Vega risk and the smile

Allan M. Malz

Abstract

ABSTRACT

Vega risk is analytically easy to "nest" into the standard risk management framework, but is complicated by the prevalence of volatility smiles and term structures in most option markets. Volatility smiles, in spite of their occasionally treacherous effects on option books, are often neglected by risk managers. This paper provides a guide to incorporating vega risk into a "classical" value-at-risk (VaR) model. The paper includes a tractable approach to capturing the effects of the volatility smile and term structure on vega risk and their interaction with other risk factors. The author also presents a summary of the statistical behavior of implied volatility and relates it to observed differences in the pattern of implied volatilities from that predicted by the Black-Scholes model. The VaR computation strategy employs the smile to compensate for the shortcomings of the Black-Scholes model and provide improved VaR forecasts without a specific alternative model.