Optivals stock is currently trading at $60 per share with a historical volatility of 20%. The risk-free rate is 4%. Consider a European call and put option on Optivals stock with an exercise price of $55 that expires in 2 years. Use excel or a similar program to determine the option price using the Black-Scholes formula.

(a): What is the value the European call and put option on Optivals stock with a strike price of $60?

(b): To the nearest cent, how much does the option value change for the following adjustments to the input values:

in Call Value in Put Value

stock price by $1 to $61

strike price by $1 to $56

the rF by 1% to 5%

volatility by 1% to 21%

time to maturity by 1 yr

(c): Why does the value of the call increase by less than $1 when the stock price increases by $1?

(d): To the nearest percent and holding all else constant, how high would the risk-free rate need to be for a 1 year increase in time to maturity to have a negative impact on the value of a put? Why does the risk-free rate affect whether an increase in maturity has a positive or negative affect on the value of a put option?