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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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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 98-51.

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Date of creation: 1998
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Handle: RePEc:crs:wpaper:98-51

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Cited by:
  1. Jean-Luc PRIGENT & Olivier SCAILLET, 2002. "Weak Convergence of Hedging Strategies of Contingent Claims," FAME Research Paper Series rp39, International Center for Financial Asset Management and Engineering.
  2. Prigent, J.-L. & Renault, O. & Scaillet, O., 1999. "Option Pricing with Discrete Rebalancing," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1999029, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 00 Oct 1999.
  3. Johannes Leitner, 2000. "Convergence of Arbitrage-free Discrete Time Markovian Market Models," CoFE Discussion Paper 00-07, Center of Finance and Econometrics, University of Konstanz.

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