ANALYTIC BACKWARD INDUCTION OF OPTION CASH FLOWS: A NEW APPLICATION PARADIGM FOR THE MARKOVIAN INTEREST RATE MODELS

Junwu Gan ()
Additional contact information
Junwu Gan: Applied Financial Technology, 160 Sansome Street, Suite 1200, San Francisco, CA 94104-3718, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2005, vol. 08, issue 08, 1019-1057

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.

Keywords: Markovian interest rate model; American option; early exercise premium; analytic backward induction; critical boundary (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024905003384
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:08:y:2005:i:08:n:s0219024905003384

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024905003384

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().