) Consider a one-year European call option on a stock when the stock price is $30, the strike price is $30, the risk-free rate is 5%, and the volatility is 25% per annum.

(a) Use the DerivaGem software to calculate the price, delta, gamma, vega, theta, and rho of the option.

(b) Verify that delta is correct by changing the stock price to $30.1 and recomputing the option price. Verify that gamma is correct by recomputing the delta for the situation where the stock price is $30.1. Carry out similar calculations to verify that vega, theta, and rho are correct.

(c) Suppose that over the course of one day, the stock price increases by $0.5. Find the approximate price of the call option on the next day.