Convergence of Arbitrage-free Discrete Time Markovian Market Models
AbstractWe consider two sequences of Markov chains induc- ing equivalent measures on the discrete path space. We estab- lish conditions under which these two measures converge weakly to measures induced on the Wiener space by weak solutions of two SDEs, which are unique in the sense of probability law. We are going to look at the relation between these two limits and at the convergence and limits of a wide class of bounded function- als of the Markov chains. The limit measures turn out not to be equivalent in general. The results are applied to a sequence of discrete time market models given by anobjective probability measure, describing the stochastic dynamics of the state of the market, and an equivalent martingale measure determining prices of contingent claims. The relation between equivalent martingale measure, state prices, market price of risk and the term structure of interest rates is examined. The results lead to a modification of the Black-Scholes formula and an explanation for the surpris- ing fact that continuous-time arbitrage-free markets are complete under weak technical conditions.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 00-07.
Length: 35 Pages
Date of creation: Feb 2000
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-12-17 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996.
"Towards a General Theory of Bond Markets,"
Working Paper Series in Economics and Finance
143, Stockholm School of Economics.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Hua He., 1991.
"Optimal Consumption-Portfolio Policies: A Convergence from Discrete to Continuous Time Models,"
Research Program in Finance Working Papers
RPF-209, University of California at Berkeley.
- He, Hua, 1991. "Optimal consumption-portfolio policies: A convergence from discrete to continuous time models," Journal of Economic Theory, Elsevier, vol. 55(2), pages 340-363, December.
- Jean-Philippe Lesne & Jean-Luc Prigent & Olivier Scaillet, 1998.
"Convergence of Discrete Time Option Pricing Models Under Stochastic Interest Rates,"
98-51, Centre de Recherche en Economie et Statistique.
- 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.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- Nigel J. Cutland & Ekkehard Kopp & Walter Willinger, 1993. "From Discrete to Continuous Financial Models: New Convergence Results For Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 101-123.
- Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
- Tomas BjÃrk & Andrea Gombani, 1999. "Minimal realizations of interest rate models," Finance and Stochastics, Springer, vol. 3(4), pages 413-432.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ingmar Nolte) The email address of this maintainer does not seem to be valid anymore. Please ask Ingmar Nolte to update the entry or send us the correct address.
If references are entirely missing, you can add them using this form.