A TWO-FACTOR JUMP-DIFFUSION MODEL FOR PRICING CONVERTIBLE BONDS WITH DEFAULT RISK

Radha Krishn Coonjobeharry (), Désiré Yannick Tangman () and Muddun Bhuruth
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Radha Krishn Coonjobeharry: University of Mauritius, Réduit, Mauritius
Désiré Yannick Tangman: University of Mauritius, Réduit, Mauritius
Muddun Bhuruth: University of Mauritius, Réduit, Mauritius

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 06, 1-26

Abstract: The current literature on convertible bonds (CBs) comprises only models where the stock price and the interest rate are governed by pure-diffusion processes. This paper fills a gap by developing and implementing a two-factor model where both underlying factors follow jump-diffusion processes, and which also incorporates default risk. We derive the partial integro-differential equation satisfied by the CB price in our model, and solve it by a spectral method based on Chebyshev discretizations and Clenshaw–Curtis quadratures. The conversion, call, and put constraints give rise to a linear complementarity problem, which is solved by an operator-splitting (OS) method. Through numerical experiments, we investigate the effects that the various parameters have on the CB price. In particular, our numerical experiments show that jumps in the stock price have a significant impact on the CB price, while jumps in the interest rate tend to have a minor effect on the price. In general, the dynamics of the stock price have more impact in pricing the CB than the dynamics of the interest rate.

Keywords: Convertible bonds; jump-diffusion models; Chebyshev spectral method; Clenshaw–Curtis quadrature; linear complementarity problem; operator-splitting method (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0219024916500461

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