Convergence of Discrete Time Option Pricing Models Under Stochastic Interest Rates
AbstractWe 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 InfoPaper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 98-51.
Date of creation: 1998
Date of revision:
Other versions of this item:
- O. Scaillet & J.-L. Prigent & J.-P. Lesne, 2000. "Convergence of discrete time option pricing models under stochastic interest rates," Finance and Stochastics, Springer, vol. 4(1), pages 81-93.
- 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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- 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.
- 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.
- 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.
- Jean-Luc PRIGENT & Olivier RENAULT & Olivier SCAILLET, 2002. "Option Pricing with Discrete Rebalancing," FAME Research Paper Series rp55, International Center for Financial Asset Management and Engineering.
- Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "Option Pricing with Discrete Rebalancing," Working Papers 99-61, Centre de Recherche en Economie et Statistique.
- J.L. Prigent & O. Renault & O. Scaillet., 1999. "Option pricing with discrete rebalancing," THEMA Working Papers 99-41, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- 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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