Problem
1. Consider a six-month European call option on a stock when the stock price is $30, the strike price is $30, the continuously compounded risk-free rate is 5%, and the volatility is 25% per annum. Use the DerivaGem software to calculate the price, delta, and gamma of the option. Use the DerivaGem Applications Builder functions to plot the option price, delta, and gamma, against the stock price (i.e., to plot the variables as functions of the stock price).
2. Suppose that the option in (1) will expire in one month (instead of six months). Answer all questions in (1) for this one-month option. Briefly comment on the effect of time to maturity on the option price, delta, and gamma.