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8. (12 marks) a) 6 (a) Use the Black-Scholes option pricing formula to calculate the price of a European put option on a stock when the stock price is $75, the strike price is $80, the risk-free interest rate is 3% per annum, the volatility is 20% per annum, and the time to maturity is six months. b) 6 Show that the Black-Scholes option pricing formulas for call and put options satisfy the put-call parity, i.e., show that C + Ke T = P + S(0) where C and P are the prices of call and put options, respectively