Derivatives Q&A Week 3

You own a put option on Ford stock with a strike price of $11. The option will expire in exactly six months' time. a. If the stock is trading at $6 in six months, what will be the payoff of the put? b. If the stock is trading at $21 in six months, what will be the payoff of the put? c. Draw a payoff diagram showing the value of the put at expiration as a function of the stock price at expiration.

A) 5 B) 0 C) Draw

You own a call option on Intuit stock with strike price of $35. The option will expire in exactly three months' time. a. If the stock is trading at $46 in three months, what will be the payoff of the call? b. If the stock is trading at $31 in three months, what is the value of the call? c. Draw a payoff diagram showing the value of the call at expiration as a function of the stock price at expiration.

A)11 B) 0 C) Draw

Assume you have shorted a put option on Ford stock with a strike price of $8. The option will expire in exactly six months' time. a. If the stock is trading at $5 in six months, what will you owe? b. If the stock is trading at $19 in six months, what will you owe? c. Draw a payoff diagram showing the amount you owe at expiration as a function of the stock price at expiration.

A)3 B)0 C) draw

What is the difference between an American and a European option?

An American option can be exercised any time up to the expiration date. A European option can be exercised only on the expiration date.

The continuously compounded dividend yield on the EURO STOXX 50 is 3%, and the current stock index level is 3,500. The continuously compounded annual interest rate is 0.15%. Based on the carry arbitrage model, the three-month futures price will be closest to: A.3,473.85. B.3,475.15. C.3,525.03.

B) Solution: F = Se(r-Δ)T = 3500 e(.0015 - 0.03)(3/12) = 3475.15

Suppose we bought a one-year forward contract at 102 and there are now three months to expiration. The underlying is currently trading for 110, and interest rates are 5% on an annual compounding basis. If there are no other carry cash flows, the forward value of the existing contract will be closest to: A.−10.00. B.9.24. C.10.35.

B) Solution: V = S - F(0)/(1+r)T-t = 110 - 102/(1.05).25 = 9.2366

Assume that at Time 0 we entered into a one-year forward contract with price F0(T) = 105. Nine months later, at Time t = 0.75, the observed price of the stock is S0.75 = 110 and the interest rate is 5%. The value of the existing forward contract expiring in three months will be closest to: A.−6.34. B.6.27. C.6.34.

B) Solution: V = S - F(0)/(1+r)T-t = 110 - 105/(1.05).25 = 6.2730

The treasurer of a corporation is trying to choose between options and forward contracts to hedge the corporation's foreign exchange risk. Discuss the advantages and disadvantages of each.

Forward contracts lock in the exchange rate that will apply to a particular transaction in the future. Options provide insurance that the exchange rate will not be worse than some level. The advantage of a forward contract is that uncertainty is eliminated as far as possible. The disadvantage is that the outcome with hedging can be significantly worse than the outcome with no hedging. This disadvantage is not as marked with options. However, unlike forward contracts, options involve an up-front cost.

What are the four types of option positions?

Long call, short call, long put, and short put.

Boring Unreliable Gadget Inc.'s (BUG) stock price S is $50 today. It pays dividends of $1 after 2 months and $1.05 after 5 months. If the continuously compounded interest rate is 4% pa, what is the price of a six-month forward contract on BUG?

The data: • Today is time zero and the forward matures after six months at time T. • BUG's stock price S = $50 today. • BUG pays div = $1 dollar after time t1 = 2 months or 2/12 = 0.1667 year. • The continuously compounded interest rate r = 0.04 per year. Today's zero-coupon bond prices are: • The price of a zero maturing after two months is .9934.0$),0( 12/204.011 1 === −− eetBBrt • The price of a zero maturing after six months is .9802.0$),0( 12/604.0 === −− eeTBBrT • Today's zero-coupon bond prices are B1 B(0, t1) = 0.9934, B B(0, T) = 0.9802 and .9835.0$),0( 12/504.022 2 === −− eetBBrt S - (B1div1 + B2div2) = BF Plugging in the values and rearranging terms gives the forward price F = [S - (B1div1 + B2div2)]/B = (50 - 0.9934 × 1 - 0.9835 × 1.05) / 0.9802 = $48.94.

Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.

The holder of an American option has all the same rights as the holder of a European option and more. It must therefore be worth at least as much. If it were not, an arbitrageur could short the European option and take a long position in the American option.

Explain why an American option is always worth at least as much as its intrinsic value.

The holder of an American option has the right to exercise it immediately. The American option must therefore be worth at least as much as its intrinsic value. If it were not, an arbitrageur could lock in a sure profit by buying the option and exercising it immediately.

Kellogg will buy 2 million bushels of oats in 2 months. The company has found that ratio of standard deviation of change in spot and futures prices over a period of 2 months is 0.83 and correlation coefficient between two-month change in spot price of ats and two-month change in its futures price is 0.7. What is the optimal hedge ratio given the data above and how many contracts do they need to hedge their position (the size of each oats contract is 5000 bushels).

The information we need for computing the hedge ratio, h, is: • The ratio of the standard deviation of change in spot and futures prices over a two-month period for oats is (sdS / sdF ) = 0.83. • The correlation coefficient between the two-month change in price of oats and the two-month change in its futures price is corrS,F = 0.7. • The size of the planned cash/spot holding is n = 2 million bushels of oats. • The number of units of the underlying commodity in one cattle futures contract is f = 5,000 bushels. The optimal hedge ratio is .5810.07.083.0, === FSFScorrsdsdh The company should buy (go long) 4.2325810.0000,5000,000,2 === hfnq or 232 contracts.

Carefully explain the difference between writing a put option and buying a call option

Writing a put gives a payoff of min( 0) T S K− . Buying a call gives a payoff of max( 0) T S K− . In both cases, the potential payoff is T S K− . The difference is that for a written put the counterparty chooses whether you get the payoff (and will allow you to get it only when it is negative to you). For a long call, you decide whether you get the payoff (and you choose to get it when it is positive to you.)