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EXAMPLES OF FINANCIAL MARKET MODELS OBTAINED BY EULER DISCRETIZATION OF CONTINUOUS MODELS

We present a methodology to study discrete time financial models with one risky asset and a risk free asset that may thought to result as a discretization of a suitable continuous time model. In a numerical example we compare the pricing results, obtained with these models, with results obtained from the related continuous time models. Our approach relies on some known important results describing a particular class of discrete time models – the conditionally Gaussian models – a class that, regardless of its particular definition, contains many interesting instances. We aim at a better understanding of the implications of the discretization procedures which are inevitable, both at the parameter estimation and derivative price computation moments, by reason of the observational and computational limitations. We also present a preliminary study of a a model of stochastic differential equations for commodity spot and futures prices that may be studied with the proposed methodology. For that purpose we summarize a naive theory of Ito integration in Hilbert space. The first author dedicates this work to Hans Föllmer to whom he owes warm encouragement in the beginning of his career and the most important initiatives that launched Financial Mathematics studies in Portugal.