13. a) Shares in El Cortez plc are currently trading at 11 each with volatility of 23% per annum. The risk-free rate of interest is 4.5% per annum. A European-style call option written on El Cortez stock with an exercise price of 9.75 matures in nine months. What according to the Black-Scholes model should be the price of this option? (30 marks) b) El Cortez plc features in the SDX100 stock index which is currently trading at 7,500 index points. The index has volatility of 24% per annum and a continuously compounded dividend yield of 2.5% per annum. The contract multiple is 10 per full index point. Calculate, using the Black-Scholes-Merton (1973) approach, the price of the following options written on the SDX100 index: (1) A six-month European call with an exercise price of 7225 (35 marks) (ii) A six-month European put with exercise price of 7775 (35 marks)