Volume 5 - Derivatives Flashcards
Derivative Instrument and Derivative Market Features
define a derivative and describe basic features of a derivative instrument
describe the basic features of derivative markets, and contrast over-the-counter and exchange-traded derivative markets
Counterparties to a derivatives contract exchange cash flows based on the performance of the underlying. The contract buyer has long exposure to the price of the underlying and the seller has a short position.
Key features of derivatives include:
- Contracts can be structured as forward commitments (e.g., forwards, futures, and swaps) or contingent claims (e.g., options).
- Derivatives can be used to pursue strategies (e.g., short positions) that would be more difficult to execute in the cash market.
- Index-based derivatives can help investors quickly and easily diversify their portfolios.
- Large exposures can be achieved with relatively small cash outlays.
- Transaction costs are typically lower and liquidity is generally higher compared to trading underlying assets in the spot market.
- Derivatives are critical to the risk management process because they can be used to adjust, hedge, or eliminate exposure to certain risks.
Commodities :
Can be classified as hard or soft. Hard commodities include natural resources (e.g., oil, gold) that are used to sustain life or support economic activity. Soft commodities include agricultural products, such as corn and cattlte.
Other “assets” that serve as the underlying for derivatives contracts include weather, cryptocurrencies, and longevity risk related to insurance policies and defined benefit pension plans. These relatively new derivatives are more difficult to price than better-known instruments such as commodity futures and interest rate swaps.
Embedded derivatives are part of other assets, such as callable bonds, and cannot be traded separately in derivatives markets.
OTC derivative markets are driven by dealers, also known as market makers, which are typically financial intermediaries (e.g., banks). Market participants, such as investors and companies, are seeking to hedge their risks or to take speculative positions and dealers are willing to act as counterparties.
Exchange-Traded Derivative (ETD) Markets :
Unlike OTC derivatives, these contracts have standardized terms with respect to matters such as contract size, delivery method, definition of the underlying, and maturity date. ETD markets are also highly transparent, with details of all trades being recorded by exchanges and disclosed to regulators.
ETD markets are characterized by efficient clearing and settlement operations. Clearing is the process of verifying the identities of counterparties and confirming trade execution, while settlement refers to ensuring that final payments are made and delivery terms are met
ETD markets compared to OTC :
- Liquidity: Typically higher for ETD markets
- Trading costs: Lower for ETD markets
- Transparency: Greater for ETD markets
- Standardization: Higher for ETD markets
- Flexibility/Customization: Lower for ETD markets
- Counterparty credit risk: Lower for ETD markets due to margin requirements
A central counterparty (CCP) is mandated to bear the credit risk of each party to a contract, as well as to provide clearing and settlement services. This change in the nature of the OTC derivative market has not eliminated risk, but rather concentrated it in one entity. So safeguards are necessary to ensure that the central counterparty’s risk is properly managed.
The central clearing process for interest rate swaps, which is also used for other OTC derivatives, involves three steps:
Step 1: Two parties (typically financial intermediaries) reach a swap agreement through a swap execution facility (SEF), which is an online trading platform used by dealers.
Step 2: The details of the SEF transaction are submitted to the CCP.
Step 3: The CCP replaces the existing trade and enters into two separate swaps with each of the parties based on the terms of their agreement. This step, known as the novation process eliminates bilateral credit risk by having the CCP act as the counterparty to each of the parties to the original transaction. The CCP also provides clearing and settlement services.
Which of the following comments about over-the-counter (OTC) derivatives and exchange-traded derivatives is least accurate?
A
All exchange traded derivatives are more liquid than OTC derivatives
B
Compared to exchange traded derivatives, OTC derivatives are less regulated
C
Both exchange traded derivatives and OTC derivatives can be used to hedge ris
Like exchange traded derivatives, OTC derivatives are also used to hedge risk. OTC derivatives have the same function as the exchange traded derivatives, but trade in the less regulated OTC market where investors are considered to be sufficiently aware of the risks they take. Derivatives that trade on organized exchanges are not necessarily more liquid than those that trade in the OTC market. Ultimately, liquidity is a function of trading interest. There are heavily-traded OTC derivatives and very illiquid exchange traded derivatives.
Forward Commitment and Contingent Claim Features and Instruments
- define forward contracts, futures contracts, swaps, options (calls and puts), and credit derivatives and compare their basic characteristics
- determine the value at expiration and profit from a long or a short position in a call or put option
- contrast forward commitments with contingent claims
Derivatives can be classified as forward commitments or contingent claims. Forward commitments are an obligation to trade, while contingent claims provide the buyer with the right to trade.
A forward contract is an agreement to make a trade at a future date. One party agrees to pay the forward price for an underlying asset and the other party agrees to sell at that price on a specific date.
Futures :
A futures contract is similar to a forward contract in that there is an agreement to purchase an underlying asset for a specific price on a specified date.
Differences between forwards and futures include:
- Futures contracts are standardized, while forward contracts are customized terms.
- Futures contracts trade on a public exchange with a clearinghouse that guarantees the performance of all traders. Forward contracts trade OTC with no performance guarantees, so traders must do their own assessment of counterparty credit risk.
- Futures contracts are marked to market, which allows traders to realize gains or losses at the end of each day. By contrast, gains and losses for forward contracts are not realized until expiration.
- Futures contracts are highly liquid instruments because it is much easier to take offsetting positions when trading standardized contracts. By contrast, forward contracts are usually held to maturity.
Futures exchanges limit their exposure to default risk by requiring an initial margin deposit (typically less than 10% of the futures price) from both parties upon initiation. Cover any future losses
Daily settlement, all contracts are marked to the end-of-day settlement price.
At the end of the day, clearinghouse credits gains and debits loss from one party to the other
A margin call is made if an account balance drops below the maintenance margin. After receiving a margin call, a party must deposit sufficient funds to bring the account balance back to the initial margin level.
The amount required to bring an account back up to the initial margin level is known as the variance margin. A party that fails to meet a margin call will be required to close out its contract and cover any of its losses.
Futures exchanges retain the right to change margin requirements depending on market conditions.
Exchanges may also impose price limits that require trades to occur within a specified range of the previous day’s settlement price. If the spot price breaches these limits, a circuit breaker is triggered and trading is paused.
The number of outstanding contracts for a particular underlying and settlement day is known as the open interest. As the settlement date approaches, parties may close out their positions by either buying out their counterparty before maturity or by taking an offsetting position in another contract
A futures contract with the same settlement price as a forward contract on the same underlying will provide the same overall payoff, but the timing will be different. Forward contracts realize the full amount at maturity, while returns to futures contracts are accumulated incrementally over time through the daily settlement process.
A swap can be thought of as a series of forward contracts, meaning that cash flows are exchanged on more than one date. OTC transactions and each party is exposed to the risk that the other party will default.
Because a swap has the same value to both parties at inception, no money is exchanged when the contract is signed. The periodic payments are a percentage of the contract’s notional principal, although the principal amount is typically not exchanged.
Obligations are typically netted so that only one payment is made per period. The floating-rate obligation is reset after each payment period.
Which of the following terms of a futures contract is least likely to be specified by the exchange?
A
Price
B
Quantity
C
Underlying asset
Price is the only negotiated term of a futures contract and it is agreed upon by the two parties at initiation.
In order to function efficiently, futures exchanges can only have a limited number of standardized contracts. Investors seeking more customized terms would be better served by the forward market.
A swap is an over-the-counter forward commitment.
It is over-the-counter and not exchange-traded because it is a private, customizable transaction and not a public, standardized good.
Options can be settled by physical delivery of the underlying asset or with a cash payment based on the difference between the spot price of the underlying and the strike price.
European-style options can only be exercised at maturity, while American-style options can be exercised any time after initiation.
- Buyers of calls and puts have limited loss potential.
-Sellers of call options are exposed to unlimited potential losses.
Sellers of put options can incur substantial (but not unlimited) losses.
Time value based on the potential for price movements that benefit the owner. This time value is always positive during the option’s lifetime before falling to zero at maturity.
Credit default swap (CDS) contracts are the most common type of credit derivative. These instruments are insurance-like contingent claims based on an underlying issue or index, with the buyer getting protection against adverse credit events (e.g., bankruptcy, failure to pay, involuntary restructuring). The credit protection buyer makes a series of cash payments in return for compensation from the credit protection seller if a defined loss event occurs.
The pricing of CDS contracts is based on a credit spread (CDS spread), which reflects the probability of default (POD) and the loss given default (LGD).
Another way to acquire an asset is to sell a put option. This can be particularly attractive for investors who want to avoid overpaying.
Derivative Benefits, Risks, and Issuer and Investor Uses
describe benefits and risks of derivative instruments
compare the use of derivatives among issuers and investors
Risk Allocation, Transfer, and Management :
Achieve price certainty now rather than waiting until later to trade in the cash market. For example;
- An airline can use futures contracts to lock in a price for fuel.
- A mining company can use a currency forward contract to lock in an exchange rate for converting the proceeds of a large export sale into domestic currency units.
Overcome timing issues. For example, investors who do not currently have sufficient funds to trade in the cash market can gain exposure to the price of an underlying asset with little or no upfront payment required in the derivatives market.
Information Discovery :
Provide information beyond the cash market.
- Equity futures prices give an indication of investors’ expectations about where the market is going.
- Interest rate futures contracts reflect expectations about central bank monetary policies.
- Commodity futures prices reveal information about the dynamics of the relationships between producers and consumers.
- Options prices imply assumptions about the volatility of the underlying assets.
Operational Advantages :
- Lower transaction costs
- Lower cash requirements
- Greater liquidity due to lower capital requirements
- The ability to easily take short positions
Market Efficiency : Asset prices can adjust more quickly to new information as it becomes available. Additionally, the ability to take short positions forces assets to trade closer to their intrinsic value.
Derivative Risks
Potential for Speculative Use : take very risky, highly leveraged speculative positions.
Lack of Transparency :
Market participants may not fully understand the full implications of derivative trading. Compared to stand-alone derivatives, these instruments can be more costly, less liquid, and less transparent.
Basis Risk ;
Basis risk is incurred when the derivative underlying does not match the exposure being hedged.
Liquidity Risk :
Mismatches in the timing of cash flows create exposure to liquidity risk. For example, an investor who is expecting a large cash inflow in six months may choose to enter a futures contract rather than waiting to trade the underlying in the cash market. However, the investor is exposed to the risk of receiving a margin call before the expected payment is received.
Counterparty Credit Risk ;
Forward contracts are over-the-counter derivatives that leave both parties fully exposed to the possibility that their counterparty will fail to meet its obligations.
Futures exchanges seek to eliminate counterparty credit risk by requiring margin deposits and marking positions to market at the end of each day. These requirements may be changed at the exchange’s discretion based on market and credit conditions.
Destabilization and Systemic Risk :
Derivatives have played a role in contributing to crises that have been felt throughout the global economy.
Since 2008; reforms have included standardizing swap contracts and mandating a central counterparty (CCP) with the ability to require margin deposits.
Individual derivatives market participants are least likely to be able to manage their exposure to:
A
liquidity risk.
B
systemic risk.
C
counterparty credit risk.
Derivatives have been cited as contributing to increased systemic risk, which is the threat of destabilizing events that have a negative impact throughout the global economy. Because systemic risk stems from the cumulative impact of the activities of all derivatives market participants, it cannot be mitigated by any one individual. Rather, the responsibility for mitigating systemic risk belongs to regulators.
Individual market participants can manage their exposure to liquidity risk and counterparty credit risk through their choices related to, for example, which derivative instruments are best suited for their specific objectives and constraints.
Issuers :
Common derivative-based hedging strategies used by issuers include:
- Both forward commitments and contingent claims can be used to create a cash flow hedge. For example, an American exporter that is expecting to receive a large euro-denominated payment can use a forward currency contract to lock in a dollar amount to be received. Similarly, a company that has issued floating rate debt can enter an interest rate swap to achieve certainty over its outgoing interest payments.
- A fair value hedge is used to establish certainty over the fair value of an asset or liability. For example, an oil producer can sell futures contracts to preserve the value of its inventory in anticipation of a decrease in the price of crude oil. Using an interest rate swap to convert the nature of an obligation from fixed-rate to floating-rate is another example of a fair value hedge.
- A company can execute a net investment hedge by using either a foreign currency bond or a derivative instrument (e.g., currency forward, currency swap) to offset the exchange rate exposure of the equity in its foreign operations.
Gains and losses on qualifying derivative positions are recorded at the same time as those that are attributable to the transaction that is being hedged. Changes in the mark-to-market value of hedging derivatives bypass the income statement and are recorded directly in Other Comprehensive Income, which is an equity account.
Investors :
Examples of possible uses of derivatives by investors include:
- A hedge fund can use oil futures contracts to speculate on movements in the price of the underlying commodity without having to make a significant cash outlay or incur storage costs.
- A defined-benefit pension plan can enter an interest rate swap to increase the duration of its fixed-income portfolio without having to purchase any new bonds.
- A university endowment with a bullish view about a company can pay a premium for a call option to gain leveraged exposure to its stock.
- A foundation that expects equity prices to remain relatively stable can enhance its returns by selling a call option on an underlying stock index that it currently owns.
Derivative-based strategies allow investors to isolate their risk exposures to factors about which they have views while eliminating their exposure to other risk factors.
Derivative-based strategies allow investors to isolate their risk exposures to factors about which they have views while eliminating their exposure to other risk factors.
An American company that enters a USD/GBP forward contract to manage the currency risk exposure attributable to expected sales generated by its UK-based subsidiary is most likely executing a:
A
fair value hedge.
B
cash flow hedge.
C
net investment hedge
Entering a forward currency contract based on a foreign subsidiary’s expected sales is an example of a cash flow hedge.
A fair value hedge is used to offset fluctuations in the fair value of an asset or liability.
Net investment hedges are implemented to manage the exchange rate risk attributable to a foreign operation’s equity.
Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
explain how the concepts of arbitrage and replication are used in pricing derivatives
explain the difference between the spot and expected future price of an underlying and the cost of carry associated with holding the underlying asset
Derivatives are priced according to the no-arbitrage principle, which is also known as the law of one price. This law is violated if investors have an arbitrage opportunity, which is the chance to a profit without putting any of their own capital at risk.
In derivatives markets, arbitrage opportunities exist if two assets that provide the same future cash flow are selling for different prices. Another example is if an asset with a known future price is not trading at the present value of that future price discounted at the risk-free rate.
Replication :
Derivatives are used to replicate the cash flows that would be generated by taking long or short positions in the cash market and borrowing or lending at the risk-free rate.
Another replication strategy involving derivatives is to purchase the underlying asset in the spot market and sell it forward. If a forward contract is priced according to the no-arbitrage principle, this strategy will earn the risk-free rate.
Other costs of ownership include storage, transportation, insurance, and spoilage.
Financial assets typically do not impose any carrying costs beyond the opportunity cost of the risk-free rate.
Benefits of ownership include cash flows, such as dividends from stocks and coupon payments from fixed-income securities. A non-cash benefit, known as a convenience yield may be observed in prices when economic conditions cause investors to prefer holding the physical underlying.
Reducing the foward price
Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities
Explain how the value and price of a forward contract are determined at initiation, during the life of the contract, and at expiration
Explain how forward rates are determined for an underlying with a term structure and describe their uses
The spot rate (or zero rate) for period T can be represented as zT. It is also known as the zero rate for the period because it can be thought of the yield on a zero-coupon bond with a maturity of T.
Forward contracts on interest rates are called forward rate agreements (FRAs). The over-the-counter agreements are essentially interest rate swaps that only have one settlement rather than a series of periodic settlements.
In practice, FRAs are almost exclusively used by financial intermediaries to manage the interest rate exposure of their assets and liabilities.
A forward rate agreement is initiated at time 0 with a fixed rate for a loan that begins at time A and settles at time B .This forward rate specified in this agreement is set ensure that the contract has no net value to either party at initiation.
The contract is settled for the present value of this amount at time A. As the fixed rate payer, the long party benefits if the MRR has risen above the fixed rate (and vice versa).
Buyer pays fixed and receives Floating (MRR)
Pricing and Valuation of Futures Contracts
compare the value and price of forward and futures contracts
explain why forward and futures prices differ
If the underlying is a portfolio, such as an equity index, continuous compounding is preferred.
Because exchanges mark positions to market on a daily basis, the value of a futures contract is reset to zero at the end of each trading day. The value of a forward contract at maturity will be approximately equal to the cumulative realized mark-to-market gain or loss for an equivalent futures position.
Note that the futures price is inversely related to the MRR. In other words, a lower MRR will produce a higher futures price (and vice versa).
Importantly, the long party to an interest rate futures contract is considered to be the lender and accrues gains as the MRR falls. Conversely, a short interest rate futures position is consistent with the expectation that the MRR will rise. This is the opposite of how the long/short convention is used for forward rate agreements.
The basis point value (BPV) of an interest rate futures contract is defined as the change in price for a shift of one basis point (0.01%) in the underlying MRR.
The prices of a forward contract and a futures contract on the same underlying for the same maturity will only match if the following conditions are met:
1- The interest rate curve is flat
2-Futures prices and interest rates are uncorrelated
If there is a positive correlation between futures prices and interest rates, a long futures position will be more attractive than an equivalent long forward position. This is because an increase in the price of the underlying will generate profits that can be reinvested at higher interest rates.
Conversely, the price of a futures contract will be below that of an equivalent forward contract if futures prices and interest rates are negatively correlated.
Most open futures contracts are settled within the next year. Over such a relative short time horizon, most investors are able to borrow near the risk-free rate. As a result, observed discrepancies between futures and forward prices are typically minimal.
One exception to this general rule is convexity bias, which can be observed in the difference in the payoffs of a forward rate agreement (FRA) and an interest rate futures contract expiring at the same time with the same underlying rate. Recall that an FRA’s payoff is the present value of the net difference in interest rates multiplied by the notional principal at maturity. By contrast, an equivalent futures contract provides the full payoff immediately at maturity without being discounted.
The advantage of an interest rate futures contract is that its payoffs have a linear relationship with the underlying rate, while the FRA payoffs have a nonlinear relationship with the rate.
Due to this convexity bias, an increase in the value of a long futures position is greater as the underlying rate falls lower when compared to an equivalent short FRA (receive-fixed) position.
Mandatory central clearing requirements impose margin requirements on financial intermediaries similar to those of standardized exchange-traded futures markets, who often pass these costs and/or requirements on to their clients. Answers B and C are incorrect, as the MTM gains on the forward contracts are not realized until maturity.
Pricing and Valuation of Interest Rates and Other Swaps
describe how swap contracts are similar to but different from a series of forward contracts
contrast the value and price of swaps
Swaps are like forward contracts in the following ways:
- No-arbitrage pricing is used to ensure that the contract has no net value to either party at initiation.
- The value of the contract fluctuates after initiation and positions can be marked to market based on changes in the underlying.
- Payments are based on a notional principal.
- Settlement involves a net payment from the “losing” party to the “winning” party.
- Payoffs are symmetrical.
- Parties are exposed to counterparty credit risk.
Interest rate swaps are more popular with corporate issuers and investors. In practice, interest rate swaps are often used by companies to change the nature of their debt obligations from fixed to floating. For example, companies that have issued floating-rate debt can use an interest rate swap to create fixed obligations and protect themselves against a potential increase in interest rates.
The fixed rate in an interest rate swap is set to match the present value of all expected cash flows based on the current levels of the relevant floating rates.
A swap contract’s fixed rate is known as the par rate because it is the rate of level payments that would make a fixed-rate bond of the same maturity trade at par.
The present value of fixed payments must equal the present value of floating-rate payments at current rates.
A swap is a series of implicit forward contracts with the expiration of each forward contract corresponding to a swap payment date. Each forward contract will be created at the fixed price that corresponds to the fixed price of a swap of the same maturity with payments made at the date as the series of the forward contract. This means that some of the forward contracts in a swap will have positive values and some will have negative values, but their combined value will be zero at initiation.
Receiving the fixed-rate leg is a bet that interest rates will fall, while taking the floating leg is consistent with a view that interest rates will rise.
An upward sloping forward rate reflects an expectation that spot rates will be higher in the future. In this environment, the swap rate will be set above the relatively low rates for early periods and below the relatively high rates that are expected in later periods. As a result, the fixed-rate receiver will expect to receive net payments in earlier periods and the floating-rate receiver will expect to receive net payments in later periods. But the swap rate will be set at a level that makes the present value of these expectations equal for both parties at initiation.
An upward-sloping yield curve reflects an expectation that future spot rates will be higher than the current spot rate. The par rate for an interest rate swap that is initiated in this environment will fall between the relatively low current spot rate and the relatively high future spot rates that are implied by the yield curve. A party that enters an interest rate swap as the fixed-rate receiver will expect to receive net payments in the contract’s early years and make net payments in the years closer to maturity.
The value of an interest rate swap does not reset to zero at each settlement date.
Since the client receives fixed and pays floating swap, in a rising-rate environment, PV(Floating) > PV(Fixed) , and it will therefore owe more in future floating-rate settlements than it will receive in fixed-rate settlements, resulting in an MTM loss for the client and an increase in Ace’s MTM exposure.
Pricing and Valuation of Options
explain the exercise value, moneyness, and time value of an option
contrast the use of arbitrage and replication concepts in pricing forward commitments and contingent claims
identify the factors that determine the value of an option and describe how each factor affects the value of an option
If an option underlying has costs, using the forwards logic, the foward price will be higher, there for makin a put cheaper and a call more expensive
If an option underlying has dividend/income, using the forwards logic, the foward price will be lower, there for makin a put more expensive and a call cheape
An option’s exercise value, also known as its intrinsic value, is the amount that the owner would earn by exercising the option immediately.
An option’s time value represents the potential for beneficial movements in the price of the underlying.
Time value is positively related to the volatility of the underlying. A more volatile underlying means that there is a greater likelihood of a beneficial price movement.
As an option moves toward maturity, its time value approaches zero. This process is known as time value decay.
Note that premiums that have already been paid (or received) are not counted toward the value of an option position. Rather, these impact an investor’s profit or loss.
For a European-style call option, the lower bound is the exercise value, which is the spot price if the underlying minus the present value of the option’s exercise price. An option that is trading below its exercise value violates the no-arbitrage principle.
And the upper bound for the option’s no-arbitrage price is the spot price of the underlying, because no investor would pay more for the right to purchase the underlying than its current market price.
A European-style put option cannot trade for less than its exercise value.
And the upper bound for a put option’s no-arbitrage price is its exercise price because its maximum possible value is achieved when the price of the underlying falls to zero at maturity.
If it was known with certainty that the underlying asset would be trading above the exercise price at maturity (St > X), a long call option strategy could be replicated by borrowing the present value of the exercise price at initiation and using the proceeds to purchase the underlying.
A short put option strategy can be replicated by selling the underlying short at inception and lending the proceeds at the risk-free rate. If it was known in advance that the put option would expire in the money (i.e., St < X), the accumulated funds could be used to purchase the underlying at maturity.
Because the outcomes are uncertain, replicating an option strategy requires borrowing (for a long call) or lending (for a short put) a portion of the present value of the exercise price based on the likelihood of the option expiring in the money.
The value of a call option cannot exceed the value of the underlying because a call option is only a means of acquiring the stock and it can never give the holder more benefit than the underlying.
The value of a put option can never be worth less than zero because its owner cannot be forced to exercise it. However, it can be worth less than the value of the underlying.
For both calls and puts, the more they are in the money, the more sensitive they will be to the price of the underlying.
We can describe the relationship between the option value and exercise price as being inverse for calls and direct for puts :
- Call options become more valuable if the exercise price is lower and less valuable if the exercise price is higher.
- A higher exercise price increases the value of a put option and a lower exercise price reduces its value.
Factors affecting Option Value :
1- Value of the Underlying
2- Exercise Price
3- Time to Expiration
4- Risk-Free Interest Rate : An increase in the risk-free rate reduces the present value of the call owner’s (potential) future payment. For put option holders, a higher risk-free rate reduces the present value of the payment that they would receive by exercising their right to sell.
5- Volatility of the Underlying
6- Income or Costs Related to Owning the Underlying
The value of a European call is directly related to the risk-free rate, while the value of a European put is inversely related.
By holding call options, investors can gain from rising asset prices without incurring the carrying costs.
All else equal, benefits from underlying assets reduce the value of calls and increase the value of puts. Carrying costs have the opposite effect.
The relationship between time to expiration and the value of a European put option is usually direct as well. However, it is possible for this relationship to be inverse if the put option is deep in-the-money and the risk-free rate is relatively high. This is because the option holder could theoretically exercise the option and invest the proceeds at the risk-free rate, so a higher rate makes the current value of exercising the option more attractive compared to holding the option.
Call option -> longer time to maturity = increase ( never reduce) the value
With respect to a European call option, which of the following is least accurate?
A
The value of the option is directly related to the exercise price
B
The value of the option is directly related to the risk-free interest rate
C
The value of the option is directly related to the volatility of the underlying
A) : The value of a European call option is inversely related to the exercise price. As the exercise price increases, the value of the European call option decreases.
Option Replication Using Put–Call Parity
explain put–call parity for European options
explain put–call forward parity for European options
A fiduciary call is composed of a risk-free asset with a face value of X to be paid at time T plus a call option c.
A protective put is composed of a long underlying asset S plus a put option p.
Options Strategies Based on Put-Call Parity :
- A long put position is equivalent to being long a call, short the underlying, and long a risk-free bond
-A long call position is equivalent to being long the underlying, long a put, and short a risk-free bond
-Owning the underlying can be replicated by buying a call, selling a put, and owning a risk-free bond
-Owning a risk-free bond can be replicated by owning the underlying, buying a put, and selling a call
Covered call strategy, which is executed by owning an underlying asset and selling a call. Investors can use this strategy to enhance their returns if they expect that assets in their portfolios are unlikely to appreciate significantly.
The put-call forward parity formula can be rearranged to show that the combination of a long put and a short call is equivalent to holding a risk-free bond and taking a short forward position.
Owning the underlying asset and taking a short forward position will generate a risk-free rate of return. This equivalence makes it possible to create a protective put portfolio with a synthetic underlying asset.
No-arbitrage forward prices are set so that the economics of owning an asset can be replicated by combining a long position in a risk-free bond with a long forward position.
The payoff available to debtholders is most accurately described as:
A
the maximum of zero or the value of a firm’s debt.
B
the minimum of the value of a firm’s assets or the value of its debt.
C
the minimum of the value of a firm’s net assets or the value of its debt.
B) : If a firm’s total value is greater than the value of its debt (Vt > D), its debtholders will receive the full value of the firm’s debt (D) with any residual value going to shareholders.
If the total value is less than the value of its debt (Vt < D), the firm is insolvent and its debtholders will receive the full value of its remaining assets (Vt).
The payoff to debtholders can be summarized as the minimum of firm assets or the value of its debt
Valuing a Derivative Using a One-Period Binomial Model
explain how to value a derivative using a one-period binomial model
describe the concept of risk neutrality in derivatives pricing
The Binomial Model :
To value an option, we must make assumptions about the future price of its underlying asset. The price of the underlying, S0, will increase by a factor of
u to S+ (Su1) or decrease by a factor of d
to S- (Sd1).
A forward commitment can be hedged by taking an offsetting position in the underlying asset.
If the price of the underlying rises :
Vu1 = h*Su1 - cu1
= h * Ru * S0 - Max(0,Su1 - X)
If the price of the underlying falls:
Vd1 = h*Sd1 - cd1
= h * Rd * S0 - Max(0,Sd1 - X)
For price risk to be hedged, the portfolio must have the same value in either scenario : Vu1 = Vd1
Making h = (cu1 - cd1) / Su1 - Sd1
Because the perfectly hedged portfolio is risk-free, its value at time 1 is equal to its value at time 0 accumulated at the risk-free rate, r. Alternatively, we can say that the portfolio’s value at time 0 is equal to its value at time 1 discounted at the risk-free rate.
Adjusting to risk-neutral probabilities, denominated by pi, pi = (1+r - Rd) / Ru - Rd
R are return factors, which are the factors of movement in price.
Ex: Up movement of 10%, Ru = 1.1
c0 = (Picu1) + (1-Pi)cd1 / (1+r) ^ T
p0 = (Pipu1) + (1-Pi)pd1 / (1+r) ^ T
Since the par swap rate represents the fixed rate at which the present value of fixed and future cash flows equal one another, we first solve for the implied forward rate per period using zero rates, then discount each implied forward rate back to the present using zero rates, and solve for s3 to get 3.605%.
