A Note on Callability of Convertible Bonds

Song-Ping Zhu and Lin Ai
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Song-Ping Zhu: School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia
Lin Ai: School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia

New Mathematics and Natural Computation (NMNC), 2024, vol. 20, issue 03, 621-646

Abstract: The Convertible Bonds (CBs) market has witnessed an unprecedented level of activity over the last few years not only in developed countries such as the United States but also in BRICK countries such as China. Exploring new properties of CBs or CBs with clauses becomes important for academia communities in financial mathematics. In this paper, we build two coupled partial differential equations (PDEs) for pricing a callable CB, and find a newly identified inherent property of this bond. The new property is that the conversion ratio will not affect the critical recall time indicating the time beyond the callability. Besides this property, we also find that solving the critical recall time separately and superimposing later using a non-callable CB is the same as the method of a hybrid free boundary (the critical recall time) and a moving boundary (the optimal conversion price) though the callability and the American-style conversion are nonlinearly coupled.

Keywords: Convertible bond; incomplete Fourier transform; integral equation; conversion ratio (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S1793005724500340

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