Mathematical finance Flashcards
Define Financial Markets
A market where people trade financial instruments such as bonds stocks etc
Types of financial markets
Exchange traded markets
Over the trade markets
Define exchange traded markets
Trading is done under the supervision of a exchange.
Where individual trade standardised contracts that have been defined by exchange
Define over the counter market
- Where trade is done over phone or computer networks without supervision of exchange
- Small and mid cap companies
Define exchange
Exchange or a trading exchange or trading venue is a organised market where tradable securities, commodities, foreign exchange, future and options are bought and sold.
Define security
A traceable financial asset
Debt securities
Banknotes, bonds, debentures
Types of securities
- Debt security
- Equity
- Derivatives
What are Derivatives in finance
Forwards, Futures, Swaps, Options
What is the company issuing the security called
Issuer
Define Bonds
An agreement where an investor lends money to a company or government for a period of time in exchange for regular interest payment.
Define debenture
A market security issued by a company to raise money for a long term activity and growth
Define commodities
A substance or good that can be traded, bought or sold and has full substantial fungibility
Define fungibility
The ability of an asset to be interchanged with other individual good or asset of the same type
Types of commodities
- Soft –> Goods that are grown
- Hard —> Goods that are mined
Define forgein exchange
International market for exchange of national currencies also known as forex
Factors affecting value of a currency
Trade, Tourism, Investment and Geo-Political risk
Currency trade transactions fall under?
Bank of International Settlements
Define derivative
A contract that derives its value from the performance of underlying commodity.
Define liquidity
The ability of a commodity to be converted into cash without affecting the market price
Types of derivatives
Future, forward, swap, option
Types of positions in traditional
Short and long
Define position in trading
Position determines whether a stock value will rise or drop
Define long position
Buying the stock expecting the prises will rise
Define short position
Buying a stock expecting the prices to drop
Types of traders in stock market
- Hedger
- Speculators
- Arbitrageurs
Forward Contract
- It is a contract in which one party commits to buy and the other party commits to buy an specified quantity of an agreed upon asset for a pre determined price at a specific data in the future
- It is a customised contract in the sense that the terms of the contract are agreed upon by the individual parties. Hence it is traded OTC
Example of forward contract
Refer lecture 4
Risk in Forward Contract
- Credit Risk- Does the other party have the means to pay ?
- Operational Risk-Will the other party make delivery? Will the other party accept delivery?
- Liquidity Risk-Incase other party wants to opt out of the contract, how to find another counter party?
Terminology in forward
- Long Position-Buyer
- Short Position-Seller
- Spot Price-Price of the asset in the spot market(market price)
- Delivery/Forward Price-Price of the asset at the delivery date
Future Contarct
- It is a standardized forward contract
- It is traded on Organised Exchange
Standardisations in future contract
a. Quantity/Quality of under lying
b. Delivery dated and procedure
c. Price quotes
Examples of future contract
Refer lecture 4
Types of future contracts
a. Stock Future Trading(dealing with shares)
b. Commodity Future Trading(dealing with gold Future, crude oil Future, etc.)
c. Index Future Trading(dealing with stock market indices)
Closing a Future Position
- Most future contracts are hold till expiry, but closed before that.
- If held till expiry, they are generally settled by delivery (2-3%)
- By closing a future contract before expiry, the net diff is settled b/w traders, without physical delivery of the underlying.
Contract Size(Future)
The amount of asset that has to be delivered under one contract. All futures are sold in multiples of lots which is decided by the Exchange board
Eg. If the lot size of TATA Steel is 500 shares, then one future contract is necessarily 500 shares
Contract cycle(Future)
The period for which a contract is trades. The future on the NSE have one(near) month, two(next) months, three(far) months expiry cycles
Expiry Cycle(Future)
Usually Last Thursday of every month or previous day if Thursday ia public holiday
Strike price(Future)
The argeed price of the deal
Cost of carry(Future)
Difference between strike price and current price
Margins
- It is an amount of money that must be deposited with the clearing house by both buyers and sellers in a margin account in order to open a Future Contract.
- Its aim is to minimize the risk of default by either counterparty.
- It ensures performance of the terms of the contract
Initial Margin
Deposit that a trader must make before trading any futures, usually 10% of the contract size
Maintenance Margin
When margin reaches a minimum maintenance level, the trader is required to bring the margin to its initial level. The maintenance margin is generally about 75% of the initial margin.
Variation Margin
Additional margin required to bring an account up to the required level
Margin call
If amount in the margin A/C fails below the maintenance level, a margin call is fill the gap
Marking to Markets
This is the practice of periodically adjusting the margin A/C by adding or substracting funds based on changes in market value to reflect the investor’s gain or loss.
- It leads to change in margin amounts daily.
- This ensures that there are no defaults by the parties.
Characteristics of Future Contract that are not of forward
- Trade on organised exchange
- Use standardized contract terms
- Use of associate clearing houses to guarantee contract fulfillment
- Require margin payments and daily settlements
- Markets are transparent
- Marked to Market daily
- Closed prior to delivery
- Profits or losses realised daily
Option
- Contracts that give the holder the option to buy/sell specified quantity of the underlying assets at a particular price on or before a specified time period
- the word option means that the holder has the right but not the obligation to buy/sell underlying assets
Types of options
a. Call : It gives the buyer the right, but not the obligation to buy a given quantity of the underlying assets, at a given price on or before a particular date by paying a premium.
b. Put : It gives the buyer the right, but not the obligation to sell a given quantity of the underlying assets, at a given price on or before a particular date by paying a premium.
The other two types are -
- European Style Options : Option that can be exercised on the maturity of the option, also known as the expiry date
- American Style Option : Options that can be exercised at any time before and on the expiry date.
Features of Options
- a fixed maturity date on which they expire(Expiry date)
- The price at which the option is exercised is called the exercise price or strike price.
- the person who writes the option and is the seller is referred as the option writer and who holds the option and is a buyer is called option holder
- the premium is the price paid for the option by the buyer to the seller.
- A clearing house in interposed b/w the writer and the buyer which guarantees performance of the contract.
Call Option
- In the money –> Spot price > Strike price
- At the money –> Spot price = Strike price
- Out of the money –> Spot price < Strike price
Put Option
- In the money –> Spot price < Strike price
- At the money –> Spot price = Strike price
- Out of the money –> Spot price > Strike price
Terminology in options
- Underlying : Specific security or asset
- Money ness : Concept that refers to the potential profit or loss from the exercise of the option
Put Call Ratio
to ratio of Puts to the Calls traded in market
Option Series
A series that consists of all the options of a given class with the same expiry date and strike price
Expiration rate & Exercised date
a. Date on which option expires
b. Date on which option is exercised
a.Option interest
b.Option classes
a. Total no. of option contracts that have not yet been expired
b. all listed options of a type on a particular instrument
Define Derivative
A finacial instrument whose value depends on the values of other more basic underlying variables like - forgein currency, interest rate, a share
Example of derivative
Stock option is a derivative, whose value depends on the price of stock
Define Derivative exchange
A market where individual trade standardised contract that have been defined by the exchange.
Define exchange trade derivative
A financial contract that is listed and traded on a regulated exchange.
Define Bonds
Fixed income securities which gives the owner right to a fixed pre determined payment to a future pre determined date
Party that promises to pay an amount
Debator
Party that will get paid ?
Creditor
Define Stock
A security that gives its owner the right to a proportion of any profits that might be distributed by the firm that issues the stock.
Define short selling
Consists of borrowing the stock from someone who owns it and then sells it, short seller hopes that the price of the stock will drop and later they can buy back stock at a lower price and give it back to lender
Define forward contract
It is an agreement to guy or sell an asset at a certain future time for a certain price.
Long position in forward contract
Party who agrees to buy and asset
Short position
Party whi agrees to sell the asset
Forward price
Price paid at the end of expiration date is called forward price
Spot price
Current price of an asset
Define future Contract
An agreement between two parties to buy or sell an asset at a certain time in future for a certain price where trading is done over exchange market
Define Option
A financial derivative that gives its owner the right to buy or sell another security on or before a future date for a price that is pre-determined.
Define call option
Owner has right to buy the underlying stock
Define put option
Where the owner has the right to sell the underlying option
Position in Option
Buyer is in Long Position
Seller is in Short Position
Define Hedgers
Traders that try to reduce risk with forward contracts and options
Define speculators
Risk taking traders who wish to take a position in the market betting on whether price of asset will rise of fall
Define Arbitragers
They try to lock a risk free portfolio by simultaneously entring into transactions in two or more markets
Define treasury rates
Rates an investor earns on treasury bills
Define LIBOR
London Interbank offered rate
Rate at which a bank is ready to make a large wholesale deposit with other banks
Define Repurchase Agreement
A contract where investment dealer who owns securities agree to sell them to another company now and buy them back later
Define Repo rate
Difference of price between which the security is sold and the price at which it is repurchased is the interest earned called the repo rate
Define Zero coupon rate
n-year zero. coupon rate is the rate of interest earned on an investment that starts today and last for n-years. All the interest and principal is realised at the end of n-years. There are no intermediate payments.
Defien bond yeild
Single discount rate which when applied to all cash flows, gives bond price equal to its market price
Define par yeild
For certain bond maturity the coupon rate that causes the bond price to equal its par value.
Define Forward Rates
Rate of interest implied by current zero rates
Lognormal
Property of Stock Prices
Model of Black Scholes and Merton of stock price behaviour assumes that a percentage changes in the stock price in a short period of time are normally distributed.
Define Volatility
a measure of our uncertainty about the return provided by the stock
Define unbaised estimate
The estimate is unbaised if the var exists and the sample value drawn independently with replacement
