ON THE CALCULATION OF RISK MEASURES USING LEAST-SQUARES MONTE CARLO

Abstract

The paper establishes a convergence result for the Least-Squares Monte Carlo method, applied to the estimation of risk measures (such as VaR) depending on the distribution of the future value of some derivative contract (or portfolio). We extend previous results in the literature by focusing on the specific case where the distribution of the underlying factors is known. In particular, we are able to remove the requirement of bounded conditional variance which is usually not satisfied by common financial models and payoffs at the cost of using a weaker notion of convergence. Our main result shows the convergence of the empirical distribution function when the number of simulations [Formula: see text] and of basis variables [Formula: see text] are jointly sent to infinity under certain conditions on the payoff and the basis. With a suitable choice of basis functions, we finally prove that convergence can be ensured when [Formula: see text].