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Indifference Pricing and Hedging for Volatility Derivatives

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  • M. R. Grasselli
  • T. R. Hurd
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    Abstract

    Utility based indifference pricing and hedging are now considered to be an economically natural method for valuing contingent claims in incomplete markets. However, acceptance of these concepts by the wide financial community has been hampered by the computational and conceptual difficulty of the approach. This paper focuses on the problem of computing indifference prices for derivative securities in a class of incomplete stochastic volatility models general enough to include important examples. A rigorous development is presented based on identifying the natural martingales in the model, leading to a nonlinear Feynman-Kac representation for the indifference price of contingent claims on volatility. To illustrate the power of this representation, closed form solutions are given for the indifference price of a variance swap in the standard Heston model and in a new “reciprocal Heston” model. These are the first known explicit formulas for the indifference price for a class of derivatives that is important to the finance industry.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 14 (2007)
    Issue (Month): 4 ()
    Pages: 303-317

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    Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:303-317

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    Related research

    Keywords: Volatility risk; exponential utility; Heston model; variance swap; incomplete markets; certainty equivalent; volatility derivative;

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    Cited by:
    1. Ichihara, Naoyuki, 2012. "Large time asymptotic problems for optimal stochastic control with superlinear cost," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1248-1275.
    2. Ming Pu & Gang-Zhi Fan & Seow Ong, 2012. "Heterogeneous Agents and the Indifference Pricing of Property Index Linked Swaps," The Journal of Real Estate Finance and Economics, Springer, vol. 44(4), pages 543-569, May.
    3. Colin Lizieri & Gianluca Marcato & Paul Ogden & Andrew Baum, 2012. "Pricing Inefficiencies in Private Real Estate Markets Using Total Return Swaps," The Journal of Real Estate Finance and Economics, Springer, vol. 45(3), pages 774-803, October.

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