(Option pricing with sigma) A stock traded for $25 today. The annual standard deviation of the stock returns is 50%. If the interest rate is 3%,

a. What is the value today of a 1-year European call option on the stock with an exercise price of $30?

b. Calculate the value today of a 1-year European put option on the stock with an exercise price of $30.

c. Show that put–call parity holds: That is, parts a and

b, show that Call price X

r + Stock price today Put price