SWITCHING TO NONAFFINE STOCHASTIC VOLATILITY: A CLOSED-FORM EXPANSION FOR THE INVERSE GAMMA MODEL

Abstract

We examine the inverse gamma (IGa) stochastic volatility model with time-dependent parameters. This nonaffine model compares favorably in terms of volatility distribution and volatility paths to classical affine models such as the Heston model, while being as parsimonious (only four stochastic parameters). In practice, this means more robust calibration and better hedging, explaining its popularity among practitioners. Closed-form volatility-of-volatility expansions are obtained for the price of vanilla options, which allow for very fast pricing and calibration to market data. Specifically, the price of a European put option with IGa volatility is approximated by a Black–Scholes price plus a weighted combination of Black–Scholes Greeks, with weights depending only on the four time-dependent parameters of the model. The accuracy of the expansion is illustrated on several calibration tests on foreign exchange market data. This paper shows that the IGa model is as simple, more realistic, easier to implement and faster to calibrate than classical transform-based affine models. We therefore hope that the present work will foster further research on nonaffine models favored by practitioners such as the IGa model.