MGT 890: Corporate Finance and Options
Bonus Assignment Set #3
Due 5:00pm February 27, 2001
1. Options: Put-Call Parity
The following table lists options on General Motors and their prices as of February 14. At the time these quotes were taken, the stock was selling for 73 15/16 per share.
March 2000CALLS / PUTS
Symbol / Last / Open Interest / Strike
Price / Symbol / Last / Open Interest
GM-CL / 16 / 347 / 60 / GM-OL / 1/4 / 1243
GM-CM / 14 3/4 / 1088 / 65 / GM-OM / 1/2 / 628
GM-CN / 6 1/8 / 880 / 70 / GM-ON / 1 1/2 / 1061
GM-CO / 3 1/4 / 3663 / 75 / GM-OO / 3 1/2 / 1373
GM-CP / 1 9/16 / 1523 / 80 / GM-OP / 6 7/8 / 1148
GM-CQ / 9/16 / 2453 / 85 / GM-OQ / 8 / 5600
GM-CR / 3/16 / 2332 / 90 / GM-OR / 10 3/8 / 259
The rule for expiration dates is as follows (right from the CBOE): Stock options expire on the Saturday immediately following the third Friday of the expiration month; however, brokerage firms may set an earlier deadline for notification of an option buyer's intention to exercise. If Friday is a holiday, the last trading day will be the preceding Thursday. In this case the options expire March 18.
For each option pair, use the Put-Call parity relationship to calculate the risk free rate. Annualize your answer. Can you explain why you do not get the exact same answer in each case?
2. The Black-Scholes Formula
For each CALL option in the above table, calculate the stock's "implied volatility." To calculate this number plug the option's price and the stock's price into the Black-Scholes formula along with the risk free rate, and then solve for the variance. You will need to download the spreadsheet program for the Black-Scholes model (the link is on our course website) to accomplish this. Use the risk free rates you calculated in Question 1 to answer this question.
3. Binomial Option Pricing
Recently some investment banks have tried to calculate the probability a stock will move up or down though the use of option prices. This question is designed to show you roughly how it is done.
Assume there is only one period between February 14 and March 18. In this period the stock can go up or down by some fixed percentage. Assume that the percentages are such that an up followed by a down, produces the same price as a down followed by an up (so d=1/u). For each CALL option listed in the above table (of Question 1), find a value for the up percentage that produces that call option's market price. For the risk free rate, use your answers from Question 1. Be sure to use the interest rate you calculated for the put-call pair with the same strike price as the call option you are now valuing.
Hints: You will need a spreadsheet program to solve this problem. Assume that if the stock moves down the option will have a value of zero. Each value of u produces a unique stock price. Since you know the stock's current market price this also produces a unique value for the option. Now have your spreadsheet find the u that yields the option's actual market value.
4. In 1990, the Australian firm BBA Corporation sold a share in some land that it owned near Paris for $111 million and as result boosted its 1990 earnings by $75 million. In 1991, a television program revealed that the buyer was actually given a put option to sell its share in the land back to BBA for $111 million and that BBA had paid $20 million for a call option to repurchase the share in the land for $111 million.
a). What happens if the land is worth more than $111 million when the options expire? What if it is worth less than $111 million?
b). Please use payoff (i.e., position) diagrams to show the net effect of the land sale and the option transactions.
c). The television program argued that it was misleading to record a profit on the sale of land. What do you think? Why?