Vega Risk and the Smile

Abstract

Vega risk can be a large part of the risk of a portfolio containing options. 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. In our discussion, we will present several examples using a high-quality database of foreign exchange implied volatilities.

JEL Classification: G13, G14