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Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing

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Modeling, Stochastic Control, Optimization, and Applications

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 164))

Abstract

In this chapter, we present recent developments in using the tools of continuous-time Markov chains for the valuation of European and path-dependent financial derivatives. We also survey results on a newly proposed regime switching approximation to stochastic volatility, and stochastic local volatility models. The presented framework is part of an exciting recent stream of literature on numerical option pricing, and offers a new perspective that combines the theory of diffusion processes, Markov chains, and Fourier techniques. It is also elegantly connected to partial differential equation (PDE) approaches.

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Author information

Authors and Affiliations

  1. School of Business, Stevens Institute of Technology, Hoboken, NJ, 07030, USA

    Zhenyu Cui

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30318, USA

    J. Lars Kirkby

  3. Department of Mathematics, Marist College, Poughkeepsie, NY, 12601, USA

    Duy Nguyen

Authors
  1. Zhenyu Cui
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  2. J. Lars Kirkby
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  3. Duy Nguyen
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Corresponding author

Correspondence to Duy Nguyen .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, USA

    George Yin

  2. Department of Mathematics, University of Georgia, Athens, GA, USA

    Qing Zhang

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Cui, Z., Lars Kirkby, J., Nguyen, D. (2019). Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing. In: Yin, G., Zhang, Q. (eds) Modeling, Stochastic Control, Optimization, and Applications. The IMA Volumes in Mathematics and its Applications, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-030-25498-8_6

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