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A Note on Callability of Convertible Bonds

Author

Listed:
  • 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)

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.

Suggested Citation

  • Song-Ping Zhu & Lin Ai, 2024. "A Note on Callability of Convertible Bonds," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 621-646, November.
    • Handle: RePEc:wsi:nmncxx:v:20:y:2024:i:03:n:s1793005724500340
    DOI: 10.1142/S1793005724500340
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