1. A stock index is at a level of 100 with a dividend yield of 1.2% per annum. The volatility of the index return is 30%. The 6-month risk-free rate is 3%. Both the risk-free rate and dividend yield are continuously compounded. (a) Estimate the 6-month index futures price. (5 marks) (b) Under the Black-Scholes-Merton model, what is the price of a European call option on the stock index with a strike price of 90 and an expiration of 6 months? (5 marks) (c) Under a two-period binomial model, what is the price of an American put option on the index with a strike price of 90 and an expiration of 6 months? (5 marks) 1. A stock index is at a level of 100 with a dividend yield of 1.2% per annum. The volatility of the index return is 30%. The 6-month risk-free rate is 3%. Both the risk-free rate and dividend yield are continuously compounded. (a) Estimate the 6-month index futures price. (5 marks) (b) Under the Black-Scholes-Merton model, what is the price of a European call option on the stock index with a strike price of 90 and an expiration of 6 months? (5 marks) (c) Under a two-period binomial model, what is the price of an American put option on the index with a strike price of 90 and an expiration of 6 months