The Monte Carlo Framework, Examples from Finance and Generating Correlated Random Variables

Suppose we wish to estimate some quantity, θ = E[h(X)], where X = {X 1 ,. .. , X n } is a random vector in R n , h(·) is a function from R n to R, and E[|h(X)|] < ∞. Note that X could represent the values of a stochastic process at different points in time. For example, X i might be the price of a particular stock at time i and h(·) might be given by h(X) = X 1 +. .. + X n n so then θ is the expected average value of the stock price. To estimate θ we use the following algorithm: Note: If n is large, it may be necessary to keep track of i h i within the for loop, so that we don't have to store each value of h i .