Risk Management with Local Least Squares Monte Carlo

The least squares Monte Carlo method has become a standard approach in the insurance and financial industries for evaluating a company’s exposure to market risk. However, the non-linear regression of simulated responses on risk factors poses a challenge in this procedure. This article presents a novel approach to address this issue by employing an a-priori segmentation of responses. Using a K-means algorithm, we identify clusters of responses that are then locally regressed on their corresponding risk factors. The global regression function is obtained by combining the local models with logistic regression. We demonstrate the effectiveness of the proposed local least squares Monte Carlo method through two case studies. The first case study investigates butterfly and bull trap options within a Heston stochastic volatility model, while the second case study examines the exposure to risks in a participating life insurance scenario.