Problem 1: Consider a six-month put option on a stock with a strike price of $32. The current stock price is $30 and over the next six months, it is expected to rise to $36 or fall to $27. The risk-free interest rate is 6%. What is the risk-neutral probability of the stock rising to $36?
a. 0.365
b. 0.415
c. 0.435
d. 0.465
e. 0.664
Problem 2: Consider a six-month put option on a stock with a strike price of $32. The current stock price is $30 and over the next six months, it is expected to rise to $36 or fall to $27. The risk-free interest rate is 6%. What position in the stock is necessary to hedge a long position in one put option?
a. Short 0.444 shares
b. Long 0.444 shares
c. Short 0.555 shares
d. Long 0.555 shares
e. None of the above