parameters: the current spot price of an asset is $50,

the annualized volatility is 11.5%, and

the interest rate is 3% per year

1. What is the probability that in a years time, at option expiration, the spot price is above $55? What is the probability it is above $60? (hint: you know the entire terminal distribution)

2. Show how the put and call premium imply the forward price. What is the forward price? Explain your answer. (hint: use the put-call parity relationship)

Comparative statistics for a call

3. Use the Black-Scholes formula to calculate the premium for a call with a strike of $50, a strike of $55 (already done), and a strike of $60. All other parameters are as in last assignment.

4. Use the Black-Scholes formula to calculate the premium for a call with a strike of $55 and an interest rate of 3%, 6%, and 9%. All other parameters are as in the last assignment.

5. Use the Black-Scholes formula to calculate the premium for a call with a strike of $55, an interest rate of 3% and a volatility of 10%, 15%, and 20%. All other parameters are as in the last assignment.

Comparative statistics for a put

6, 7, 8: Repeat questions 3 through 5 for a put.