Chapter 17

Managing Volatility Risk*

Options are nonlinear instruments whose value depends on, among other things, a volatility parameter. Thus trading options involves taking volatility bets as well as directional bets on the underlying asset prices. Previous chapters have covered the Black-Scholes pricing formula as well as partial derivatives. This chapter examines more advanced models involving volatility trading.

Section 17.1 explains how an implied volatility can be recovered from option market prices. A notable example is the Volatility Index (VIX), which is the implied volatility measure for U.S. stocks that has become widely watched as a broad measure of risk. More generally, VIX should be extended to various maturities and strike prices, which leads to the concept of an implied volatility surface. Option portfolios present special challenges for risk measurement. Complicated portfolios require modeling the entire volatility surface for all the underlying risk factors, which is a complex undertaking.

At the portfolio level, comparisons of volatilities lead to the concept of average correlations, which are discussed in Section 17.2. Next, Section 17.3 presents derivative contracts whose values are directly tied to the realized variance or correlation. Section 17.4 then turns to the interpretation of dynamic hedging. Risk managers need to have a good understanding of these strategies because they give important insights into many active trading strategies.

Finally, Section ...