A new elementary geometric approach to option pricing bounds in discrete time models

Yann Braouezec and Cyril Grunspan

European Journal of Operational Research, 2016, vol. 249, issue 1, 270-280

Abstract: The aim of this paper is to provide a new straightforward measure-free methodology based on 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 asset framework.

Keywords: Finance; Incomplete markets; Option pricing bounds; Convex hulls; Barycentric coordinates (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:249:y:2016:i:1:p:270-280

DOI: 10.1016/j.ejor.2015.08.024

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