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

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  • Junwu Gan

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.

Suggested Citation

  • Junwu Gan, 2001. "Analytically inducting option cash flows for Markovian interest rate models: A new application paradigm," Finance 0110003, EconWPA.
  • 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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    File URL: http://econwpa.repec.org/eps/fin/papers/0110/0110003.pdf
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    References listed on IDEAS

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    1. 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 637-654, May-June.
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    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 1011-1029, December.
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    More about this item

    Keywords

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

    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; Programming Models; Mathematical and Simulation Modeling

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