Three Make a Dynamic Smile - Unspanned Skewness and Interacting Volatility Components in Option Valuation

63 Pages Posted: 18 Mar 2011

See all articles by Peter H. Gruber

Peter H. Gruber

University of Lugano - Institute of Finance

Roberto Renò

University of Verona - Department of Economics

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance; Bocconi University - Department of Finance; Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research

Fabio Trojani

Swiss Finance Institute; University of Geneva

Date Written: March 15, 2011

Abstract

We study a new class of three-factor affine option pricing models with interdependent volatility dynamics and a stochastic skewness component unrelated to volatility shocks. These properties are useful in order (i) to model a term structure of implied volatility skews more consistent with the data and (ii) to capture comovements of short and long term skews largely unrelated to the volatility dynamics. We estimate our models using about fourteen years of S&P 500 index option data and find that on average they improve the out-of-sample pricing accuracy of benchmark two- and three-factor affine models by 20%. Using an appropriate decomposition of volatility and skewness, highlighting the main directions of improvements produced by our setting, we show that the enhanced fit results from an improved modeling of the term structure of implied-volatility skews. The largest pricing improvements tend to concentrate during periods of financial crises or market distress, suggesting volatility- unrelated skewness as a potentially useful reduced-form risk factor for reproducing some of the crisis-related dynamics of index option smiles.

Keywords: Option Pricing, Stochastic Volatility, Stochastic Leverage, Short and Long Run Volatility Risk, Matrix Affine Jump Diffusions

JEL Classification: G10, G12, G13

Suggested Citation

Gruber, Peter H. and Renò, Roberto and Tebaldi, Claudio and Trojani, Fabio, Three Make a Dynamic Smile - Unspanned Skewness and Interacting Volatility Components in Option Valuation (March 15, 2011). Available at SSRN: https://ssrn.com/abstract=1786408 or http://dx.doi.org/10.2139/ssrn.1786408

Peter H. Gruber (Contact Author)

University of Lugano - Institute of Finance ( email )

Via Buffi 13
CH-6900 Lugano
Switzerland

Roberto Renò

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance ( email )

Via Roentgen 1
Milan, 20136
Italy

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research ( email )

Via Roentgen 1
Milan, 20136
Italy

Fabio Trojani

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva ( email )

Geneva, Geneva
Switzerland

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