Value‐at‐risk forecasting via dynamic asymmetric exponential power distributions

Abstract

In the value-at-risk (VaR) literature, many existing works assume that the noise distribution is the same over time. To take into account the potential time-varying dynamics of stock returns, we propose a dynamic asymmetric exponential distribution-based framework. The new method includes a time-varying shape parameter to control the dynamic shape of the distribution, a time-varying probability parameter to control the dynamic proportion of positive returns, and a time-varying scale parameter to control the dynamic volatility. We combine the generalized method of moments and the exponentially weighted moving average (EWMA) approach to derive specifications for these time-varying parameters. Empirical applications demonstrate the superior performance of the proposed method when compared with various GARCH and EWMA approaches without time variation in the innovations.

Transformational Approach to Analytical Value-at-Risk for near Normal Distributions

“…In fact, the Basel II committee recommends scaling VaR estimate by a multiple, which in turn depends upon the exceptions observed from the internal VaR estimates. For example, Gupta and Liang (2005) and Ou and Zhao (2020) apply similar multiples while estimating required capital for hedge funds and exchange traded funds, respectively. Thus, any improvement in VaR estimation technique also leads to improvements in capital estimates.…”