Department of
Applied
Mathematics

Valuation of Derivatives using Binomial Trees with Infinitesimals

Jiøí Witzany

Abstract

Financial Derivatives that have gained an extreme importance on international financial markets are usually valued using the stochastic calculus. The main notions of the calculus can be quite easily explained in a discrete set-up using the binary (binomial) trees but full scale results are obtained in the advanced theory of continuous time stochastic processes. So called nonstandard analysis allows to use infinitesimal time steps and so the continuous time results can be correctly obtained using the intuitive discrete arguments. I will indicate how to construct so called equivalent martingale measure that is a key tool for valuation of many complex derivatives. A real life example will be given.