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Analytic properties of American option prices under a modified Black-Scholes equation with spatial fractional derivatives

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  • Wenting Chen
  • Kai Du
  • Xinzi Qiu

Abstract

This paper investigates analytic properties of American option prices under the finite moment log-stable (FMLS) model. Under this model the price of American options is characterised by the free boundary problem of a fractional partial differential equation (FPDE) system. Using the technique of approximation we prove that the American put price under the FMLS model is convex with respect the underlying price, and specify the impact of the tail index on option prices.

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  • Wenting Chen & Kai Du & Xinzi Qiu, 2017. "Analytic properties of American option prices under a modified Black-Scholes equation with spatial fractional derivatives," Papers 1701.01515, arXiv.org.
    • Handle: RePEc:arx:papers:1701.01515
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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. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    3. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    4. Xinfu Chen & John Chadam & Lishang Jiang & Weian Zheng, 2008. "Convexity Of The Exercise Boundary Of The American Put Option On A Zero Dividend Asset," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 185-197, January.
    5. S. James Press, 1967. "A Compound Events Model for Security Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 317-317.
    6. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
    7. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
    8. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    9. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    10. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-646.
    11. 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.
    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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