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Analytically inducting option cash flows for Markovian interest rate models: A new application paradigm

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Author Info
Junwu Gan

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Abstract

This paper develops a new computational approach for general multi- factor Markovian interest rate models. The early exercise premium is derived for general American options. The option cash flows are decomposed into fast and slowly varying components. The fast components are option independent and derived analytically. The slow components are calculated by controlled expansion for finite time intervals. The option price is obtained by iterating the analytic expressions of one time interval. For one-factor models, the critical boundary for American options has a universal form near maturity. For American put stock options, analytic expressions are derived to approximate the critical boundary. The put price calculated from the boundary has relative precision better than $10^{-5}$ in all cases.

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File URL: http://129.3.20.41/eps/fin/papers/0110/0110003.pdf
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Publisher Info
Paper provided by EconWPA in its series Finance with number 0110003.

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Length: 38 pages
Date of creation: 23 Oct 2001
Date of revision:
Handle: RePEc:wpa:wuwpfi:0110003

Note: Type of Document - Tex; prepared on IBM PC - BcTex; to print on Any printer; pages: 38; figures: included. There is a C++ program available upon request which calculates American put stock price from analytic expressions for the critical boundary with precision that is only matched by CRR binomial tree with over 100K time steps.
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Web page: http://129.3.20.41

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Related research
Keywords: Interest rate models; American options; Early exercise premium; Crtical boundary; Analytical backward induction; Analytic results; New computational approach.;

Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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.:
  1. 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. [Downloadable!] (restricted)
  2. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September. [Downloadable!] (restricted)
  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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