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

Paper:ewp-fin/0110003
From:    
Date: Tue, 23 Oct 2001 11:52:29 -0500

Title: Analytically inducting option cash flows for Markovian interest rate models: A new application paradigm
Author: Junwu Gan
Contact:
Comments: 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.
Keywords: Interest rate models, American options, Early exercise premium, Crtical boundary, Analytical backward induction, Analytic results, New computational approach.
JEL: G13, E4, C5, C6
EWPA-references:
Report-no: Gan_AFT_20011015

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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