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Simple Binomial Processes as Diffusion Approximations in Financial Models

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Author Info
Nelson, Daniel B
Ramaswamy, Krishna
Abstract

A binomial approximation to a diffusion is defined as " computationally simple" if the number of nodes grows at most linearly in the number of time intervals. It is shown how to construct computationally simple binomial processes that converge weakly to commonly employed diffusions in financial models. The convergence of the sequence of bond and European option prices from these processes to the corresponding values in the diffusion limit is also demonstrated. Numerical examples from the constant elasticity of variance stock price and the Cox, Ingersoll, and Ross (1985) discount bond price are provided. 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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Article provided by Oxford University Press for Society for Financial Studies in its journal Review of Financial Studies.

Volume (Year): 3 (1990)
Issue (Month): 3 ()
Pages: 393-430
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Handle: RePEc:oup:rfinst:v:3:y:1990:i:3:p:393-430

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  1. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  2. Leisen, D. P. J. & M. Reimer, 1995. "Binomial Models for Option Valuation - Examining and Improving Convergence," Discussion Paper Serie B 309, University of Bonn, Germany. [Downloadable!]
  3. Dietmar P.J. Leisen, 1997. "The Random-Time Binomial Model," Finance 9711005, EconWPA, revised 29 Nov 1998. [Downloadable!]
  4. Massimo Costabile, 2006. "On pricing lookback options under the CEV process," Decisions in Economics and Finance, Springer, vol. 29(2), pages 139-153, November. [Downloadable!] (restricted)
  5. Anlong Li, 1992. "Binomial approximation in financial models: computational simplicity and convergence," Working Paper 9201, Federal Reserve Bank of Cleveland. [Downloadable!]
  6. Ariste Ruolz & Pierre Lasserre, 2001. "La gestion optimale d'une forêt exploitée pour son potentiel de diminution des gaz à effet de serre et son bois," Cahiers de recherche du Département des sciences économiques, UQAM 20-03, Université du Québec à Montréal, Département des sciences économiques. [Downloadable!]
  7. Nobuhiro Nakamura, 2004. "Numerical Approach to Asset Pricing Models with Stochastic Differential Utility," Asia-Pacific Financial Markets, Springer, vol. 11(3), pages 267-300, September. [Downloadable!] (restricted)
  8. Damiano Brigo, 2008. "The general mixture-diffusion SDE and its relationship with an uncertain-volatility option model with volatility-asset decorrelation," Quantitative Finance Papers 0812.4052, arXiv.org. [Downloadable!]
  9. Akihiko Takahashi & Takao Kobayashi & Naruhisa Nakagawa, 2001. "Pricing Convertible Bonds with Default Risk: A Duffie-Singleton Approach," CIRJE F-Series CIRJE-F-140, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  10. Massimo Costabile & Arturo Leccadito & Ivar Massabó, 2009. "Computationally simple lattice methods for option and bond pricing," Decisions in Economics and Finance, Springer, vol. 32(2), pages 161-181, November. [Downloadable!] (restricted)
  11. Mark Broadie & Jérôme B. Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO. [Downloadable!]
  12. Dietmar Leisen, 2004. "Mixed Lognormal Distributions for Derivatives Pricing and Risk-Management," Computing in Economics and Finance 2004 48, Society for Computational Economics. [Downloadable!]
  13. Acharya, Viral V & Carpenter, Jennifer, 2002. "Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy," CEPR Discussion Papers 3328, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  14. Jerzy Filar & Boda Kang & Malgorzata Korolkiewicz, 2008. "Pricing Financial Derivatives on Weather Sensitive Assets," Research Paper Series 223, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  15. Marat Kramin & Timur Kramin & Stephen Young & Venkat Dharan, 2005. "A Simple Induction Approach and an Efficient Trinomial Lattice for Multi-State Variable Interest Rate Derivatives Models," Review of Quantitative Finance and Accounting, Springer, vol. 24(2), pages 199-226, January. [Downloadable!] (restricted)
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