Alternative Value-at-Risk Models for Options

Abstract

The aim of this paper is to evaluate the performance of different value-at-risk models. While most previous studies focus on linear positions, this paper investigates the suitability of alternative approaches for positions in stock-options. Risk measurement for options is more complex, since movements in the underlying risk factor (stock-prices) have a non-linear impact on option prices and option prices themselves depend on volatility, which is not directly observable on capital markets. Standard models based on the Black-Scholes analysis and models, that build in the stochastic volatility option pricing model by Hull and White are compared using transaction data from the Austrian stock market. It is found that while the Hull-White model is the only model that passes a proportion of failures test, it substantially underestimates losses in those cases, where the loss exceeds the value-at-risk. All value-at-risk models work better for calls, options with a shorter time to maturity and for at or out of the money options.