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On the pricing and hedging of volatility derivatives

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  • Sam Howison
  • Avraam Rafailidis
  • Henrik Rasmussen

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.

Suggested Citation

  • Sam Howison & Avraam Rafailidis & Henrik Rasmussen, 2004. "On the pricing and hedging of volatility derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(4), pages 317-346.
    • Handle: RePEc:taf:apmtfi:v:11:y:2004:i:4:p:317-346
    DOI: 10.1080/1350486042000254024
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    References listed on IDEAS

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    1. Steven Heston & Saikat Nandi, 2000. "Derivatives on volatility: some simple solutions based on observables," FRB Atlanta Working Paper 2000-20, Federal Reserve Bank of Atlanta.
    2. Jérôme Detemple & Carlton Osakwe, 2000. "The Valuation of Volatility Options," Review of Finance, European Finance Association, vol. 4(1), pages 21-50.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Realised power variation and stochastic volatility models," Economics Papers 2001-W18, Economics Group, Nuffield College, University of Oxford.
    4. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
    Full references (including those not matched with items on IDEAS)

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