HEDGING UNDER STOCHASTIC VOLATILITY

K. Ronnie Sircar
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K. Ronnie Sircar: Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA

Chapter 5 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume II), 2001, pp 147-162 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe present a family of hedging strategies for a European derivative security in a stochastic volatility environment. The strategies are robust to specification of the volatility process and do not need a parametric description of it or estimation of the volatility risk premium. They allow the hedger to control the probability of hedging success according to risk aversion. The formula exploits the separation between the time-scale of asset price fluctuation (ticks) and the longer time-scale over which volatility fluctuates, that is, the observed "persistence" of volatility. We run simulations that demonstrate the effectiveness of the strategies over the classical Black-Scholes strategy.

Date: 2001
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