Question: 1. You buy a put option with strike price of $40. Currently, the market value of the underlying asset is $44. The put option premium is $2.75. Assume that the contract is for 100 units of the underlying asset. Assume the interest rate is 0%.
a. What is the intrinsic value of the put option?
b. What is the time value of the put option?
c. What is your net cash flow if the market value of the options' underlying asset is $48 on the expiration date?
d. What is your net cash flow if the market value of the options' underlying asset is $34 on the expiration date?
e. Draw a diagram depicting the net payoff (profit diagram) of your position at expiration as a function of the market value of the underlying asset.
f. A call option with strike price of $40 on the same underlying asset has a premium of $6.25. Suppose that a trader sells one call option and two of the $40 strike put options. What are the breakeven stock prices above and below which the trader makes a profit? In other words, under what circumstances does the trader make a profit?
2. The following applies to stock options. Fill in the blanks:
a. As the stock's price increases, a call option on the stock ___________ in value.
b. As the stock's price increases, a put option on the stock ___________ in value.
c. Given two put options on the same stock with the same time to expiration, the put with the greater strike price will cost ________ than the put option with the lower strike price.
d. Given call put options on the same stock with the same time to expiration, the call with the greater strike price will cost ________ than the put option with the lower strike price.
e. Given two call options on the same stock with the same strike price, the call with the greater time to expiration will cost ________ than the call option with less time to expiration.
f. As the stock price becomes more volatile, then a call option on the stock ___________ in value.
g. How and why would the premium on an option differ depending on whether the stock pays a dividend prior to expiration or not.
3. Nine months ago, you bought €50,000,000 1-year forward at the forward rate of 1.38 $/€. If current 3-month interest rates are 10% p.a. in the U.S. and 4% p.a. in the Eurozone, and the current spot exchange rate for euros is 1.43 $/€, then how much is your forward contract worth right now? If the forward contract were terminated today, would you expect to have to pay or receive this amount?
4. Construct diagrams depicting the payoff at expiration and the net payoff (i.e., profit diagram) of the following positions:
a. You buy 1 call @ K = 45 (C = 9, sell 2 calls @ K = 50 (C = 6), and buy 1 call @ K = 60 (C = 2). Ignore time-value. Clearly mark on your diagram appropriate coordinates on each axis, such as minimum and maximum payoffs, breakeven points, etc.
b. You buy 1 put @ K = 40 (P = 7), sell 1 put @ K = 45 (P = 8), sell 1 put @ K = 50 (P = 9), buy 1 put @ K = 55 (P = 11). Clearly mark on your diagram appropriate coordinates on each axis, such as minimum and maximum payoffs, breakeven points, etc.
c. You buy 1 put @ K = 45 (P = 3), sell 2 puts @ K = 55 (P = 9), and buy 1 put @ K = 60 (P = 12). Clearly mark on your diagram appropriate coordinates on each axis, such as minimum and maximum payoffs, breakeven points, etc.
d. You enter into a short futures contract @ f = 35 and sell a put option @ K = 30 (P = 2).
e. You buy 2 puts @ K = 50 (P = 4), sell 3 puts @ K = 55 (P = 7), and buy 1 put @ K = 60 (P = 10).
Assume the interest rate is zero.
5. Given: 3-month p.a. interest rates are 3% in the U.S. and 1% in Japan. The spot exchange rate for Japanese yen is 112.4 ¥/$ and the 3-month forward rate is F3-mo = 111.3 ¥/$. You wish to borrow yen. How can you effectively (synthetically) borrow ¥100,000,000 for three months without using the Japanese money market? (List each transaction you would make including the amounts of each currency involved.) What is the implied interest rate on your synthetic yen loan? Should you borrow yen directly or synthetically?
6. Mark to market a short Eurodollar futures position with June delivery at 94.75 if daily IMM Index settlement prices are
i. Day 1: 94.50
ii. Day 2: 95.00
iii. Day 3: 95.25
iv. Day 4: 94.75
List the margin account balances at the end of each trading day and specify (i) whether an additional margin is required on any given day and, (ii) if a margin call is issued, how much must be deposited to your margin account. Assume that the initial margin is $3,000; the maintenance margin is $2,000, and the tick value is 1 b.p. = $25.
7. Company A and Company B have been quoted the following rates:
Company A fixed 5.60% or floating LIBOR + 160 basis points
Company B fixed 4.35% or floating LIBOR + 75 basis points
a. Design a swap that will produce a net gain of 20 basis points per annum for each of the two companies.
b. Design a swap that will produce a net gain of 15 basis points per annum for Company A and a net gain of 25 basis points per annum for Company B.
c. Design a swap that will produce a net gain of 15 basis points per annum for each of the two companies and a 10 basis point fee for an intermediary.
8. Given: C = $4.75, P = $3.25, S = $42, K = $40, T = 6 months, r = 2% p.a.
a. What would you do to exploit these quotes? (List the transactions.) What would be your riskless arbitrage profit?
b. How could you synthetically short-sell an asset using only options and borrowing or lending at the risk-free rate? Would you be better off short-selling the stock, or synthetically short-selling it using options?
9. For a call option on a non-dividend-paying stock, the stock price is $53, the strike price is $45, the risk-free interest rate is 4% per annum, the standard deviation of the stock's expected return is 40% per annum and the time to maturity is three months. What is the price of the option if it is a European call? (You may want to use a table for N(x), or you can use Excel's ‘normsdist' function.
10. Given: Today's stock price is 30. One month from now, the stock price will be either 26 or 34. If it is 34, then the following month the stock price will be either 39 or 31. If it is 26 one month from now, then the following month the price will be either 21 or 31. The risk-free rate of interest is 1% per month. How much should one be willing to pay today for a call option on the stock with K = 32 and T = 2 months? Construct the binomial tree for a European call option. At each node, provide the call premium (i.e., value) as well as Δ and B.