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Convergence of Discrete Time Option Pricing Models Under Stochastic Interest Rates

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  • Jean-Philippe Lesne

    (Crest)

  • Jean-Luc Prigent

    (Crest)

  • Olivier Scaillet

    (Crest)

Abstract

We analyze the joint convergence of sequences of discounted stock prices and Radon-Nicodym derivatives of the minimal martingale measure when interest rates are stochastic. Therefrom we deduce the convergence of option values in either complete or incomplete markets. We illustrate the general result by two main examples: a discrete time i.i.d. approximation of a Merton type pricing model for options on stocks and the trinomial tree of Hull and White for interest rate derivatives.
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Suggested Citation

  • Jean-Philippe Lesne & Jean-Luc Prigent & Olivier Scaillet, 1998. "Convergence of Discrete Time Option Pricing Models Under Stochastic Interest Rates," Working Papers 98-51, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:98-51
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    Cited by:

    1. J.L. Prigent & O. Scaillet, 2000. "Weak Convergence of Hedging Strategies of Contingent Claims," THEMA Working Papers 2000-50, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Beliaeva, Natalia & Nawalkha, Sanjay, 2012. "Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 151-163.
    3. Jean-Luc Prigent, 2001. "Option Pricing with a General Marked Point Process," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 50-66, February.
    4. Patrick Jaillet & Ehud I. Ronn & Stathis Tompaidis, 2004. "Valuation of Commodity-Based Swing Options," Management Science, INFORMS, vol. 50(7), pages 909-921, July.
    5. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
    6. Markus Leippold & Zvi Wiener, 2005. "Efficient Calibration of Trinomial Trees for One-Factor Short Rate Models," Review of Derivatives Research, Springer, vol. 7(3), pages 213-239, October.
    7. Prigent, Jean-Luc & Renault, Olivier & Scaillet, Olivier, 2004. "Option pricing with discrete rebalancing," Journal of Empirical Finance, Elsevier, vol. 11(1), pages 133-161, January.
    8. Leitner, Johannes, 2000. "Convergence of Arbitrage-free Discrete Time Markovian Market Models," CoFE Discussion Papers 00/07, University of Konstanz, Center of Finance and Econometrics (CoFE).
    9. H'el`ene Halconruy, 2021. "The insider problem in the trinomial model: a discrete-time jump process approach," Papers 2106.15208, arXiv.org, revised Sep 2023.

    More about this item

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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