Article published by Yann Braouezec and Cyril Grunspan in the European Journal of Operational Research of Elsevier in February 2016. Cyril Grunspan is head of financial engineering departement at ESILV and researcher of Devinci Research Center – Finance Group at Pôle Léonard de Vinci
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.
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