Smile from the Past: A General Option Pricing Framework with Multiple Volatility and Leverage Components

33 Pages Posted: 28 Sep 2013 Last revised: 14 Apr 2014

See all articles by Adam Majewski

Adam Majewski

Capital Fund Management

Giacomo Bormetti

University of Bologna - Department of Mathematics

Fulvio Corsi

University of Pisa - Department of Economics; City University London

Date Written: April 2014

Abstract

In the current literature, the analytical tractability of discrete time option pricing models is guaranteed only for rather specific types of models and pricing kernels. We propose a very general and fully analytical option pricing framework, encompassing a wide class of discrete time models featuring multiple-component structure in both volatility and leverage, and a flexible pricing kernel with multiple risk premia. Although the proposed framework is general enough to include either GARCH-type volatility, Realized Volatility or a combination of the two, in this paper we focus on realized volatility option pricing models by extending the Heterogeneous Autoregressive Gamma (HARG) model of Corsi, Fusari, La Vecchia (2012) to incorporate heterogeneous leverage structures with multiple components, while preserving closed-form solutions for option prices. Applying our analytically tractable asymmetric HARG model to a large sample of S&P 500 index options, we demonstrate its superior ability to price out-of-the-money options compared to existing benchmarks.

Suggested Citation

Majewski, Adam and Bormetti, Giacomo and Corsi, Fulvio, Smile from the Past: A General Option Pricing Framework with Multiple Volatility and Leverage Components (April 2014). Available at SSRN: https://ssrn.com/abstract=2331317 or http://dx.doi.org/10.2139/ssrn.2331317

Adam Majewski

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Giacomo Bormetti (Contact Author)

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

Fulvio Corsi

University of Pisa - Department of Economics ( email )

via Ridolfi 10
I-56100 Pisa, PI 56100
Italy

HOME PAGE: http://people.unipi.it/fulvio_corsi/

City University London ( email )

Northampton Square
London, EC1V OHB
United Kingdom

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