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A computational weighted finite difference method for American and barrier options in subdiffusive Black-Scholes model

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  • Grzegorz Krzy.zanowski
  • Marcin Magdziarz

Abstract

Subdiffusion is a well established phenomenon in physics. In this paper we apply the subdiffusive dynamics to analyze financial markets. We focus on the financial aspect of time fractional diffusion model with moving boundary i.e. American and barrier option pricing in the subdiffusive Black-Scholes (B-S) model. Two computational methods for valuing American options in the considered model are proposed - the weighted finite difference (FD) and the Longstaff-Schwartz method. In the article it is also shown how to valuate numerically wide range of barrier options using the FD approach.

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  • Grzegorz Krzy.zanowski & Marcin Magdziarz, 2020. "A computational weighted finite difference method for American and barrier options in subdiffusive Black-Scholes model," Papers 2003.05358, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:2003.05358
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    3. Bernd Engelmann & Matthias Fengler & Morten Nalholm & Peter Schwendner, 2006. "Static versus dynamic hedges: an empirical comparison for barrier options," Review of Derivatives Research, Springer, vol. 9(3), pages 239-264, November.
    4. Grzegorz Krzy.zanowski & Marcin Magdziarz & {L}ukasz P{l}ociniczak, 2019. "A weighted finite difference method for subdiffusive Black Scholes Model," Papers 1907.00297, arXiv.org, revised Apr 2020.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. Aleksander Janicki & Aleksander Weron, 1994. "Can One See Alpha-stable Variables and Processes?," HSC Research Reports HSC/94/01, Hugo Steinhaus Center, Wroclaw University of Technology.
    7. Brockman, Paul & Turtle, H. J., 2003. "A barrier option framework for corporate security valuation," Journal of Financial Economics, Elsevier, vol. 67(3), pages 511-529, March.
    8. Eugene F. Fama, 1968. "Risk, Return And Equilibrium: Some Clarifying Comments," Journal of Finance, American Finance Association, vol. 23(1), pages 29-40, March.
    9. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    10. Longstaff, Francis A. & Santa-Clara, Pedro & Schwartz, Eduardo S., 2001. "Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaptions market," Journal of Financial Economics, Elsevier, vol. 62(1), pages 39-66, October.
    11. Marcin Magdziarz & Janusz Gajda, 2012. "Anomalous dynamics of Black–Scholes model time-changed by inverse subordinators," HSC Research Reports HSC/12/04, Hugo Steinhaus Center, Wroclaw University of Technology.
    12. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Cited by:

    1. Grzegorz Krzy.zanowski & Andr'es Sosa, 2020. "Performance analysis of Zero Black-Derman-Toy interest rate model in catastrophic events: COVID-19 case study," Papers 2007.00705, arXiv.org, revised Jul 2020.

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