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Nonlinear Financial Models: Finite Markov Modulation And Its Limits

In: Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume III)

Author

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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)

Abstract

We 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.

Suggested Citation

  • Mogens Bladt & Pablo Padilla, 2002. "Nonlinear Financial Models: Finite Markov Modulation And Its Limits," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume III), chapter 7, pages 159-171, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812778451_0007
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    Keywords

    Quantitative Analysis; Financial Markets;

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