Pricing and Inference with Mixtures of Conditionally Normal Processes

49 Pages Posted: 3 Jul 2007 Last revised: 16 Jun 2009

See all articles by Henri Bertholon

Henri Bertholon

Conservatoire National des Arts et Métiers (CNAM)

Alain Monfort

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST); National Bureau of Economic Research (NBER); Maastricht University

Fulvio Pegoraro

Banque de France - Economics and Finance Research Center; CREST - Laboratoire de Finance et Assurance

Multiple version iconThere are 2 versions of this paper

Date Written: March 1, 2009

Abstract

The main objective of this paper is to exploit important properties of the mixtures of normal distributions and of conditionally normal processes in order to propose flexible and tractable discrete-time option pricing models, based on the exponential-affine stochastic discount factor (SDF) modeling principle. These models deal simultaneously and coherently with the historical and risk-neutral worlds, they can be static or dynamic and, moreover, they can be parametric or semi-parametric. In the static setting our approach provide explicit historical and risk-neutral stock returns distributions and closed-form formulas for European option prices of any residual maturity. These pricing formulas turn out to be convex combinations of Black and Scholes formulas.

The previous approach is extended to the dynamic case in several ways. First, by assuming that a Mixed Normal distribution is valid for the standardized error terms. Second, by considering mixtures of conditionally Gaussian processes and, third, by adopting a semi-parametric approach which estimates the distribution of standardized error terms by mixtures of normals based on a kernel method. Some numerical exercise shows the ability of our European option pricing models to replicate implied volatility smiles, volatility skews and volatility surfaces coherently with observations.

Keywords: Derivative Pricing, Stochastic Discount Factor, Implied Volatility, Mixture of Normal Distributions, Mixture of Conditionally Normal Processes, Nonparametric Kernel Estimation, Mixed-Normal GARCH Processes, Switching Regime Models

JEL Classification: C1, C5, G1

Suggested Citation

Bertholon, Henri and Monfort, Alain and Pegoraro, Fulvio, Pricing and Inference with Mixtures of Conditionally Normal Processes (March 1, 2009). Available at SSRN: https://ssrn.com/abstract=997975 or http://dx.doi.org/10.2139/ssrn.997975

Henri Bertholon

Conservatoire National des Arts et Métiers (CNAM) ( email )

Paris
United States

Alain Monfort

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST) ( email )

15 Boulevard Gabriel Peri
Malakoff Cedex, 1 92245
France
+33 1 4117 6079 (Phone)
+33 1 4117 6046 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Maastricht University

P.O. Box 616
Maastricht, Limburg 6200MD
Netherlands

Fulvio Pegoraro (Contact Author)

Banque de France - Economics and Finance Research Center ( email )

31 rue Croix des Petits Champs
75049 Paris Cedex 01 France
France
00.33.(0)1.42.92.91.67 (Phone)
00.33.(0)1.42.92.48.18 (Fax)

CREST - Laboratoire de Finance et Assurance ( email )

15, Boulevard Gabriel Péri
Bureau 1112 - Timbre J320
92245 Malafokk Cedex France, 92245
France
00.33.(0)1.41.17.77.97 (Phone)
00.33.(0)1.41.17.76.66 (Fax)

HOME PAGE: http://www.crest.fr/pageperso/pegoraro/pegoraro.htm

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