Indifference Pricing and Hedging for Volatility Derivatives
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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.