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Volterra equation for pricing and hedging in a regime switching market

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  • Anindya Goswami
  • Ravi Kant Saini

Abstract

It is known that the risk minimizing price of European options in Markov-modulated market satisfies a system of coupled PDE, known as generalized B-S-M PDE. In this paper, another system of equations, which can be categorized as a Volterra integral equations of second kind, are considered. It is shown that this system of integral equations has smooth solution and the solution solves the generalized B-S-M PDE. Apart from showing existence and uniqueness of the PDE, this IE representation helps to develop a new computational method. It enables to compute the European option price and corresponding optimal hedging strategy by using quadrature method.

Suggested Citation

  • Anindya Goswami & Ravi Kant Saini, 2014. "Volterra equation for pricing and hedging in a regime switching market," Cogent Economics & Finance, Taylor & Francis Journals, vol. 2(1), pages 1-11, December.
    • Handle: RePEc:taf:oaefxx:doi:10.1080/23322039.2014.939769
    DOI: 10.1080/23322039.2014.939769
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    1. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    2. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413, October.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Anindya Goswami & Kedar Nath Mukherjee & Irvine Homi Patalwala & Sanjay N. S, 2022. "Regime recovery using implied volatility in Markov modulated market model," Papers 2201.10304, arXiv.org, revised Mar 2022.
    2. Milan Kumar Das & Anindya Goswami & Tanmay S. Patankar, 2016. "Pricing Derivatives in a Regime Switching Market with Time Inhomogeneous Volatility," Papers 1611.02026, arXiv.org.

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