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A More Accurate Finite Difference Approximation for the Valuation of Options

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  • Courtadon, Georges

Abstract

Schwartz [3] proposed a model to solve for the value of a warrant or an option when a closed-form solution of the valuation equation cannot be obtained. This model is based on a difference approximation of the valuation equation and uses standard numerical methods. We intend to show here that the same methods can be used to derive a difference approximation of the solution of the valuation equation which has a greater level of accuracy than Schwartz's approximation.

Suggested Citation

  • Courtadon, Georges, 1982. "A More Accurate Finite Difference Approximation for the Valuation of Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(5), pages 697-703, December.
    • Handle: RePEc:cup:jfinqa:v:17:y:1982:i:05:p:697-703_01
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    Cited by:

    1. Zhongdi Cen & Anbo Le & Aimin Xu, 2012. "A Second-Order Difference Scheme for the Penalized Black–Scholes Equation Governing American Put Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 49-62, June.
    2. Yedidya Rabinovitz, 2017. "A new S.D.E. and instantaneous mean reversion rate formula (presented via a numerical empirical model comparison)," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-22, June.
    3. Jonathan A. Batten & Karren Lee-Hwei Khaw & Martin R. Young, 2014. "Convertible Bond Pricing Models," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 775-803, December.
    4. Wen Li & Song Wang, 2014. "A numerical method for pricing European options with proportional transaction costs," Journal of Global Optimization, Springer, vol. 60(1), pages 59-78, September.
    5. Elli Kraizberg, 2023. "Non-fungible tokens: a bubble or the end of an era of intellectual property rights," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-20, December.
    6. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    7. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    8. Riadh Belhaj, 2006. "The Valuation of Options on Bonds with Default Risk," Multinational Finance Journal, Multinational Finance Journal, vol. 10(3-4), pages 277-306, September.
    9. Ben-Ameur, Hatem & de Frutos, Javier & Fakhfakh, Tarek & Diaby, Vacaba, 2013. "Upper and lower bounds for convex value functions of derivative contracts," Economic Modelling, Elsevier, vol. 34(C), pages 69-75.
    10. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    11. Gerald Buetow, Jr. & Joseph Albert, 1998. "The Pricing of Embedded Options in Real Estate Lease Contracts," Journal of Real Estate Research, American Real Estate Society, vol. 15(3), pages 253-266.
    12. Muthuraman, Kumar, 2008. "A moving boundary approach to American option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3520-3537, November.
    13. P. Baecker & G. Grass & U. Hommel, 2010. "Business value and risk in the presence of price controls: an option-based analysis of margin squeeze rules in the telecommunications industry," Annals of Operations Research, Springer, vol. 176(1), pages 311-332, April.
    14. Mojtaba Hajipour & Alaeddin Malek, 2015. "Efficient High-Order Numerical Methods for Pricing of Options," Computational Economics, Springer;Society for Computational Economics, vol. 45(1), pages 31-47, January.
    15. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, December.
    16. Murillas Maza, Arantza, 2000. "Uncertainty and Real Options. Investment and Development of Fishing Resources (II)," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    17. San–Lin Chung & Mark B. Shackleton, 2007. "Generalised Geske‐‐Johnson Interpolation of Option Prices," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 34(5‐6), pages 976-1001, June.
    18. S. Dyrting, 2004. "Pricing equity options everywhere," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 663-676.
    19. Junkee Jeon & Geonwoo Kim, 2022. "Analytic Valuation Formula for American Strangle Option in the Mean-Reversion Environment," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    20. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    21. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    22. Mohammad R. Rahman & Ruppa K. Thulasiram & Parimala Thulasiraman, 2005. "Wavelet Optimized Finite-Difference Approach to Solve Jump-Diffusion type Partial Differential Equation for Option Pricing," Computing in Economics and Finance 2005 471, Society for Computational Economics.
    23. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    24. Burcu Aydoğan & Ümit Aksoy & Ömür Uğur, 2018. "On the methods of pricing American options: case study," Annals of Operations Research, Springer, vol. 260(1), pages 79-94, January.

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