Use the BlackScholes formula to price options with time to expiration 6 months, on a stock with price $80 and volatility 20% per year. The annualized continuously compounded interest rate is 3%. You may use the following data on the CDF of the standard normal distribution:

d 0.623 0.393 0.252 0.109 0.057 0.298 0.409 0.581

N(d) 0.267 0.347 0.401 0.457 0.523 0.617 0.659 0.719

a) Show that a call with exercise price $85 has a premium of $2.985.

b) Use the putcall parity to compute the premium of a put with the same exercise price.

c) If you sell the call in a), how many shares should you buy to hedge your price risk from the call? (Hint: Compute the hedge ratio of the call.)

d) Compute again the number of shares in c) if the only change is an increase of the stock price to $90. Explain the change in the hedge ratio.

e) If the stock volatility was 30% instead of 20%, would the call premium in a) be higher or lower? And the put premium in b)? Explain briefly.