Nonparametric estimation of conditional value-at-risk and expected shortfall based on extreme value theory
نویسنده
چکیده
Abstract. We propose nonparametric estimators for conditional value-at-risk (VaR) and expected shortfall (ES) 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 fully 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 conditional VaR and ES. 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.
منابع مشابه
Technical supplement to Nonparametric estimation of conditional value-at-risk and expected shortfall based on extreme value theory
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