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Comparison of q-optimal Option Prices in a Stochastic Volatility Model with
Correlation
Vicky
Henderson, David Hobson, Sam Howison, Tino Kluge
Abstract
This paper investigates option prices in an incomplete stochastic
volatility model with correlation. In a general setting, we prove an
ordering result which says that prices for European options with convex payoffs
are decreasing in the market price of volatility risk. As an example, and
as our main motivation, we investigate option pricing under the class of
q-optimal pricing measures. Using the ordering result, we prove comparison
theorems between option prices under the minimal martingale, minimal
entropy and variance-optimal pricing measures. As a concrete example, we
specialise to a variant of the Heston model. For this example we are able
to deduce that option prices are decreasing in the parameter q.
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