Effect of Volatility Clustering on Indifference Pricing of Options by Convex Risk Measures

Rohini Kumar

Applied Mathematical Finance, 2015, vol. 22, issue 1, 63-82

Abstract: In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance . Advance online publication. doi:10.1111/mafi.12015). The indifference price in their article is obtained by using dynamic convex risk measures given by backward stochastic differential equations. Volatility clustering is modelled by a fast mean-reverting volatility in a stochastic volatility model for stock price. Asymptotics of the indifference price of options and their corresponding implied volatility are obtained in this article, as the mean-reversion time approaches zero. Correction terms to the asymptotic option price and implied volatility are also obtained.

Date: 2015
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DOI: 10.1080/1350486X.2014.949805

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