Mark Broadie

Pricing and hedging volatility derivatives

Coauthor(s): Ashish Jain.

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Abstract:
Volatility is the key variable in option pricing models and for risk management in general. Not surprisingly, this has led to the recognition that volatility uncertainty is an important risk factor. This realization, in turn, has given rise to derivative instruments tied to volatility, such as variance swaps, volatility swaps, and options on both variance and volatility, which are specifically designed to help manage this risk. To price these contracts, a model is needed for the volatility process. This article develops full pricing and risk management models for these instruments in the context of a Heston square root stochastic volatility model, including expressions for all of the standard Greek letters and a couple of new ones for the parameters of the volatility process. In addition, the authors provide a procedure for setting up optimal hedges of variance and volatility contracts using a finite set of options as an operational approximation to the full solution requiring a continuum of options.

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