Risk management with local least squares monte-carlo

The method of least squares Monte-Carlo (LSMC) has become a standard in the insurance and financial sectors for computing the exposure of a company to market risk. The sensitive point of this procedure is the non-linear regression of simulated responses to risk factors. This article proposes a novel approach for this step, based on an apriori segmentation of responses. Using a K-means algorithm, we identify clusters of responses that are next locally regressed on corresponding risk factors. A global function of regression is obtained by combining local models and a logistic regression. The efficiency of the Local Least squares Monte-Carlo (LLSMC) is checked in two illustrations. The first one focuses on butterfly and bull trap options in a Heston stochastic volatility model. The second illustration analyzes the exposure to risks of a participating life insurance.