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Valuing Derivative Securities Using the Explicit Finite Difference Method

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Author Info
Hull, John
White, Alan

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Abstract

This paper suggests a modification to the explicit finite difference method for valuing derivative securities. The modification ensures that, as smaller time intervals are considered, the calculated values of the derivative security converge to the solution of the underlying differential equation. It can be used to value any derivative security dependent on a single state variable and can be extended to deal with many derivative security pricing problems where there are several state variables. The paper illustrates the approach by using it to value bonds and bond options under two different interest rate processes.

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File URL: http://journals.cambridge.org/abstract_S002210900000702X
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Publisher Info
Article provided by Cambridge University Press in its journal Journal of Financial and Quantitative Analysis.

Volume (Year): 25 (1990)
Issue (Month): 01 (March)
Pages: 87-100
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:jfinqa:v:25:y:1990:i:01:p:87-100_00

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  1. Dennis Kristensen & Antonio Mele, 2009. "Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous Time Models," CREATES Research Papers 2009-14, School of Economics and Management, University of Aarhus. [Downloadable!]
  2. Arantza Murillas, 2000. "Uncertainty and Real Options. Investment and Development of Fishing Resources (II)," BILTOKI 200002, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística). [Downloadable!]
  3. Anlong Li, 1992. "Binomial approximation in financial models: computational simplicity and convergence," Working Paper 9201, Federal Reserve Bank of Cleveland. [Downloadable!]
  4. Klaassen, Pieter, 1997. "Solving stochastic programming models for asset/liability management using iterative disaggregation," Serie Research Memoranda 0010, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  5. Simona Sanfelici, 2004. "Galerkin infinite element approximation for pricing barrier options and options with discontinuous payoff," Decisions in Economics and Finance, Springer, vol. 27(2), pages 125-151, December. [Downloadable!] (restricted)
  6. Pavel Cizek & Karel Komorad, 2005. "Implied Trinomial Trees," SFB 649 Discussion Papers SFB649DP2005-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  7. Maza, Arantza Murillas, 2004. "Common Property Under Management Flexibility: Valuation, Optimal Exploitation, And Regulation," Marine Resource Economics, Marine Resources Foundation, vol. 19(2). [Downloadable!]
  8. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," Serie Research Memoranda 0011, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  9. Yuji Yamada & James Primbs, 2004. "Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging," Asia-Pacific Financial Markets, Springer, vol. 11(3), pages 335-365, September. [Downloadable!] (restricted)
  10. Hatem Ben-Ameur & Michèle Breton, 2004. "A Dynamic Programming Approach for Pricing Options Embedded in Bonds," Computing in Economics and Finance 2004 237, Society for Computational Economics. [Downloadable!]
  11. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO. [Downloadable!]
  12. K. Ben Nowman & Ghulam Sorwar, 2003. "Implied option prices from the continuous time CKLS interest rate model: an application to the UK," Applied Financial Economics, Taylor and Francis Journals, vol. 13(3), pages 191-197, January. [Downloadable!] (restricted)
  13. Timothy Riddiough & Paul Childs & Steven Ott, 2001. "Noise, Real Estate Markets, and Options on Real Assets: Applications," Wisconsin-Madison CULER working papers 01-06, University of Wisconsin Center for Urban Land Economic Research. [Downloadable!]
  14. Nikolaus Hautsch & Yangguoyi Ou, 2008. "Yield Curve Factors, Term Structure Volatility, and Bond Risk Premia," SFB 649 Discussion Papers SFB649DP2008-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  15. 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. [Downloadable!]
  16. Phelim P. Boyle, Yisong (Sam) Tian, 1998. "An explicit finite difference approach to the pricing of barrier options," Applied Mathematical Finance, Taylor and Francis Journals, vol. 5(1), pages 17-43, March. [Downloadable!] (restricted)
  17. Christopher F. Baum & Olin Liu, 1994. "An Alternative Strategy for Estimation of a Nonlinear Model of the Term Structure of Interest Rates," Boston College Working Papers in Economics 275., Boston College Department of Economics. [Downloadable!]
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