An Implicit Martingale Restriction in a Closed-Form Higher Order Moments Option Pricing Formula Based on Multipoint Padé Approximants

20 Pages Posted: 4 Mar 2007

See all articles by Guillaume Bagnarosa

Guillaume Bagnarosa

ESC Rennes

Charles J. Corrado

Deakin University - School of Accounting, Economics & Finance

Emmanuel Jurczenko

Glion Institute of Higher Education

Bertrand B. Maillet

EMLyon Business School (Paris Campus)

Multiple version iconThere are 2 versions of this paper

Abstract

The purpose of this paper is to develop a new non-parametric method to price options based on normalized Multipoint Padé Approximants. Following the seminal paper of Padé (1892), we propose to approximate the risk-neutral distribution by a rational function of polynomials that can accommodate the asymmetric and leptokurtic characteristics of the implied state price densities. After recalling the general framework of Padé Approximants we present an analytical formula where we use a power series expansion of the risk-neutral density in order to infer the coefficients of the rational function of polynomials. A suitable alternative to this method will be to use various points of local expansion, resulting from the capability of the Padé to respect such a confluence. By manipulating the base option pricing formula with risk-neutral density (see Cox and Ross, 1976), both of these methods is implicitly satisfying the martingale constraint (see Longstaff, 1995 and Jurczenko, et al., 2006). We then investigate from simulated option prices the shape of the risk-neutral density Padé approximations to compare their radius of convergence.

Keywords: Option Pricing Models, Martingale Restriction, Padé Approximants.

JEL Classification: G.10, G.12, G.13.

Suggested Citation

Bagnarosa, Guillaume and Corrado, Charles J. and Jurczenko, Emmanuel and Maillet, Bertrand B., An Implicit Martingale Restriction in a Closed-Form Higher Order Moments Option Pricing Formula Based on Multipoint Padé Approximants. Available at SSRN: https://ssrn.com/abstract=967755 or http://dx.doi.org/10.2139/ssrn.967755

Guillaume Bagnarosa (Contact Author)

ESC Rennes ( email )

2, RUE ROBERT D'ARBRISSEL
Rennes, 35065
France

Charles J. Corrado

Deakin University - School of Accounting, Economics & Finance ( email )

221 Burwood Highway
Burwood, Victoria 3215
Australia
61492446214 (Phone)

Emmanuel Jurczenko

Glion Institute of Higher Education ( email )

Route de Glion 111
Montreux, 1823
Switzerland

Bertrand B. Maillet

EMLyon Business School (Paris Campus) ( email )

23 Avenue Guy de Collongue
Ecully, 69132
France

Register to save articles to
your library

Register

Paper statistics

Downloads
32
Abstract Views
331
PlumX Metrics