1) Consider a stock priced at $30 with a standard deviation of 0.3. The risk-free rate is 0.05. There are put and call options available at exercise prices of 30 and a time to expiration of six months. The calls are priced at $2.89 and the puts cost $2.15. There are no dividends on the stock and the options are European. Assume that all transactions consist of 100 shares or one contract (100 options). Use this information to answer the following questions. Briefly discuss your results.
What is your profit if you buy a call, hold it to expiration and the stock price at expiration is $37?
What is the breakeven stock price at expiration on the transaction described in part a?
What is the maximum profit on the transaction described in problem a?
What is the maximum profit that the writer of a call can make?
2) Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4 percent. Assume a one-period world. Answer the following questions about a call with an exercise price of 80. Use the formulas for these. Briefly discuss.
a. What would be the call's price if the stock goes up?
b. What would be the call's price if the stock goes down?
c. What is the hedge ratio?
d. What is the theoretical value of the call?
3) a. Suppose S = 70, X = 65, r = 0.05, p = 0.6, Cu = 7.17, Cd = 1.22 and there is one period left in an American call's life. What will the option be worth?
B) in a one-period binomial model with Su = 49.5, Sd = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?
4) The following information is given about options on the stock of a certain company. Briefly discuss.
S0 = 23 X = 20
rc = 0.09 T = 0.5
s2 = 0.15
A) What value does the Black-Scholes-Merton model predict for the call?
B) The price of a put on the stock is? Price of a call? Assume no dividends.
C) to construct a riskless hedge, the number of puts per 100 shares purchased is?
D) if the company issues .70 cents dividend how does this answer compare to part a and why?