Alternative Value-At-Risk Models For Options

Risk management has become an important issue for banks and corporations, not only because of regulation but also because of risk adjusted performance measurement. Value-at-risk has become an industry standard in risk measurement. The aim of this paper is to evaluate the performance of different value-at-risk models and find out the driving factors of model performance. 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 the Austrian stock market. Simple tests as well as numerically intense methods are used for testing model performance. 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, when the loss exceeds the value-at-risk. Value-at-risk models work better for calls, options with a shorter time to maturity and for at or out of the money options.