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AN ANALYTICAL APPROXIMATION FOR CONVERTIBLE BONDS

Part of: Mathematical finance

Published online by Cambridge University Press:  20 June 2022

JOANNA GOARD Open the ORCID record for JOANNA GOARD [Opens in a new window]
JOANNA GOARD*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW2522, Australia
*
e-mail: joanna@uow.edu.au
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Abstract

This paper looks at adapting the method of Medvedev and Scaillet for pricing short-term American options to evaluate short-term convertible bonds. However unlike their method, we provide explicit formulae for the coefficients of our series solution. This means that we do not need to solve complicated recursive systems, and can efficiently provide fast solutions. We also compare the method with numerical solutions, and find that it performs extremely well, giving accurate bond prices as well as accurate optimal conversion prices.

Keywords

convertible bondsanalytical approximationsoptimal conversion pricefree boundary problems

MSC classification

Primary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 64 , Issue 2 , April 2022 , pp. 135 - 148
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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