Advanced Equity Derivatives: Volatility and Correlation

Chapter 5Volatility Derivatives

Option traders who hedge their delta have long realized that their option book is exposed to many other market variables, chief of which is volatility. In fact we will see that the P&L on a delta-hedged option position is driven by the spread between two types of volatility: the instant realized volatility of the underlying stock or stock index, and the option's implied volatility. Thus option traders are specialists of volatility, and naturally they want to trade it directly. This prompted the creation of a new generation of derivatives: forward contracts and options on volatility itself.

5.1 Volatility Trading

Delta-hedged options may be used to trade volatility, specifically the gap between implied volatility σ^* and realized volatility σ—another word for historical volatility. To see this consider the P&L breakdown of an option position over a time interval Δt:

where δ, Γ, Θ, ρ, are the option's Greeks, ΔS is the change in underlying spot price, Δr is the change in interest rate, Δσ^* is the change in implied volatility, and “” are high-order terms completing the Taylor expansion.

Assuming that the option is delta-hedged, the interest rate and ...