DERIV: Basics of Derivative Pricing and Valuation

A. forward contracts, each created at the swap price.

1. A swap is equivalent to a series of: A. forward contracts, each created at the swap price. B. long forward contracts, matched with short futures contracts. C. forward contracts, each created at their appropriate forward prices.

A. one position is illiquid.

1. An arbitrage opportunity is least likely to be exploited when: A. one position is illiquid. B. the price differential between assets is large. C. the investor can execute a transaction in large volumes.

B. They are equal, ignoring the time value of money.

1. Which of the following best describes how futures contract payoffs differ from forward contract payoffs? A. Forward contract payoffs are larger. B. They are equal, ignoring the time value of money. C. Futures contract payoffs are larger if the underlying is a commodity.

C. The percentage of the investor's assets invested in the option

1. Which of the following factors does not affect the value of a European option? A. The volatility of the underlying B. Dividends or interest paid by the underlying C. The percentage of the investor's assets invested in the option

B. The difference between the up and down factors

1. Which of the following terms directly represents the volatility of the underlying in the binomial model? A. The standard deviation of the underlying B. The difference between the up and down factors C. The ratio of the underlying value to the exercise price.

C. American calls should be exercised early only if there is a dividend or other cash payment on the underlying.

1. With respect to American calls, which of the following statements is most accurate? A. American calls should be exercised early if the underlying has reached its expected maximum price. B. American calls should be exercised early if the underlying has a lower expected return than the risk-free rate. C. American calls should be exercised early only if there is a dividend or other cash payment on the underlying.

A. lower than if the net cost of carry was zero.

10. If the net cost of carry of an asset is positive, then the price of a forward contract on that asset is most likely: A. lower than if the net cost of carry was zero. B. the same as if the net cost of carry was zero. C. higher than if the net cost of carry was zero.

C. higher than the spot price compounded at the risk-free rate: When a commodity's storage costs exceed its convenience yield benefits, the net cost of carry (benefits less costs) is negative. Subtracting this negative amount from the spot price compounded at the risk-free rate results in an addition to the compounded spot price.

11. If the present value of storage costs exceeds the present value of its convenience yield, then the commodity's forward price is most likely: A. less than the spot price compounded at the risk-free rate. B. the same as the spot price compounded at the risk-free rate. C. higher than the spot price compounded at the risk-free rate.

C. Convenience yield

12. Which of the following factors most likely explains why the spot price of a commodity in short supply can be greater than its forward price? A. Opportunity cost B. Lack of dividends C. Convenience yield

B. equal to forward prices.

13. When interest rates are constant, futures prices are most likely: A. less than forward prices. B. equal to forward prices. C. greater than forward prices.

C. is marked-to-market daily.

14. In contrast to a forward contract, a futures contract: A. trades over-the-counter. B. is initiated at a zero value. C. is marked-to-market daily.

A. negatively correlated.

15. To the holder of a long position, it is more desirable to own a forward contract than a futures contract when interest rates and futures prices are: A. negatively correlated. B. uncorrelated. C. positively correlated.

B. is obtained through replication.

16. The value of a swap typically: A. is non-zero at initiation. B. is obtained through replication. C. does not fluctuate over the life of the contract.

C. is obtained through a process of replication.

17. The price of a swap typically: A. is zero at initiation. B. fluctuates over the life of the contract. C. is obtained through a process of replication.

B. net cash flow payments from the swap.

18. The value of a swap is equal to the present value of the: A. fixed payments from the swap. B. net cash flow payments from the swap. C. underlying at the end of the contract.

B. the same value: if they have the same underlying and exercising price then their values are 0.

19. A European call option and a European put option are written on the same underlying, and both options have the same expiration date and exercise price. At expiration, it is possible that both options will have: A. negative values. B. the same value. C. positive values.

A. transaction costs are low.

2. An arbitrageur will most likely execute a trade when: A. transaction costs are low. B. costs of short-selling are high. C. prices are consistent with the law of one price.

A. Long asset, long put, short call: The combination of a long asset, long put, and short call is risk free because its payoffs produce a known cash flow of the value of the exercise price. The other two combinations do not produce risk-free positions. You should work through the payoffs of these three combinations

2. From put-call parity, which of the following transactions is risk-free? A. Long asset, long put, short call B. Long call, long put, short asset C. Long asset, long call, short bond

C. The party whose stream of payments to be received is greater has to pay the other party the present value difference.

2. If the present value of the payments in a forward contract or swap is not zero, which of the following is most likely to be true? A. The contract cannot legally be created. B. The contract must be replicated by another contract with zero value. C. The party whose stream of payments to be received is greater has to pay the other party the present value difference.

A. make early exercise less likely.

2. The effect of dividends on a stock on early exercise of a put is to: A. make early exercise less likely. B. have no effect on early exercise. C. make early exercise more likely.

C. The volatility of the forward price is different from the volatility of the futures price.

2. Which of the following conditions will not make futures and forward prices equivalent? A. Interest rates are known. B. Futures prices are uncorrelated with interest rates. C. The volatility of the forward price is different from the volatility of the futures price.

C. The probability that the underlying will go up: the actual probabilities of the up and down moves are irrelevant to pricing options.

2. Which of the following is not a factor in pricing a call option in the binomial model? A. The risk-free rate B. The exercise price C. The probability that the underlying will go up

B. A higher stock price relative to the exercise price

2. Which of the following statements imply that a European call on a stock is worth more? A. Less time to expiration B. A higher stock price relative to the exercise price C. Larger dividends paid by the stock during the life of the option

C. greater than the underlying price.

20. At expiration, a European put option will be valuable if the exercise price is: A. less than the underlying price. B. equal to the underlying price. C. greater than the underlying price.

B. value of the underlying minus the exercise price.

21. The value of a European call option at expiration is the greater of zero or the: A. value of the underlying. B. value of the underlying minus the exercise price. C. exercise price minus the value of the underlying.

B. positive time value: A European call option with two months until expiration will typically have positive time value, where time value reflects the value of the uncertainty that arises from the volatility in the underlying. The call option has a zero exercise value if the spot price is below the exercise price.

22. For a European call option with two months until expiration, if the spot price is below the exercise price, the call option will most likelyhave: A. zero time value. B. positive time value. C. positive exercise value.

A. in-the-money.

23. When the price of the underlying is below the exercise price, a put option is: A. in-the-money. B. at-the-money. C. out-of-the-money.

A. decrease.

24. If the risk-free rate increases, the value of an in-the-money European put option will most likely: A. decrease. B. remain the same. C. increase.

A. exercise price: The option value will be greater the lower the exercise price. For a higher exercise price, the opposite is true.

25. The value of a European call option is inversely related to the: A. exercise price. B. time to expiration. C. volatility of the underlying.

B. time to expiration: look at euro option pricing table

27. The value of a European put option can be either directly or inversely related to the: A. exercise price. B. time to expiration C. volatility of the underlying.

B. present value of the exercise price minus the value of the underlying: look at low pricing equation for puts

28. Prior to expiration, the lowest value of a European put option is the greater of zero or the: A. exercise price minus the value of the underlying. B. present value of the exercise price minus the value of the underlying. C. value of the underlying minus the present value of the exercise price.

C. dividend payments: reduces value of underlying which increases value of put

29. A European put option on a dividend-paying stock is most likely to increase if there is an increase in: A. carrying costs. B. the risk-free rate. C. dividend payments

C. at the start of the holding period.

3. An arbitrage transaction generates a net inflow of funds: A. throughout the holding period. B. at the end of the holding period. C. at the start of the holding period.

C. The expected payoff based on risk-neutral probabilities is discounted at the risk-free rate.

3. Which of the following best describes the binomial option pricing formula? A. The expected payoff is discounted at the risk-free rate plus a risk premium. B. The spot price is compounded at the risk-free rate minus the volatility premium. C. The expected payoff based on risk-neutral probabilities is discounted at the risk-free rate.

A. The cost of waiting to receive the exercise price is higher.

3. Why might a European put be worth less the longer the time to expiration? A. The cost of waiting to receive the exercise price is higher. B. The risk of the underlying is lower over a longer period of time. C. The longer time to expiration means that the put is more likely to expire out-of-the-money.

C. accumulated gain since the previous settlement, which resets to zero upon settlement.

3. With respect to the value of a futures contract, which of the following statements is most accurate? The value is the: A. futures price minus the spot price. B. present value of the expected payoff at expiration. C. accumulated gain since the previous settlement, which resets to zero upon settlement.

A. long bond.

30. Based on put-call parity, a trader who combines a long asset, a long put, and a short call will create a synthetic: A. long bond. B. fiduciary call. C. protective put.

B. Long asset, long put, short bond: based on put-call parity

31. Which of the following transactions is the equivalent of a synthetic long call position? A. Long asset, long put, short call B. Long asset, long put, short bond C. Short asset, long call, long bond

C. Actual probabilities of the up and down moves: The actual probabilities of the up and down moves in the underlying do not appear in the binomial option pricing model, only the pseudo or "risk-neutral" probabilities.

32. Which of the following is least likely to be required by the binomial option pricing model? A. Spot price B. Two possible prices one period later C. Actual probabilities of the up and down moves

C. greater than its exercise value: Prior to expiration, an American call option will typically have a value in the market that is greater than its exercise value. Although the American option is at-the-money and therefore has an exercise value of zero, the time value of the call option would likely lead to the option having a positive market value

33. An at-the-money American call option on a stock that pays no dividends has three months remaining until expiration. The market value of the option will most likely be: A. less than its exercise value. B. equal to its exercise value. C. greater than its exercise value.

B. the same as European call options.

34. At expiration, American call options are worth: A. less than European call options. B. the same as European call options. C. more than European call options.

A. Dividends are declared

35. Which of the following circumstances will most likely affect the value of an American call option relative to a European call option? A. Dividends are declared B. Expiration date occurs C. The risk-free rate changes

A. fiduciary call: generates the same outcome as a fiduciary call (long call, rf bond)

36. Combining a protective put with a forward contract generates equivalent outcomes at expiration to those of a: A. fiduciary call B. long call combined with a short asset. C. forward contract combined with a risk-free bond.

A. Time value decay

4. The loss in value of an option as it moves closer to expiration is called what? A. Time value decay B. Volatility diminution C. Time value of money

B. is the amount paid at expiration.

4. The price of a forward contract: A. is the amount paid at initiation. B. is the amount paid at expiration. C. fluctuates over the term of the contract.

C. greater than the value of the contract.

5. Assume an asset pays no dividends or interest, and also assume that the asset does not yield any non-financial benefits or incur any carrying cost. At initiation, the price of a forward contract on that asset is: A. lower than the value of the contract. B. equal to the value of the contract. C. greater than the value of the contract.

A. The exercise price is adjusted for the time value of money: refer to the min value of call and put formula

5. How does the minimum value of a call or put option differ from its exercise value? A. The exercise price is adjusted for the time value of money: refer to the min value of call and put formula B. The minimum value reflects the volatility of the underlying. C. The underlying price is adjusted for the time value of money

B. only the value fluctuates: the value of the forward contract will adjust as market conditions adjust, price is fixed

6. With respect to a forward contract, as market conditions change: A. only the price fluctuates. B. only the value fluctuates C. both the price and the value fluctuate.

A. positive to the long party if the spot price is higher than the forward price.

7. The value of a forward contract at expiration is: A. positive to the long party if the spot price is higher than the forward price. B. negative to the short party if the forward price is higher than the spot price. C. positive to the short party if the spot price is higher than the forward price.

B. future value of the spot price.

8. At the initiation of a forward contract on an asset that neither receives benefits nor incurs carrying costs during the term of the contract, the forward price is equal to the: A. spot price. B. future value of the spot price. C. present value of the spot price.

A. lower: The forward price of each stock is found by compounding the spot price by the risk-free rate for the period and then subtracting the future value of any benefits and adding the future value of any costs.

9. Stocks BWQ and ZER are each currently priced at $100 per share. Over the next year, stock BWQ is expected to generate significant benefits whereas stock ZER is not expected to generate any benefits. There are no carrying costs associated with holding either stock over the next year. Compared with ZER, the one-year forward price of BWQ is most likely: A. lower. B. the same. C. higher.

C. Risk neutral

An investor who requires no premium to compensate for the assumption of risk is said to be which of the following? A. Risk seeking B. Risk averse C. Risk neutral

A. A hedge portfolio is used that eliminates arbitrage opportunities.

Which of the following best describes how derivatives are priced? A. A hedge portfolio is used that eliminates arbitrage opportunities. B. The payoff of the underlying is adjusted downward by the derivative value. C. The expected future payoff of the derivative is discounted at the risk-free rate plus a risk premium.

A. The forward price is fixed at the start, and the value starts at zero and then changes.

Which of the following best describes the difference between the price of a forward contract and its value? A. The forward price is fixed at the start, and the value starts at zero and then changes. B. The price determines the profit to the buyer, and the value determines the profit to the seller. C. The forward contract value is a benchmark against which the price is compared for the purposes of determining whether a trade is advisable.

B. The forward rate implied by the term structure

Which of the following best describes the forward rate of an FRA? A. The spot rate implied by the term structure B. The forward rate implied by the term structure C. The rate on a zero-coupon bond of maturity equal to that of the forward contract

A. minus the forward price.

Which of the following best describes the value of the forward contract at expiration? The value is the price of the underlying: A. minus the forward price. B. divided by the forward price. C. minus the compounded forward price.

B. An optimistic expected outlook for the asset: An optimistic forecast for the asset is not a benefit of holding the asset, but it does appear in the valuation of the asset as a high expected price at the horizon date. Convenience yields and dividends and interest are benefits of holding the asset.

Which of the following does not represent a benefit of holding an asset? A. The convenience yield B. An optimistic expected outlook for the asset C. Dividends if the asset is a stock or interest if the asset is a bond

C. Whether the investor is risk averse, risk seeking, or risk neutral

Which of the following factors does not affect the forward price? A. The costs of holding the underlying B. Dividends or interest paid by the underlying C. Whether the investor is risk averse, risk seeking, or risk neutral

C. The price recently paid by other investors

Which of the following factors does not affect the spot price of an asset that has no interim costs or benefits? A. The time value of money B. The risk aversion of investors C. The price recently paid by other investors

C. It may not always be possible to raise sufficient capital to engage in arbitrage.

Which of the following is a limit to arbitrage? A. Clearinghouses restrict the transactions that can be arbitraged. B. Pricing models do not show whether to buy or sell the derivative. C. It may not always be possible to raise sufficient capital to engage in arbitrage.