IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v19y2016i06ns0219024916500461.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024916500461
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024916500461?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    2. 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.
    3. 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.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. 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.
    7. 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.
    8. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    9. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    10. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Njike Leunga, Charles Guy & Hainaut, Donatien, 2019. "Interbank Credit Risk Modelling with Self-Exciting Jump Processes," LIDAM Discussion Papers ISBA 2019017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lin, Shih-Kuei & Wang, Shin-Yun & Chen, Carl R. & Xu, Lian-Wen, 2017. "Pricing Range Accrual Interest Rate Swap employing LIBOR market models with jump risks," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 359-373.
    2. Moreno, Manuel & Serrano, Pedro & Stute, Winfried, 2011. "Statistical properties and economic implications of jump-diffusion processes with shot-noise effects," European Journal of Operational Research, Elsevier, vol. 214(3), pages 656-664, November.
    3. Dotsis, George & Psychoyios, Dimitris & Skiadopoulos, George, 2007. "An empirical comparison of continuous-time models of implied volatility indices," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3584-3603, December.
    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.
    5. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    6. Jin-Yu Zhang & Wen-Bo Wu & Yong Li & Zhu-Sheng Lou, 2021. "Pricing Exotic Option Under Jump-Diffusion Models by the Quadrature Method," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 867-884, October.
    7. DiCesare, Joe & Mcleish, Don, 2008. "Simulation of jump diffusions and the pricing of options," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 316-326, December.
    8. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous‐Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    9. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    10. R. Merino & J. Pospíšil & T. Sobotka & J. Vives, 2018. "Decomposition Formula For Jump Diffusion Models," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-36, December.
    11. Raul Merino & Jan Posp'iv{s}il & Tom'av{s} Sobotka & Josep Vives, 2019. "Decomposition formula for jump diffusion models," Papers 1906.06930, arXiv.org.
    12. Ying Chang & Yiming Wang & Sumei Zhang, 2021. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    13. Ben Hambly & Juozas Vaicenavicius, 2015. "The 3/2 Model As A Stochastic Volatility Approximation For A Large-Basket Price-Weighted Index," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-25.
    14. Bruti-Liberati Nicola & Nikitopoulos-Sklibosios Christina & Platen Eckhard, 2006. "First Order Strong Approximations of Jump Diffusions," Monte Carlo Methods and Applications, De Gruyter, vol. 12(3), pages 191-209, October.
    15. Rodríguez Nava Abigail & Francisco Venegas Martínez, 2010. "Efectos del tipo de cambio sobre el déficit público: modelos de simulación Monte Carlo," Contaduría y Administración, Accounting and Management, vol. 55(3), pages 11-40, septiembr.
    16. Feng Zhao & Robert Jarrow & Haitao Li, 2004. "Interest Rate Caps Smile Too! But Can the LIBOR Market Models Capture It?," Econometric Society 2004 North American Winter Meetings 431, Econometric Society.
    17. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, July-Dece.
    18. Ciprian Necula, 2008. "Asset Pricing in a Two-Country Discontinuous General Equilibrium Model," Advances in Economic and Financial Research - DOFIN Working Paper Series 24, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    19. Maya Briani & Lucia Caramellino & Giulia Terenzi & Antonino Zanette, 2016. "Numerical stability of a hybrid method for pricing options," Papers 1603.07225, arXiv.org, revised Dec 2019.
    20. Belssing Taruvinga, 2019. "Solving Selected Problems on American Option Pricing with the Method of Lines," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2019, January-A.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:19:y:2016:i:06:n:s0219024916500461. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.