# Ola Hammarlid: Computing the expected value using Monte Carlo simulation and stochastic separation of the integral

**Time: **
Wed 2023-02-22 15.15 - 16.00

**Location: **
Cramér room, Albano

**Participating: **
Ola Hammarlid, Swedbank

### Abstract

Monte Carlo method is used to estimate the expected value when other analytical or numerical methods fail. This is common practice in finance. In the most complicated calculation (for XVA), the problem of nested simulation arises. These nested simulations might be under a different measure as well. 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. In this talk, 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 case of nested simulations. This also works in the case of having different measures of the simulations. The method is a analogy to the binomial model, with a stochastic generated tree in higher dimension.