatility
Kvol: is the volatility strike
Nvol: is a preagreed notional amount.

variance sway
The features of a variance swap include:
the variance strike
the realized variance
the vega notional: Like other swaps, the payoff is determined based on a notional amount that is never exchanged. However, in the case of a variance swap, the notional amount is specified in terms of vega, to convert the payoff into dollar terms.
The payoff of a variance swap is given as follows:
[variance notional (a.k.a. variance units) - annualised realised variance] x variance strike

hedging exotic option
dynamic option replication
1. 大牛市中保本策略是大幅跑输市场的，但是风险资产的投资比重也是不断上升的，分享了一部分市场走强带来的收益，但其回撤真是小得让人嫉妒。

2. 大熊市中OBPI保本策略是能够打败市场的，但是其也小幅亏损了，由于保本比率设置为95%，所以其亏损幅度也是满足要求的。并且在股灾2.0期间，风险资产的占比接近于0，基本完全持有国债了，所以其表现还是可圈可点的。
3. 震荡市中，保本策略小幅盈利，虽然跑输了大盘，但是走的比较平稳，风险资产与无风险资产的仓位一直都保持得比较稳定。

static option replication
与Delta对冲相比，该对冲的好处在于不需要经常调整头寸。静态期权复制的应用范围非常广泛，尤其在障碍期权的对冲中十分常见。

gap options
There are two strike price. X1 is the exercise price and X2 is the trigger price

X1 could different from X2
if X1 =X2, gap option equals on ordinary European option.

for a gap call, if X2 >X1:
if S > X2, payoff = S - X1
if S <= X2 payoff = 0

for a gap put, if X2 < X1:
if S < X2, payoff = X1 - S
if S >= X2 payoff = 0

forward start option
start at a specified future date with an expiration date set further in the future
从指定的将来日期开始，并在以后设置的到期日期

compound options (复合期权)
call on call
investor has the right to buy the underlying call option on the expiration date
call on put
investor has the right to buy the underlying put option on the expiration date
put on call
investor has the right to sell the underlying call option on the expiration date
put on put
investor has the right to sell the underlying put option on the expiration date

chooser option
long position has the right to choose whether the option is a call or put
the value of the chooser option at this point is MAX(c,p)

Barrier option:

knock-out options
触发障碍，期权失效
down-and-out call / up-and-out call
down-and-out put / up-and-out put

know-in options 
触发障碍，期权生效
down-and-out call / up-and-out call
down-and-out put / up-and-out put
page 41

binary options
cash-or-nothing 
payoff of either a fixed amount money or nothing 
asset-or-nothing 
payoff  of either an asset or nothing 

lookback option
Also known as a hindsight option, a lookback option allows the holder the advantage of knowing history when determining when to exercise their option. This type of option reduces uncertainties associated with the timing of market entry and reduces the chances the option will expire worthlessly. Lookback options are expensive to execute, so these advantages come at a cost.

可让买家最大程度地减少后悔。
回溯选项仅在柜台（OTC）上可用，而在任何主要交易所中均不可用。
这些选择的建立成本很高，而潜在的利润通常被成本抵消。

回溯期权：回溯期权的bai收益依附于标的资产在某个du确定的时段(称为zhi回溯时段)中达到的最dao大或最小价格(又称为回溯价)，根据是资产价还是执行价采用这个回溯价格。

a good solution to memory for call option:
for European call option: V = MAX(0, S - X)
for fixed lookback call option:V = MAX(0, Smax - K)
for floating lookback call option:V = MAX(0, S - Smin)

memory for put option:
for European call option: V = MAX(0, S - X)
for fixed lookback call option: V = MAX(0, K - Smin)
for floating lookback call option: V = MAX(0, Smax - S)

Shout options
A shout option is an exotic option contract that allows the holder to lock in intrinsic value at defined intervals while maintaining the right to continue participating in gains without a loss of locked-in monies. The option buyer “shouts” at the option writer to lock in the gain, yet the contract still remains open. The shout guarantees a minimum of profit, even if the intrinsic value decreases after the shout. If the option increases in value after the shout, the option buyer can still participate in that.

1. A shout option allows the buyer to lock in the intrinsic value of an option by “shouting” at the writer to do so.
2. Shout options are exotic options, and therefore their terms can be negotiated.
3. Shout options are more expensive than standard options because of their flexibility to lock in profit while still participating in future profit.

Holders can “shout” to the writer at one time during it life
receive either the usual payoff from a European option or the intrinsic value at the time of the shout, whichever is greater

Asian option
c = MAX(Save(t, T) - X, 0)
cheaper than regular options

Exchange options
Exchange one asset for another

rainbow options
1. two or more sources of uncertainty
2. call or put on the best or worst of n underlying, or options which pay the best or worst of n assets
3. Right for the short position to pick up the most appropriate bond to deliver
E.g. T-bond futures contract

Basket
higher leverage, low tax burden, and flexibility

Question 123

17. exchange, OTC derivatives, DPCs and SPVs

Answer 123

Function of exchange 
alleviate counterparty risk (减轻交易对手风险) ：
1. product standardization (标准化产品)
2. trading venue (提供交易渠道)
3. Reporting services (信息披露)

Clearing page 44
clearing forms:
1. direct clearing
2. clearing rings

tips:

1. participants in the ring had to be willing to accept substitutes for their original counterparties
2. an informal means of reducing exposure (counterparty risk) and enhancing liquidity
3. unlikely to be seem as beneficial by all participants

distinct mechanisms for clearing and settlement:
page 44
1. bilateral for OTC derivatives
2. central for exchange-traded structures

risk mitigation in OTC Markets
special purpose vehicles (SPVs)
transform counterparty risk into consolidation
Bankruptcy-remote

derivatives product companies (DPCs) depends on:

1. minimizing market risk
2. support from a parent
3. credit risk management and operational guidelines

monolines :
financial guarantee companies
credit derivative product companies (CDPCs)

Question 124

18. basic principle of central clearing (CCP)

Answer 124

mechanics of CCPs:
clearing and settlement 
Auction
margining 
novation and netting 
loss mutualization 

advantages of central clearing in OTC derivatives
transparency
offsetting: increasing flexibility, reduction cost
loss mutualization
legal and operational efficiency:
1. increase operational efficiency and reduce costs
2. reduce legal risks
liquidity
default management

disadvantage of CCPs
Moral hazard (道德风险)
adverse selection（逆向选择）
bifurcations （分岔）
procyclicality（亲周期性）