Deriv Flashcards
Q: What is a derivative?
A: A derivative is a security that derives its value from another security or variable (e.g., interest rate, stock index) at a specific future date.
Q: What is the underlying asset in a derivative contract?
A: The security or variable that determines the value of a derivative, such as a stock, bond, index, currency, interest rate, or commodity.
: What are key terms of a forward contract?
A: - Underlying asset: Security being bought/sold
Forward price: Agreed-upon price
Settlement date: Future date when the exchange occurs
Contract size: Quantity of the underlying asset
Q: How do gains and losses work in a forward contract?
A: - Buyer gains when the market price is above the forward price.
Seller gains when the market price is below the forward price.
Gains and losses are symmetric between parties.
Q: What is the difference between a deliverable and a cash-settled forward contract?
.
A: - Deliverable: The underlying asset is physically exchanged.
Cash-settled: Only the difference in value is paid in cash
Q: How can derivatives be used for hedging and speculation?
A: - Hedging: Reduces existing risk by taking an offsetting derivative position.
Speculation: Increases risk by taking a position to profit from price changes.
Q: What is a forward contract?
A: A forward contract is an agreement between two parties where one commits to buy and the other to sell an asset at a specific price on a future date. The buyer benefits if the asset’s price increases, while the seller benefits if the price decreases.
Q: How does a futures contract differ from a forward contract?
A: Futures contracts are standardized, exchange-traded, subject to regulation, and involve daily mark-to-market settlements. They also require margin deposits to mitigate counterparty risk.
Q: What are initial and maintenance margin requirements in futures trading?
A: Initial margin is the minimum deposit required before trading. Maintenance margin is the minimum balance required to keep a position open. If the balance falls below this level, the trader must add funds to restore the account to the initial margin level.
Q: What are call and put options?
A: A call option gives the holder the right (but not the obligation) to buy an asset at a specified price before expiration. A put option gives the holder the right to sell an asset at a specified price before expiration.
Q: What is a swap contract?
A: A swap is a derivative where two parties exchange cash flows based on a predetermined formula, such as fixed vs. floating interest rates (interest rate swaps) or currency exchange (currency swaps).
Q: What are credit derivatives?
A: Credit derivatives are financial instruments used to transfer credit risk from one party to another. Examples include credit default swaps (CDS), where one party pays a premium in exchange for protection against a borrower’s default.
Q: What is a swap?
A: A swap is an agreement between two parties to exchange a series of payments on multiple settlement dates over a specified period, with only the net difference paid at each settlement.
Q: What is a fixed-for-floating interest rate swap?
.
A: It is a swap where one party makes payments at a fixed rate, while the other pays a floating rate based on a market reference rate, such as SOFR
Q: How do swaps expose parties to counterparty credit risk?
A: Since swaps trade in a dealer market, parties risk default unless a central counterparty structure with margin deposits and mark-to-market payments is used.
Q: In a $10 million interest rate swap with a fixed rate of 2% and quarterly payments, what is the fixed-rate payment each quarter?
A: The fixed-rate payment is $10,000,000 × 0.02 / 4 = $50,000.
Q: How can a company use a swap to hedge floating-rate debt?
A: By entering as a fixed-rate payer, the company converts its floating-rate liability into a fixed one, reducing uncertainty in future payments.
Q: How can a swap be replicated using forward contracts?
A: A swap is equivalent to a series of forward contracts where the underlying is a floating rate and the forward price is a fixed rate, settling at different points in time.
Interest rate swaps are:
A)
highly regulated.
B)
equivalent to a series of forward contracts.
C)
contracts to exchange one asset for another.
Incorrect Answer
Explanation
A swap is an agreement to buy or sell an underlying asset periodically over the life of the swap contract. It is equivalent to a series of forward contracts. (Module 67.2, LOS 67.a)
Explanation
A swap is an agreement to buy or sell an underlying asset periodically over the life of the swap contract. It is equivalent to a series of forward contracts. (Module 67.2, LOS 67.a)
A call option is:
A)
the right to sell at a specific price.
B)
the right to buy at a specific price.
C)
an obligation to buy at a certain price.
Explanation
A call gives the owner the right to call an asset away (buy it) from the seller. (Module 67.2, LOS 67.a)
At expiration, the exercise value of a put option is:
A)
positive if the underlying asset price is less than the exercise price.
B)
zero only if the underlying asset price is equal to the exercise price.
C)
negative if the underlying asset price is greater than the exercise price.
Explanation
The exercise value of a put option is positive at expiration if the underlying asset price is less than the exercise price. Its exercise value is zero if the underlying asset price is greater than or equal to the exercise price. The exercise value of an option cannot be negative because the holder can allow it to expire unexercised. (Module 67.2, LOS 67.b)
At expiration, the exercise value of a call option is the:
A)
underlying asset price minus the exercise price.
B)
greater of zero or the exercise price minus the underlying asset price.
C)
greater of zero or the underlying asset price minus the exercise price.
Explanation
If the underlying asset price is greater than the exercise price of a call option, the value of the option is equal to the difference. If the underlying asset price is less than the exercise price, a call option expires with a value of zero. (Module 67.2, LOS 67.b)
Which of the following derivatives is a forward commitment?
A)
Stock option.
B)
Interest rate swap.
C)
Credit default swap.
Explanation
This type of custom contract is a forward commitment. (Module 67.2, LOS 67.c)
Front: What are the key ways derivatives help manage risk?
Back: Derivatives allow risk transfer, risk allocation changes, and risk management without cash market transactions. Examples include hedging exchange rate risk, modifying interest rate exposures, and creating unique risk exposures.
Front: How do derivatives contribute to information discovery?
Back: Derivatives prices reflect market expectations. Options prices help estimate expected volatility, while futures and forwards provide insight into expected asset prices and interest rate movements.
Front: What are the operational advantages of derivatives?
Back: Derivatives offer ease of short selling, lower transaction costs, greater leverage, and higher liquidity compared to cash markets, making them efficient trading instruments.
Front: How do derivatives improve market efficiency?
Back: Low transaction costs, leverage, liquidity, and ease of short selling allow traders to exploit mispricing, leading to more accurate market prices.
Front: Why do derivatives offer greater liquidity than cash markets?
Back: The lower capital requirements in derivatives markets enable large transactions with minimal cash, enhancing market liquidity.
Front: How do derivatives help investors modify their risk exposure?
Back: Investors can hedge, increase, or modify exposure using derivatives, such as buying forwards to gain exposure to commodities or using interest rate swaps to adjust bond portfolio duration.
Uses of derivatives by investors most likely include:
A)
hedging against price risk for inventory held.
B)
modifying the risk exposure of a securities portfolio.
C)
stabilizing the balance sheet value of a foreign subsidiary.
Explanation
Modifying the risk exposure of a securities portfolio is an example of derivatives use by investors. Hedging against price risk for inventory and stabilizing the balance sheet value of a foreign subsidiary are examples of derivatives use by issuers. (Module 68.1, LOS 68.b)
Which of the following most accurately describes a risk of derivative instruments?
A)
Derivatives make it easier for market participants to take short positions.
B)
The underlying of a derivative might not fully match a position being hedged.
C)
Volatility in underlying asset prices is implied by the prices of options on those assets.
Explanation
Basis risk arises when the underlying of a derivative differs from a position being hedged. Ease of taking short positions with derivatives compared to their underlying assets, and the information about implied volatility that is revealed by option prices, are two of the advantages of derivative instruments. (Module 68.1, LOS 68.a)
Q: What is arbitrage in the context of derivative pricing?
A: Arbitrage is the process of exploiting price differences by simultaneously buying and selling equivalent assets to earn a risk-free profit. In derivative pricing, the no-arbitrage condition ensures that derivatives are priced consistently with the underlying asset.
Q: How does the no-arbitrage condition help in pricing derivatives?
A: The no-arbitrage condition ensures that a derivative is priced based on the value of a portfolio that has identical future payoffs. If prices deviate, arbitrageurs will exploit the difference, bringing the price back to equilibrium.
Q: What is the law of one price in derivative pricing?
A: The law of one price states that two portfolios with identical future payoffs must have the same price today; otherwise, arbitrage opportunities would exist.
Q: What is replication in derivative pricing?
A: Replication involves constructing a portfolio using cash market transactions that produces the same payoff as a derivative, allowing the derivative’s price to be determined based on the portfolio’s cost.
Q: How can we replicate a long forward contract?
A: A long forward can be replicated by borrowing money at the risk-free rate to buy the underlying asset today, then repaying the loan at the forward settlement date.
Q: How does arbitrage ensure the forward price remains at its no-arbitrage level?
A: If the forward price is too high, arbitrageurs sell the forward and buy the asset. If it is too low, they buy the forward and short the asset. These actions drive the price back to equilibrium.
The underlying asset of a derivative is most likely to have a convenience yield when the asset:
A)
is difficult to sell short.
B)
pays interest or dividends.
C)
must be stored and insured.
Explanation
Convenience yield refers to nonmonetary benefits from holding an asset. One example of convenience yield is the advantage of owning an asset that is difficult to sell short when it is perceived to be overvalued. Interest and dividends are monetary benefits. Storage and insurance are carrying costs. (Module 69.1, LOS 69.b)
The forward price of a commodity will most likely be equal to the current spot price if the:
A)
convenience yield equals the storage costs as a percentage.
B)
convenience yield is equal to the risk-free rate plus storage costs as a percentage.
C)
risk-free rate equals the storage costs as a percentage minus the convenience yield.
Explanation
When the opportunity cost of funds (Rf) and storage costs just offset the benefits of holding the commodity, the no-arbitrage forward price is equal to the current spot price of the underlying commodity. (Module 69.1, LOS 69.b)
Two parties agree to a forward contract to exchange 100 shares of a stock one year from now for $72 per share. Immediately after they initiate the contract, the price of the underlying stock increases to $74 per share. This share price increase represents a gain for:
A)
the buyer.
Correct Answer
B)
the seller.
C)
neither the buyer nor the seller.
Explanation
If the value of the underlying is greater than the forward price, this increases the value of the forward contract, which represents a gain for the buyer and a loss for the seller. (Module 70.1, LOS 70.a)
Given zero-coupon bond yields for 1, 2, and 3 years, an analyst can least likely derive an implied:
A)
1-year forward 1-year rate.
B)
2-year forward 1-year rate.
C)
2-year forward 2-year rate.
Explanation
The forward rate F2,2 extends four years into the future and cannot be derived using zero-coupon yields that only extend three years. From zero-coupon bond yields for 1, 2, and 3 years, we can derive implied forward rates F1,1, F1,2, and F2,1. (Module 70.1, LOS 70.b)
Q: How do the price and value of a forward contract change over its life?
A: The price of a forward contract remains constant, but its value fluctuates with changes in the underlying asset’s price. At settlement, the forward buyer pays the difference between the spot price and the forward price.
Q: How do futures contracts differ from forwards in terms of pricing and value?
A: Futures contracts undergo daily mark-to-market (MTM) settlements, resetting their value to zero each day. Gains and losses are added to or deducted from the margin account, while forward contracts do not have daily settlements.
Q: Why do forward and futures prices differ?
A: If interest rates and futures prices are positively correlated, futures are more attractive due to higher reinvestment returns from margin gains. If negatively correlated, futures are less attractive. Without correlation, futures and forward prices are the same.
Q: What is convexity bias in interest rate forwards versus futures?
A: Interest rate forwards exhibit convexity: an increase in rates decreases their value less than a rate decrease increases it. This convexity bias causes forward and futures prices to diverge, especially for long-term rates.
For a forward contract on an asset that has no costs or benefits from holding it to have zero value at initiation, the arbitrage-free forward price must equal the:
A)
expected future spot price.
B)
future value of the current spot price.
C)
present value of the expected future spot price.
Explanation
For an asset with no holding costs or benefits, the forward price must equal the future value of the current spot price, compounded at the risk-free rate over the term of the forward contract, for the contract to have a value of zero at initiation. Otherwise an arbitrage opportunity would exist. (Module 71.1, LOS 71.a)
For a futures contract to be more attractive than an otherwise equivalent forward contract, interest rates must be:
A)
uncorrelated with futures prices.
B)
positively correlated with futures prices.
C)
negatively correlated with futures prices.
Explanation
If interest rates are positively correlated with futures prices, interest earned on cash from daily settlement gains on futures contracts will be greater than the opportunity cost of interest on daily settlement losses, and a futures contract is more attractive than an otherwise equivalent forward contract that does not feature daily settlement. (Module 71.1, LOS 71.b)
Q: How can an interest rate swap be viewed in terms of forward contracts?
A: An interest rate swap is equivalent to a series of forward rate agreements (FRAs), where each forward contract rate is equal to the swap fixed rate. However, unlike typical FRAs, not all individual forwards have zero value at initiation—some have positive values, and others have negative values, summing to zero.
Q: What is the par swap rate, and how is it determined?
A: The par swap rate is the fixed rate that makes the swap value zero at initiation. It is determined using a no-arbitrage approach by equating the present value of expected floating-rate payments with the present value of fixed-rate payments, calculated using spot rates and implied forward rates.
Q: How does a change in expected floating rates affect the value of a fixed-rate payer’s position in a swap?
A: An increase in expected future floating rates increases the value of the fixed-rate payer’s position, while a decrease in expected floating rates decreases its value. The value at any time is the present value of expected floating-rate payments minus the present value of fixed-rate payments.
Which of the following is most similar to the floating-rate receiver position in a fixed-for-floating interest-rate swap?
A)
Buying a fixed-rate bond and a floating-rate note.
B)
Buying a floating-rate note and issuing a fixed-rate bond.
C)
Issuing a floating-rate note and buying a fixed-rate bond.
Explanation
The floating-rate receiver (fixed-rate payer) in a fixed-for-floating interest-rate swap has a position similar to issuing a fixed-coupon bond and buying a floating-rate note. (Module 72.1, LOS 72.a)
The price of a fixed-for-floating interest-rate swap:
A)
is specified in the swap contract.
B)
is paid at initiation by the floating-rate receiver.
C)
may increase or decrease during the life of the swap contract.
Explanation
The price of a fixed-for-floating interest-rate swap is defined as the fixed rate specified in the swap contract. Typically a swap will be priced such that it has a value of zero at initiation and neither party pays the other to enter the swap. (Module 72.1, LOS 72.b)
Q: What is moneyness in options?
A: Moneyness refers to whether an option is in the money, at the money, or out of the money, based on the relationship between the underlying asset price and the exercise price.
Q: How do you determine if a call option is in, at, or out of the money?
A: - In-the-money: S - X > 0 (stock price is higher than the exercise price)
At-the-money: S = X (stock price equals exercise price)
Out-of-the-money: S - X < 0 (stock price is lower than the exercise price)
Q: How do you determine if a put option is in, at, or out of the money?
A: - In-the-money: X - S > 0 (exercise price is higher than stock price)
At-the-money: S = X (stock price equals exercise price)
Out-of-the-money: X - S < 0 (exercise price is lower than stock price)
Q: What are the upper bounds for European options?
A: - Call option: cₜ ≤ Sₜ (cannot exceed the stock price)
Put option: p₀ ≤ X(1 + Rf)⁻⁽ᵀ⁻ᵗ⁾ (cannot exceed the present value of the exercise price)
Q: What factors determine an option’s value?
A: - Price of the underlying asset
Exercise price
Risk-free rate
Volatility of the underlying
Time to expiration
Costs and benefits of holding the asset
Q: How does volatility affect option prices?
A: Higher volatility increases the value of both call and put options because it raises the probability of a favorable price movement before expiration.
The price of an out-of-the-money option is:
A)
less than its time value.
B)
equal to its time value.
C)
greater than its time value.
Explanation
Because an out-of-the-money option has an exercise value of zero, its price is its time value. (Module 73.1, LOS 73.a)
The lower bound for the value of a European put option is:
A)
Max(0, S – X).
B)
Max[0, X(1 + Rf)–(T–t) – S].
C)
Max[0, S – X(1 + Rf)–(T–t)].
Explanation
The lower bound for a European put ranges from zero to the present value of the exercise price less the current stock price, where the exercise price is discounted at the risk-free rate. (Module 73.1, LOS 73.b)
A decrease in the risk-free rate of interest will:
A)
increase put and call option prices.
B)
decrease put option prices and increase call option prices.
C)
increase put option prices and decrease call option prices.
Explanation
A decrease in the risk-free rate will decrease call option values and increase put option values. (Module 73.1, LOS 73.c)
The put-call-forward parity relationship least likely includes:
A)
a risk-free bond.
B)
call and put options.
C)
the underlying asset.
Explanation
The put-call-forward parity relationship is F0(T)(1 + RFR)–T + p0 = c0 + X(1 + Rf)–T, where X(1 + Rf)–T is a risk-free bond that pays the exercise price on the expiration date, and F0(T) is the forward price of the underlying asset. (Module 74.1, LOS 74.b)
Front: How do put-call parity and forward contracts relate to corporate finance?
Back: The value of a firm can be modeled using options:
Equity holders hold a call option on the firm’s value 𝑉𝑇 with strike price equal to debt 𝐷. Debt holders own a risk-free bond and are short a put option on 𝑉𝑇.
This explains why equity holders benefit from volatility and why debt holders bear default risk.
Q: What are the key inputs required to construct a one-period binomial model for pricing an option?
A: 1. Initial value of the underlying asset.
2. Exercise price of the option.
3. Possible up-move and down-move values of the underlying.
4. The risk-free rate.
Q: What is risk neutrality in derivatives pricing?
A: Risk neutrality assumes that investors are indifferent to risk, meaning all assets earn the risk-free rate in expectation. This allows us to use risk-neutral probabilities to price derivatives by discounting expected payoffs at the risk-free rate.
To construct a one-period binomial model for valuing an option, are probabilities of an up-move or a down-move in the underlying price required?
A)
No.
B)
Yes, but they can be calculated from the returns on an up-move and a down-move.
C)
Yes, the model requires estimates for the actual probabilities of an up-move and a down-move.
Explanation
A one-period binomial model can be constructed based on replication and no-arbitrage pricing, without regard to the probabilities of an up-move or a down-move. (Module 75.1, LOS 75.a)
In a one-period binomial model based on risk neutrality, the value of an option is best described as the present value of:
A)
a probability-weighted average of two possible outcomes.
B)
a probability-weighted average of a chosen number of possible outcomes.
C)
one of two possible outcomes based on a chosen size of increase or decrease.
Explanation
In a one-period binomial model based on risk-neutral probabilities, the value of an option is the present value of a probability-weighted average of two possible option payoffs at the end of a single period, during which the price of the underlying asset is assumed to move either up or down to specific values. (Module 75.1, LOS 75.b)
A one-period binomial model for option pricing uses risk-neutral probabilities because:
A)
the model is based on a no-arbitrage relationship.
B)
they are unbiased estimators of the actual probabilities.
C)
the buyer can let an out-of-the-money option expire unexercised.
Explanation
Because a one-period binomial model is based on a no-arbitrage relationship, we can discount the expected payoff at the risk-free rate. (Module 75.1, LOS 75.b)
