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A Numerical Method for Discrete Single Barrier Option Pricing with Time-Dependent Parameters

Author

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  • Rahman Farnoosh

    (Iran University of Science and Technology)

  • Hamidreza Rezazadeh

    (Iran University of Science and Technology)

  • Amirhossein Sobhani

    (Iran University of Science and Technology)

  • M. Hossein Beheshti

    (Islamic Azad university)

Abstract

In this article, the researchers obtained a recursive formula for the price of discrete single barrier option based on the Black–Scholes framework in which drift, dividend yield and volatility assumed as deterministic functions of time. With some general transformations, the partial differential equations (PDEs) corresponding to option value problem, in each monitoring time interval, were converted into well-known Black–Scholes PDE with constant coefficients. Finally, an innovative numerical approach was proposed to utilize the obtained recursive formula efficiently. Despite some claims, it has considerably low computational cost and could be competitive with the other introduced method. In addition, one advantage of this method, is that the Greeks of the contracts were also calculated.

Suggested Citation

  • Rahman Farnoosh & Hamidreza Rezazadeh & Amirhossein Sobhani & M. Hossein Beheshti, 2016. "A Numerical Method for Discrete Single Barrier Option Pricing with Time-Dependent Parameters," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 131-145, June.
    • Handle: RePEc:kap:compec:v:48:y:2016:i:1:d:10.1007_s10614-015-9506-7
    DOI: 10.1007/s10614-015-9506-7
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    References listed on IDEAS

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    1. C. F. Lo & H. C. Lee & C. H. Hui, 2003. "A simple approach for pricing barrier options with time-dependent parameters," Quantitative Finance, Taylor & Francis Journals, vol. 3(2), pages 98-107.
    2. Jin-Chuan Duan & Evan Dudley & Geneviève Gauthier & Jean-Guy Simonato, 1999. "Pricing Discretely Monitored Barrier Options by a Markov Chain," CIRANO Working Papers 99s-15, CIRANO.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Gianluca Fusai & I. Abrahams & Carlo Sgarra, 2006. "An exact analytical solution for discrete barrier options," Finance and Stochastics, Springer, vol. 10(1), pages 1-26, January.
    5. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
    6. Fusai, Gianluca & Recchioni, Maria Cristina, 2007. "Analysis of quadrature methods for pricing discrete barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 826-860, March.
    7. R. C. Heynen & H. M. Kat, 1995. "Lookback options with discrete and partial monitoring of the underlying price," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(4), pages 273-284.
    8. Antoon Pelsser, 2000. "Pricing double barrier options using Laplace transforms," Finance and Stochastics, Springer, vol. 4(1), pages 95-104.
    9. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double‐Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378, October.
    10. 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.
    11. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
    12. Phelim Boyle & Yisong Tian, 1998. "An explicit finite difference approach to the pricing of barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 17-43.
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    Cited by:

    1. Sangkwon Kim & Jisang Lyu & Wonjin Lee & Eunchae Park & Hanbyeol Jang & Chaeyoung Lee & Junseok Kim, 2024. "A Practical Monte Carlo Method for Pricing Equity-Linked Securities with Time-Dependent Volatility and Interest Rate," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 2069-2086, May.
    2. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    3. Chaeyoung Lee & Soobin Kwak & Youngjin Hwang & Junseok Kim, 2023. "Accurate and Efficient Finite Difference Method for the Black–Scholes Model with No Far-Field Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1207-1224, March.
    4. Saadet Eskiizmirliler & Korhan Günel & Refet Polat, 2021. "On the Solution of the Black–Scholes Equation Using Feed-Forward Neural Networks," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 915-941, October.
    5. Ahmad Golbabai & Omid Nikan, 2020. "A Computational Method Based on the Moving Least-Squares Approach for Pricing Double Barrier Options in a Time-Fractional Black–Scholes Model," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 119-141, January.
    6. Zhang, Xiaoyuan & Zhang, Tianqi, 2022. "Barrier option pricing under a Markov Regime switching diffusion model," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 273-280.
    7. Meihui Zhang & Xiangcheng Zheng, 2023. "Numerical Approximation to a Variable-Order Time-Fractional Black–Scholes Model with Applications in Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1155-1175, October.
    8. Darae Jeong & Minhyun Yoo & Junseok Kim, 2018. "Finite Difference Method for the Black–Scholes Equation Without Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 51(4), pages 961-972, April.

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