Machine learning in risk measurement: Gaussian process regression for value-at-risk and expected shortfall

Abstract

While machine learning and its many variants are becoming established tools in quantitative finance, their application in a risk measurement context is less developed. This paper uses a scheme from probability theory and statistics — Gaussian processes — and applies the corresponding non-parametric technique of Gaussian process regression (GPR) to ‘train’ a system suitable for revaluing instruments, as required, to determine a portfolio’s value-at-risk and expected shortfall. Time series of historical valuation parameters and prices of the portfolio’s constituents serve as the only inputs. On the example of a variety of portfolios comprising vanilla and barrier options, it is demonstrated that, even with limited training sets, GPR leads to risk figures identical to those from full revaluation and outperforms Taylor expansion. Applications for risk management and regulatory capital calculations are apparent. Research into an extension to related areas such as counterparty credit risk measurement is promising. JEL classification: C10; G13; G18.