A New Elementary Geometric Approach to Option Pricing Bounds in Discrete Time Models
33 Pages Posted: 4 May 2013 Last revised: 19 Jan 2015
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: Suggested Citation