Pricing Derivatives on Multiple Assets: Recombining Multinomial Trees based on the Pascal Simplex
Bernard Hanzon, University College Cork, Ireland
The binomial tree model is well-known in financial mathematics both as an easy-to-explain example model for the behaviour of an asset price, as well as a computational tool to compute (approximate) option prices based on a single asset. Here we present a direct generalization to the case of multiple assets based on the Pascal simplex. The resulting model describes a (so-called) complete financial market and can be used to compute (approximate) European and American option prices, based on a basket of asset prices. The goal of the presentation is to explain the basic construction of these trees and their usage in option pricing. Further details and properties can be found in the paper . Some further possible developments and applications will be mentioned.
 Dirk SIERAG, Bernard HANZON, "Pricing derivatives on multiple assets: recombining multinomial trees based on Pascal's simplex", Annals of Operations Research, July 2018, issue 1-2, pp.101-127.
 Bernard HANZON, Ralf PEETERS, " Balanced parametrizations of stable SISO all-pass systems in discrete time", Mathematics of Control, Signals and Systems, September 2000, vol. 13, issue 3, pp. 240--276.
Bernard Hanzon is professor of Mathematics and Head of Department of Mathematics at University College Cork (UCC). His Chair in Mathematics at UCC was once held by George Boole, who was the first professor of Mathematics at UCC from 1849--1864. Bernard Hanzon studied Econometrics and Mathematics at various universities in Holland and got his PhD from Erasmus University Rotterdam. He was lecturer in Mathematical Systems Theory at the Technical University Delft and Senior Lecturer/Associate Professor in Mathematical Economics and Econometrics at the Vrije Universiteit Amsterdam before moving to Cork, Ireland in 2004. There he was Associate Professor in Financial Mathematics until 2010 and holds his present position since 2011. He was co-director of the Edgeworth Centre for Financial Mathematics at UCC. His main interests are in mathematical systems theory, financial mathematics, financial econometric methods and mathematics and its applications in general.