a) (6 marks) Consider an Asian average rate call option with discrete arithmetic averaging. The option payoff is max- - K,0% where t; = iAt , k=1 N At=, K is the strike price and T is the life of the option. Assuming that the risk-free interest rate as well as volatility is constant, describe in detail how to use Monte Carlo simulation to value the option. b) (3 marks) The accuracy of the result given by Monte Carlo simulations depends on the number of trials. How do you determine the number of trials in the Monte Carlo simulations? To increase the accuracy by a factor of N, by what factor the number of trials must increase? c) (6 marks) Explain the control variate and antithetic variable techniques and how they could be used to improve numerical efficiency of the Monte Carlo simulation? a) (6 marks) Consider an Asian average rate call option with discrete arithmetic averaging. The option payoff is max- - K,0% where t; = iAt , k=1 N At=, K is the strike price and T is the life of the option. Assuming that the risk-free interest rate as well as volatility is constant, describe in detail how to use Monte Carlo simulation to value the option. b) (3 marks) The accuracy of the result given by Monte Carlo simulations depends on the number of trials. How do you determine the number of trials in the Monte Carlo simulations? To increase the accuracy by a factor of N, by what factor the number of trials must increase? c) (6 marks) Explain the control variate and antithetic variable techniques and how they could be used to improve numerical efficiency of the Monte Carlo simulation