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

TL;DR

This paper investigates how volatility clustering affects the risk indifference pricing of options using convex risk measures, providing asymptotic formulas and correction terms as mean-reversion speed increases.

Contribution

It extends the analysis of indifference prices by incorporating volatility clustering modeled via fast mean-reverting stochastic volatility, deriving new asymptotic results and correction terms.

Findings

Asymptotic formulas for indifference prices under volatility clustering

Correction terms for option prices and implied volatility

Impact of fast mean-reversion on pricing asymptotics

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.