Sub-sampling and other considerations for efficient risk estimation in large portfolios

TL;DR

This paper explores efficient risk estimation for large financial portfolios using Multilevel Monte Carlo with adaptive sampling, sub-sampling strategies, and control variates to reduce computational costs.

Contribution

It introduces a sub-sampling method with complexity independent of portfolio size and discusses control variates to enhance MLMC efficiency.

Findings

Sub-sampling complexity remains constant regardless of portfolio size.

Control variates significantly improve MLMC efficiency.

Proposed methods enable scalable risk estimation for large portfolios.

Abstract

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different risk scenarios and (b) evaluating the loss of the portfolio is expensive and the cost increases with its size. In this work, we look at applying Multilevel Monte Carlo (MLMC) with adaptive inner sampling to this problem and discuss several practical considerations. In particular, we discuss a sub-sampling strategy whose computational complexity does not increase with the size of the portfolio. We also discuss several control variates that significantly improve the efficiency of MLMC in our setting.