Volatility Clustering in Option Indifference Pricing with Convex Risk Measures

Summary

The article studies how volatility clustering affects risk-indifference prices for options. It builds on a framework in which prices are determined using dynamic convex risk measures represented by backward stochastic differential equations. Clustering is incorporated through a stochastic-volatility model for the underlying stock, with volatility that mean-reverts rapidly.

The analysis derives asymptotic expressions for option indifference prices and their corresponding implied volatility as the volatility mean-reversion time tends to zero. It also obtains correction terms to those asymptotic approximations. These results connect fast volatility fluctuations to risk-based option valuation, but the document provides no numerical examples, empirical validation, or details about the size or practical significance of the corrections. The conclusions therefore describe a mathematical pricing analysis rather than evidence that the approach improves real-world trading decisions.

Key ideas

• Option indifference prices are studied under dynamic convex risk measures defined through backward stochastic differential equations.
• A stochastic-volatility stock model represents volatility clustering with fast mean reversion.
• The analysis derives asymptotic option prices as the volatility mean-reversion time approaches zero.
• Corresponding implied-volatility asymptotics and correction terms are also obtained.
• The document summarizes a theoretical analysis and gives no empirical or numerical assessment of practical impact.

Tags

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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