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COMPARISON OF NUMERICAL AND ANALYTICAL APPROXIMATIONS OF THE EARLY EXERCISE BOUNDARY OF AMERICAN PUT OPTIONS

Part of: Miscellaneous topics - Partial differential equations Applications

Published online by Cambridge University Press:  21 December 2010

M. LAUKO  and
D. ŠEVČOVIČ
M. LAUKO
Affiliation:
Department of Applied Mathematics & Statistics, Comenius University, 842 48 Bratislava, Slovakia (email: lauko5@st.fmph.uniba.sk, sevcovic@fmph.uniba.sk)
D. ŠEVČOVIČ*
Affiliation:
Department of Applied Mathematics & Statistics, Comenius University, 842 48 Bratislava, Slovakia (email: lauko5@st.fmph.uniba.sk, sevcovic@fmph.uniba.sk)
*
✉For correspondence; e-mail: sevcovic@fmph.uniba.sk
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Abstract

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We present qualitative and quantitative comparisons of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of American put options paying zero dividends. We analyse the asymptotic behaviour of these methods close to expiration, and introduce a new numerical scheme for computing the early exercise boundary. Our local iterative numerical scheme is based on a solution to a nonlinear integral equation. We compare numerical results obtained by the new method to those of the projected successive over-relaxation method and the analytical approximation formula recently derived by Zhu [‘A new analytical approximation formula for the optimal exercise boundary of American put options’, Int. J. Theor. Appl. Finance9 (2006) 1141–1177].

Keywords

option pricingAmerican put optionearly exercise boundarylimiting behaviour close to expiry

MSC classification

Secondary: 35R35: Free boundary problems 62P05: Applications to actuarial sciences and financial mathematics

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 4 , April 2010 , pp. 430 - 448
Copyright
Copyright © Australian Mathematical Society 2010

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