4. The option problem involves the computation of an expectation on the form E[erTX]. To do this, we need to have algorithms to compute the expectation of a random variable with a given distribution but generally, this cannot be done precisely. (a) Describe the main steps used in Monte Carlo methods to approximate the expectation V(S0,0)=er(Tt)EQ[(ST)S0=s], where (ST) is the payoff of an average price Asian option at maturity T and St is the price of the underlying process that follows a Geometric Brownian motion. (6 marks) (b) A variance reduction technique is a method used to reduce the variance of a Monte Carlo simulation. By use of an example, distinguish between the Antithetic variates and Control variates methods of variance reduction in Monte Carlo simulation. (4 marks)