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Forecasting Value at Risk and expected shortfall using a model with a dynamic omega ratio

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  • Taylor, James W.

Abstract

A joint model for the Value at Risk (VaR) and expected shortfall (ES) can be estimated using a joint scoring function. Previous work has modelled the ES as the product of the VaR and a constant factor. However, this implies the same dynamics for the ES and the VaR. We propose a time-varying multiplicative factor. The ES has been expressed as the product of an expectile and a constant factor that depends on the expectile level. We rewrite this as the product of a quantile and a function of a time-varying expectile level. The expectile level is a function of the Omega ratio, which is the ratio of the expected gain to the expected loss. This leads us to model the ES as the product of the VaR and a factor that is a function of a time-varying Omega ratio. We provide empirical support using stock indices and individual stocks.

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  • Taylor, James W., 2022. "Forecasting Value at Risk and expected shortfall using a model with a dynamic omega ratio," Journal of Banking & Finance, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:jbfina:v:140:y:2022:i:c:s0378426622001133
    DOI: 10.1016/j.jbankfin.2022.106519
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    More about this item

    Keywords

    Expected shortfall; Value at Risk; Expectiles; Autoregressive models; Omega ratio;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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