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Convergence from Discrete to Continuous Time Contingent Claims Prices

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  • Hua He.
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Abstract

This article generalizes the Cox, Ross, and Rubinstein (1979) binomial option-pricing model, and establishes a convergence from discrete-time multivariate multinomial models to continuous-time multidimensional diffusion models for contigent claims prices. The key to the approach is to approximate the N-dimensional diffusion price process by a sequence of N-variate, (N+1)-nomial processes. It is shown that contingent claims prices and dynamic replicating portfolio strategies derived from the discrete time models converge to their corresponding continuous-time limits. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

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Bibliographic Info

Paper provided by University of California at Berkeley in its series Research Program in Finance Working Papers with number RPF-199.

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Date of creation: 01 Jul 1990
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Handle: RePEc:ucb:calbrf:rpf-199

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Cited by:
  1. Buss, Adrian & Uppal, Raman & Vilkov, Grigory, 2014. "Asset prices in general equilibrium with recursive utility and illiquidity induced by transactions costs," SAFE Working Paper Series 41, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
  2. J.W. Nieuwenhuis & M.H. Vellekoop, 2004. "Weak convergence of tree methods, to price options on defaultable assets," Decisions in Economics and Finance, Springer, vol. 27(2), pages 87-107, December.
  3. Wael Bahsoun & Pawel Góra & Silvia Mayoral & Manuel Morales, . "Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den," Faculty Working Papers 13/06, School of Economics and Business Administration, University of Navarra.
  4. Jérôme B. Detemple & Suresh Sundaresan, 1999. "Non-Traded Asset Valuation with Portfolio Constraints: A Binomial Approach," CIRANO Working Papers 99s-08, CIRANO.
  5. Knaut, Andreas & Madlener, Reinhard & Rosen, Christiane & Vogt, Christian, 2012. "Effects of Temperature Uncertainty on the Valuation of Geothermal Projects: A Real Options Approach," FCN Working Papers 11/2012, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
  6. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
  7. Bertsimas, Dimitris & Kogan, Leonid & Lo, Andrew W., 2000. "When is time continuous?," Journal of Financial Economics, Elsevier, vol. 55(2), pages 173-204, February.
  8. Babbs, Simon, 2000. "Binomial valuation of lookback options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1499-1525, October.
  9. Ekvall, Niklas, 1996. "A lattice approach for pricing of multivariate contingent claims," European Journal of Operational Research, Elsevier, vol. 91(2), pages 214-228, June.
  10. Dietmar P.J. Leisen, 1997. "The Random-Time Binomial Model," Finance 9711005, EconWPA, revised 29 Nov 1998.
  11. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
  12. Slade, Margaret E., 2001. "Valuing Managerial Flexibility: An Application of Real-Option Theory to Mining Investments," Journal of Environmental Economics and Management, Elsevier, vol. 41(2), pages 193-233, March.
  13. Jirô Akahori, 2005. "A discrete Itô calculus approach to He’s framework for multi-factor discrete markets," Asia-Pacific Financial Markets, Springer, vol. 12(3), pages 273-287, September.
  14. Cuny, Charles J. & Jorion, Philippe, 1995. "Valuing executive stock options with endogenous departure," Journal of Accounting and Economics, Elsevier, vol. 20(2), pages 193-205, September.
  15. Luenberger, David G., 1998. "Products of trees for investment analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1403-1417, August.
  16. Zakamouline, Valeri I., 2006. "European option pricing and hedging with both fixed and proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 1-25, January.
  17. Damgaard, Anders, 2006. "Computation of reservation prices of options with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 415-444, March.
  18. Garcia, Diego, 2003. "Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1855-1879, August.

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