article

Yann Braouezec and Cyril Grunspan


Finance Group (2016) : Option Pricing Bounds in a Finite Market Model: A Simple Geometric Approach Using Barycentric Coordinates




Option Pricing Bounds in a Finite Market Model: A Simple Geometric Approach Using Barycentric Coordinates

Yann Braouezec and Cyril Grunspan




article

European Journal of Operational Research

The aim of this paper is to provide a new straightforward textitmeasure-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.

To cite this publication :


Yann Braouezec, Cyril Grunspan: Option Pricing Bounds in a Finite Market Model: A Simple Geometric Approach Using Barycentric Coordinates. Dans: European Journal of Operational Research, 249 (1), p. 270–280, 2016, ISSN: 0377-2217.





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