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A General Derivation of the Jump Process Option Pricing Formula

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  • Page, Frank H.
  • Sanders, Anthony B.

Abstract

The following paper presents a general derivation of the jump process option pricing formula. In particular, a general jump process formula is derived via an analysis of the limiting behavior of the binomial option pricing formula. In deriving the formula, a very simple central limit theorem known as Poisson's Limit Theorem is applied. The simplicity of the analysis allows the establishment of precisely the connections between the specification of the underlying binomial stock return process and the specific form of the corresponding continuous-time jump process formula. Several examples are provided to illustrate these connections.

Suggested Citation

  • Page, Frank H. & Sanders, Anthony B., 1986. "A General Derivation of the Jump Process Option Pricing Formula," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(4), pages 437-446, December.
  • Handle: RePEc:cup:jfinqa:v:21:y:1986:i:04:p:437-446_01
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    Cited by:

    1. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    2. Benjamín Vallejo Jiménez & Francisco Venegas Martínez, 2017. "Optimal consumption and portfolio rules when the asset price is driven by a time-inhomogeneous Markov modulated fractional Brownian motion with," Economics Bulletin, AccessEcon, vol. 37(1), pages 314-326.
    3. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Tendencias y perspectivas de la ciencia financiera: Un artículo de revisión," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-15, Enero - M.
    4. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Financial Science Trends and Perspectives: A Review Article," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-15, Enero - M.
    5. 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.

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