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Convergence of discrete time option pricing models under stochastic interest rates

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Author Info
O. Scaillet () (Institut d'Administration et de Gestion and Département des Sciences Economiques, Université Catholique de Louvain, 3 Place Montesquieu, B-1348 Louvain-la-Neuve, Belgique Manuscript)
J.-L. Prigent () (THEMA, Université de Cergy-Pontoise, 33 bd du Port, F-95011 Cergy-Pontoise, France)
J.-P. Lesne () (THEMA, Université de Cergy-Pontoise, 33 bd du Port, F-95011 Cergy-Pontoise, France)

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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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Publisher Info
Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 4 (2000)
Issue (Month): 1 ()
Pages: 81-93
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Handle: RePEc:spr:finsto:v:4:y:2000:i:1:p:81-93

Note: received: January 1998; final version received: February 1999 received: January 1998; final version received: February 1999
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Related research
Keywords: Weak convergence; incomplete market; option pricing; minimal martingale measure; stochastic interest rate; trinomial tree;

Other versions of this item:

Find related papers by JEL classification:
D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

Cited by:
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  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. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!]
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