# Simulation-based Value-at-Risk for Nonlinear Portfolios

## TL;DR

This paper introduces a simulation-based method for estimating Value-at-Risk in nonlinear portfolios, improving accuracy and convergence over traditional approaches, especially for complex derivatives.

## Contribution

It proposes a generic, model selection-enhanced simulation algorithm for VaR estimation applicable to high-dimensional, nonlinear portfolios with American-style derivatives.

## Key findings

- Faster convergence of the new VaR estimation method.
- Effective handling of high-dimensional, nonlinear derivative portfolios.
- Improved accuracy over traditional delta-normal approaches.

## Abstract

Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness, however, substantially diminishes when the portfolios concerned involve a high dimension of derivative positions with nonlinear payoffs; lack of closed form pricing solution for these potentially highly correlated, American-style derivatives further complicates the problem. This paper proposes a generic simulation-based algorithm for VaR estimation that can be easily applied to any existing procedures. Our proposal leverages cross-sectional information and applies variable selection techniques to simplify the existing simulation framework. Asymptotic properties of the new approach demonstrate faster convergence due to the additional model selection component introduced. We have also performed sets of numerical results that verify the effectiveness of our approach in comparison with some existing strategies.