NONLINEAR FINANCIAL MODELS: FINITE MARKOV MODULATION AND ITS LIMITS

Mogens Bladt and Pablo Padilla
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Mogens Bladt: IIMAS–UNAM, Department of Statistics, A.P. 20–726, 01000 México, D.F. México
Pablo Padilla: IIMAS–UNAM, Department of Mathematics and Mechanics, A.P. 20–726, 01000 México, D.F. México

Chapter 7 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume III), 2002, pp 159-171 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe study a Markov modulation of the classical Black–Scholes model. We prove that, for European type of securities, a model which has any kind of pay-off distribution may be approximated arbitrarily well using Markov modulation. In the limit we obtain a model of Black–Scholes type where the parameters in the model depend on an underlying environment which is governed by a diffusion process. The price in the special two-state case which is of interest itself is derived explicitly.

Keywords: Quantitative Analysis; Financial Markets (search for similar items in EconPapers)
Date: 2002
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