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Analytic Backward Induction Of Option Cash Flows: A New Application Paradigm For The Markovian Interest Rate Models

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  • JUNWU GAN

    (Applied Financial Technology, 160 Sansome Street, Suite 1200, San Francisco, CA 94104-3718, USA)

Abstract

This paper develops a unified formulation and a new computational methodology for the entire class of the multi-factor Markovian interest rate models. The early exercise premium representation for general American options is derived for all Markovian models. The option cash flow functions are decomposed into fast and slowly varying components. The fast varying components have the same expression for all options within a model. They are calculated analytically. Only the slowly varying components are option specific. Their backward induction for a finite time interval is carried out from Taylor expansion expressions. The small coefficient of the expansion is the product of the variance and the width of the time interval. The option price is calculated by dividing its time horizon into smaller intervals and numerically iterating the Taylor expansion expressions of one time interval. Other new results include: (i) The derivation of a new "almost" Markovian LIBOR market model and its related Markovian short-rate model; (ii) the universal form of the critical boundary near the maturity for the American options in the one-factor Markovian models; and (iii) approximate analytic expressions for the entire critical boundary of the American put stock option. The put price calculated from the boundary has relative precision better than 10-5.

Suggested Citation

  • Junwu Gan, 2005. "Analytic Backward Induction Of Option Cash Flows: A New Application Paradigm For The Markovian Interest Rate Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1019-1057.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:08:n:s0219024905003384
    DOI: 10.1142/S0219024905003384
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    References listed on IDEAS

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    Cited by:

    1. Junwu Gan, 2014. "An almost Markovian LIBOR market model calibrated to caps and swaptions," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1937-1959, November.

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