Nonparametric estimation of conditional value-at-risk and expected shortfall based on extreme value theory

TL;DR

This paper introduces nonparametric estimators for conditional value-at-risk and expected shortfall using extreme value theory, applicable to financial returns with covariates, and demonstrates their theoretical properties and practical performance.

Contribution

It develops a novel nonparametric approach combining location-scale models with Pareto tail approximation for CVaR and CES estimation, with proven consistency and asymptotic normality.

Findings

Estimators are consistent and asymptotically normal.

Monte Carlo simulations show good finite sample performance.

Backtesting on commodity futures data confirms empirical viability.

Abstract

We propose nonparametric estimators for conditional value-at-risk (CVaR) and conditional expected shortfall (CES) associated with conditional distributions of a series of returns on a financial asset. The return series and the conditioning covariates, which may include lagged returns and other exogenous variables, are assumed to be strong mixing and follow a nonparametric conditional location-scale model. First stage nonparametric estimators for location and scale are combined with a generalized Pareto approximation for distribution tails proposed by Pickands (1975) to give final estimators for CVaR and CES. We provide consistency and asymptotic normality of the proposed estimators under suitable normalization. We also present the results of a Monte Carlo study that sheds light on their finite sample performance. Empirical viability of the model and estimators is investigated through a backtesting exercise using returns on future contracts for five agricultural commodities.