p. 87 - 96 An American convert close to maturity G. Alobaidi and R. Mallier Received: December 21, 2007; Accepted: August 22, 2008 Abstract. We use an asymptotic expansion to study the behavior of an American convertible bond close to maturity, under the assumptions that the underlying stock price obeys a lognormal random walk and the risk-free rate is given by either the Vasicek model or the Cox-Ingersoll-Ross model. Series solutions are obtained for the location of the free boundary and the price of the bond in that limit. Keywords: convertible securities; asymptotics; free boundary AMS Subject classification: Primary: 91B28; PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |