You are pricing options in the Black-Scholes-Merton framework on an underlying with volatility =17% and current market value S0=80. The options have a maturity of 2 years and the risk free interest per year is 1.25%. a) Price a European Call option with exercise price K=82. b) Identify time value and intrinsic value of the Call option. c) Price an Put option with exercise price K=81. d) Identify time value and intrinsic value of the Put option. e) Calculate the Delta and Vega of the Call option of a). You bought the call option of a). One year passes. Throughout this year, the volatility has increased to 0.21 and the price of the underlying moved to 83.50. f) Without calculation, describe the differing effects during this year on the option price. g) Calculate the option price of your call option. h) Calculate the Delta and Vega of the Call option of g)