Article2004

On the pricing and hedging of volatility derivatives

Sam Howison · Avraam Rafailidis · Henrik Rasmussen

94 citations0/0 files storedApplied Mathematical Finance

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Stochastic processes and financial applications Financial Risk and Volatility Modeling Risk Management in Financial Firms

Abstract

The paper considers the pricing of a range of volatility derivatives, including volatility and variance swaps and swaptions. Under risk-neutral valuation closed-form formulae for volatility-average and variance swaps for a variety of diffusion and jump-diffusion models for volatility are provided. A general partial differential equation framework for derivatives that have an extra dependence on an average of the volatility is described. Approximate solutions of this equation are given for volatility products written on assets for which the volatility process fluctuates on a timescale that is fast compared with the lifetime of the contracts, analysing both the 'outer' region and, by matched asymptotic expansions, the 'inner' boundary layer near expiry.

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1987The Pricing of Options on Assets with Stochastic Volatilities 1998Arbitrage Theory in Continuous Time 1987The Pricing of Options on Assets with Stochastic Volatilities 2000Derivatives in Financial Markets with Stochastic Volatility 1998Derivatives: The Theory and Practice of Financial Engineering 2001The Price of a Smile: Hedging and Spanning in Option Markets 2001Mathematical Methods for Foreign Exchange

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2013A regime-switching Heston model for VIX and S&P 500 implied volatilities 2013Root’s barrier: Construction, optimality and applications to variance options 2006Power and Multipower Variation: inference for high frequency data 2005Variation, Jumps, Market Frictions and High Frequency Data in Financial Econometrics 2005Pricing methods and hedging strategies for volatility derivatives 2007

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