Write your python class for the Black-Scholes model by adding the formulas for the Greeks in the Black-Scholes model, i.e. option price sensitivities with respect to the input variables in the Black-Scholes model. Answer the following with the functions you write.

a) Calculate the delta of an at-the money six-month European call option on a nondividend paying stock when the risk-free rate is 10% per annum and the stock price volatility is 25% per annum with the stock price $95 and strike $96.

b) Calculate the gamma of an at-the money six-month European call option on a nondividend paying stock when the risk-free rate is 8% per annum and the stock price volatility is 30% per annum with the stock price $95 and strike $96.