American Monte Carlo by Stochastic Separation of the Expected Value

Abstract

American Monte Carlo is a solution to the puzzle of calculating the value of derivatives with the right to an early exercise, when using Monte Carlo simulation. One of the technique uses regression of some suitable basis functions, which is a bit arbitrary, and could if made wrong render in expectation bias. It is also useful when simulating nested simulations, like pricing Credit Value Adjustment (CVA) that is when the portfolio includes derivatives that need simulation to be priced. Here, we use a simple way of calculating the price when using simulation, based on the simple fact that the expectation integral could be divided by the random numbers of the simulation. This method works well even for a small sample of simulations and it also applies to the the case of nested simulations, also in the case of having different measures of the simulations. One example of usage is to calculate different XVA's under the lifespan of the portfolio, especially focusing on Initial Margin (IM) and Marginal Value Adjustment (MVA).