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A Two-Factor Jump-Diffusion Model For Pricing Convertible Bonds With Default Risk

Author

Listed:
  • RADHA KRISHN COONJOBEHARRY

    (University of Mauritius, Réduit, Mauritius)

  • DÉSIRÉ YANNICK TANGMAN

    (University of Mauritius, Réduit, Mauritius)

  • MUDDUN BHURUTH

    (University of Mauritius, Réduit, Mauritius)

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.

Suggested Citation

  • Radha Krishn Coonjobeharry & Désiré Yannick Tangman & Muddun Bhuruth, 2016. "A Two-Factor Jump-Diffusion Model For Pricing Convertible Bonds With Default Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-26, September.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:06:n:s0219024916500461
    DOI: 10.1142/S0219024916500461
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    References listed on IDEAS

    as
    1. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
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    3. Beliaeva, Natalia & Nawalkha, Sanjay, 2012. "Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 151-163.
    4. Laura Ballotta & Ioannis Kyriakou, 2015. "Convertible bond valuation in a jump diffusion setting with stochastic interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 115-129, January.
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    7. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2008. "Simulation-based pricing of convertible bonds," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 310-331, March.
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    9. Barone-Adesi, Giovanni & Bermudez, Ana & Hatgioannides, John, 2003. "Two-factor convertible bonds valuation using the method of characteristics/finite elements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1801-1831, August.
    10. Ali Bora Yiǧitbaşioǧlu & Carol Alexander, 2006. "Pricing And Hedging Convertible Bonds: Delayed Calls And Uncertain Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 415-453.
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