Monte Carlo Simulation for Pricing European and American Basket option

Examples of the analytical approximations are provided in Milevsky and Posner 1998 [3] and [4] who compare the relative accuracy of the lognormal or the inverse gamma distribution for approximating the sum of lognormal distributions. Tree based methods were originally proposed by Cox et al 1979 [2] and adopted in Wan 2002 [5]. Monte Carlo methods were first proposed by Boyle 1977 [1] as an alternative to the closed form solution of a partial differential equation or the use of tree based methods. Monte Carlo methods can be fruitfully used to price derivatives lacking an analytical closed-form. In the more general setup, assuming a deterministic risk-free interest rate, the value of an option of European kind is given by the following expectation Pt = e R T t EQ[g(T, S)] (1)