Use the black-scholes model to price the following call option.

a. A one-year european call option on 100 shares of xyz corporation. the exercise price is $50 per share. the standard deviation (sd) of returns on xyz's shares is 0.2 per year. the current stock price is $35 per share. the risk-free rate of return is 3%.

b. now vary the terms of the call on xyz one at a time. what happens to the value of the call as sd goes from 0.2 to 0.5? as maturity goes from 0 to 3 years? as the exercise price goes from $25 to $35 to $50? as the stock price goes from $35 to $60? as the risk-free rate goes from 3% to 6%?

c. what is the value of a european put on 100 shares of xyz, with the identical terms given in part (a.) above?

d. repeat the calculations from part (b.) for the european put on xyz. what are the intuitive explanations for the changes in value you computed?