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The Minimal Entropy Martingale Measure (MEMM) for a Markov-Modulated Exponential Lévy Model

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Abstract

This paper deals with the characterization problem of the minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model. This model is characterized by the presence of a background process modulating the risky asset price movements between different regimes or market environments. This allows to stress the strong dependence of financial assets price with structural changes in the market conditions. Our main results are obtained from the key idea of working conditionally on the modulator-factor process. This reduces the problem to studying the simpler case of processes with independent increments. Our work generalizes some previous works in the literature dealing with either the exponential Lévy case or the exponential-additive case.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Montreal, CP 6128 succ. Centre-ville, Montreal, QC, H3C 3J7, Canada

    Romuald Hervé Momeya & Zied Ben Salah

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  1. Romuald Hervé Momeya
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  2. Zied Ben Salah
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Correspondence to Romuald Hervé Momeya.

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Momeya, R.H., Salah, Z.B. The Minimal Entropy Martingale Measure (MEMM) for a Markov-Modulated Exponential Lévy Model. Asia-Pac Financ Markets 19, 63–98 (2012). https://doi.org/10.1007/s10690-011-9142-8

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  • DOI: https://doi.org/10.1007/s10690-011-9142-8

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