Problem 4

4.1 To simulate Value at Risk of a call option, one needs to consider the following risk factors:

a. Underlying price

b. Volatility of the underlying

c. Interest rate

d. All of the above

4.2 Which of the Greeks has a positive sign for a call option, but negative sign for a put option?

a. Vega

d. Delta

c. Gamma

d. Theta

4.3 A one-year zero-coupon corporate note with a par value 100 and yield of 10% has a credit spread of 7%. You have enough information to find the observed value of the put on the firms assets using Mertons (1974) credit risk framework. (True / False)

4.4 A small gold mine is currently closed, but can be reopened if gold price rises above a certain threshold. The right to wait to reopen the mine until economical can be valued as a real option. (True / False)

4.5 The value of an American call option is higher than its lower bound by the value of the identical put option on the same stock. (True / False)

4.6 Option elasticity is a dollar change in the value of the option per $1 change in the value of the underlying. (True / False)

4.7 Risk-neutral probability of stock price going up in a binomial model is higher than the actual (physical) probability of stock going up. (True / False)

4.8 When dynamically hedging an option position to make it delta-neutral, the trader needs to trade

a. The underlying security

b. Another option on the same security

c. Two more options on the same security

4.9 If the Black-Scholes option-pricing model is correct, the implied volatility should be equal for an option with a high strike price and an option with a low strike price, as long as they are written on the same security and expire at the same time. (True / False)

4.10 The __________ of an option changes at a highest pace when the option is at the money

a. premium

b. delta

c. both a and b

4.11 Stock X is selling for $40 a share. An American put option on this stock with a strike price of $48 is trading at $10 per share.

1. the put is in the money
2. the put is out of the money
3. you can make arbitrage profit by buying the put and exercising it immediately
4. a and c

4.12 Writer of a call option has a positive payoff when the option is in the money, and writer of a put option has a negative payoff when the option is in the money. (True / False)

4.13 One year ago, you wrote a put option with strike price $30 and one year to expiration. Option premium was $12. Ignore the interest rate. Today is the expiration day, and you still have an open short position in the put. The underlying stock is trading at $42. Your profit is

1. Zero. You just broke even.
2. $12
3. $42
4. $18

14. Convergence property implies that on the delivery day,
    1. cost-of-carry is paid
    2. gain on the long position equals loss on the short position
    3. observed futures price equals observed spot price
    4. hedgers make money

1. 15. One of the differences between a futures and a forward contract is that forward is settled on the delivery day and futures is marked to market daily. (True / False)

1. 16. Commodity futures price

1. Is related to spot price by cost-of-carry, borrowing cost, and convenience yield
2. Increases if cost of carry decreases
3. Converges to basis at maturity
4. All of the above

1. 17. A speculator who has a _______position in wheat futures wants the futures price of wheat to _______ in the future.

1. 1. long; increase
   2. long; decrease
   3. short; increase
   4. long; stay the same
   5. short; stay the same

1. 18. For commodity futures, when convenience yield is smaller than the carrying cost, F > S (contango). (True / False)