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An American convert close to maturity

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Author(s): G. Alobaidi | R. Mallier

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXVIII;
Issue: 1;
Start page: 87;
Date: 2009;
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Keywords: convertible securities | asymptotics | free boundary

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.
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