Three Make a Smile – Dynamic Volatility, Skewness and Term Structure Components in Option Valutation

44 Pages Posted: 30 Mar 2011

See all articles by Peter H. Gruber

Peter H. Gruber

University of Lugano - Institute of Finance

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: February 1, 2010

Abstract

We propose a new modeling framework for the valuation of European options, in which dynamic short and long run volatility components drive the smile dynamics. The model state dynamics is driven by a matrix jump diffusion, provides efficient pricing formulas for plain vanilla options by means of standard transform methods, and it nests as special cases a number of affine option pricing models in the literature. In contrast to other approaches, short and long run volatility components interact dynamically with a further component linked to stochastic skewness, which we show is important in order to capture accurately the joint behavior of the implied volatility skew and the volatility term structure. We estimate our model and a number of competing benchmarks without interactions using S&P 500 index options. We find that models with dynamic interactions provide better pricing performance and a more accurate description of the joint dynamics of the implied volatility skew and term structure, both in-sample and out-of-sample. These findings support the use of option pricing models with (i) at least three dynamic volatility factors and (ii) dynamic interactions between volatility and stochastic skewness components.

Keywords: Option Pricing, Stochastic Volatility, Short and Long Term Volatility Risk, Stochastic Leverage, Wishart Diffusion

Suggested Citation

Gruber, Peter H. and Tebaldi, Claudio and Trojani, Fabio, Three Make a Smile – Dynamic Volatility, Skewness and Term Structure Components in Option Valutation (February 1, 2010). CAREFIN Research Paper No. 02/2010, Available at SSRN: https://ssrn.com/abstract=1798604

Peter H. Gruber (Contact Author)

University of Lugano - Institute of Finance ( email )

Via Buffi 13
CH-6900 Lugano
Switzerland

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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