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Indifference Pricing and Hedging for Volatility Derivatives

Indifference Pricing and Hedging for Volatility Derivatives 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. * Research supported by the Natural Sciences and Engineering Research Council of Canada and MITACS, Mathematics of Information Technology and Complex Systems Canada http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Indifference Pricing and Hedging for Volatility Derivatives

Grasselli, M. R.; Hurd*, T. R.
Applied Mathematical Finance , Volume 14 (4): 15 – Sep 1, 2007
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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...
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Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/13527260600963851
Publisher site
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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. * Research supported by the Natural Sciences and Engineering Research Council of Canada and MITACS, Mathematics of Information Technology and Complex Systems Canada

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Sep 1, 2007

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

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