Indifference Pricing and Hedging for Volatility Derivatives
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.Download Info
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Bibliographic Info
Article provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.
Volume (Year): 14 (2007)
Issue (Month): 4 ()
Pages: 303-317
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Related research
Keywords: Volatility risk; exponential utility; Heston model; variance swap; incomplete markets; certainty equivalent; volatility derivative;References
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