A New Elementary Geometric Approach to Option Pricing Bounds in Discrete Time Models

33 Pages Posted: 4 May 2013 Last revised: 19 Jan 2015

See all articles by Yann Braouezec

Yann Braouezec

IESEG School of Management, LEM CNRS, UMR 9221

Cyril Grunspan

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV)

Date Written: January 19, 2015

Abstract

The aim of this paper is to provide a new straightforward \textit{measure-free} methodology based on a convex hulls to determine the no-arbitrage pricing bounds of an option (European or American). The pedagogical interest of our methodology is also briefly discussed. The central result, which is elementary, is presented for a one period model and is subsequently used for multiperiod models. It shows that a certain point, called the forward point, must lie inside a convex polygon. Multiperiod models are then considered and the pricing bounds of a put option (European and American) are explicitly computed. We then show that the barycentric coordinates of the forward point can be interpreted as a martingale pricing measure. An application is provided for the trinomial model where the pricing measure has a simple geometric interpretation in terms of areas of triangles. Finally, we consider the case of entropic barycentric coordinates in a multi assets framework.

Keywords: Incomplete markets, option pricing bounds, convex hulls, barycentric coordinates

JEL Classification: G13, C65

Suggested Citation

Braouezec, Yann and Grunspan, Cyril, A New Elementary Geometric Approach to Option Pricing Bounds in Discrete Time Models (January 19, 2015). Available at SSRN: https://ssrn.com/abstract=2259738 or http://dx.doi.org/10.2139/ssrn.2259738

Yann Braouezec (Contact Author)

IESEG School of Management, LEM CNRS, UMR 9221 ( email )

1, parvis de la Défense
Paris-La Défense cedex, 92044
France

Cyril Grunspan

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV) ( email )

92916 Paris La Defense Cedex
France

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