STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q‐OPTIMAL MEASURE

David Hobson

Mathematical Finance, 2004, vol. 14, issue 4, 537-556

Abstract: The aim of this paper is to study the minimal entropy and variance‐optimal martingale measures for stochastic volatility models. In particular, for a diffusion model where the asset price and volatility are correlated, we show that the problem of determining the q‐optimal measure can be reduced to finding a solution to a representation equation. The minimal entropy measure and variance‐optimal measure are seen as the special cases q= 1 and q= 2 respectively. In the case where the volatility is an autonomous diffusion we give a stochastic representation for the solution of this equation. If the correlation ρ between the traded asset and the autonomous volatility satisfies ρ2

Date: 2004
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