IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v16y2016i4p573-592.html
   My bibliography  Save this article

Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion

Author

Listed:
  • Son-Nan Chen
  • Pao-Peng Hsu
  • Chang-Yi Li

Abstract

The relationship between company hazard rates and the business cycle becomes more apparent after a financial crisis. To address this relationship, a regime-switching process with an intensity function is adopted in this paper. In addition, the dynamics of both interest rates and asset values are modelled with a Markov-modulated jump-diffusion model, and a 2-factor hazard rate model is also considered. Based on this more suitable model setting, a closed-form model of pricing risky bonds is derived. The difference in yield between a risky bond and risk-free zero coupon bond is used to model a term structure of credit spreads (CSs) from which a closed-form pricing model of a call option on CSs is obtained. In addition, the degree to which the explicit regime shift affects CSs and credit-risky bond prices is numerically examined using three forward-rate functions under various business-cycle patterns.

Suggested Citation

  • Son-Nan Chen & Pao-Peng Hsu & Chang-Yi Li, 2016. "Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 573-592, April.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:4:p:573-592
    DOI: 10.1080/14697688.2015.1058520
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2015.1058520
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2015.1058520?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. Duffee, Gregory R., 1996. "On measuring credit risks of derivative instruments," Journal of Banking & Finance, Elsevier, vol. 20(5), pages 805-833, June.
    2. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    3. Liew, Chuin Ching & Siu, Tak Kuen, 2010. "A hidden Markov regime-switching model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 374-384, December.
    4. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    5. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    6. Hackbarth, Dirk & Miao, Jianjun & Morellec, Erwan, 2006. "Capital structure, credit risk, and macroeconomic conditions," Journal of Financial Economics, Elsevier, vol. 82(3), pages 519-550, December.
    7. T. R. Hurd, 2009. "Credit risk modeling using time-changed Brownian motion," Papers 0904.2376, arXiv.org.
    8. Jin‐Chuan Duan & Peter Ritchken & Zhiqiang Sun, 2006. "Approximating Garch‐Jump Models, Jump‐Diffusion Processes, And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 21-52, January.
    9. Leonard Tchuindjo, 2007. "Pricing of Multi-Defaultable Bonds with a Two-Correlated-Factor Hull-White Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 19-39.
    10. T. R. Hurd, 2009. "Credit Risk Modeling Using Time-Changed Brownian Motion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1213-1230.
    11. 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..
    12. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    13. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453, World Scientific Publishing Co. Pte. Ltd..
    14. Madan, Dilip & Unal, Haluk, 2000. "A Two-Factor Hazard Rate Model for Pricing Risky Debt and the Term Structure of Credit Spreads," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(1), pages 43-65, March.
    15. Tak Kuen Siu & Christina Erlwein & Rogemar Mamon, 2008. "The Pricing of Credit Default Swaps under a Markov-Modulated Merton’s Structural Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(1), pages 18-46.
    16. Schmid, Bernd & Kalemanova, Anna, 2002. "Applying a three-factor defaultable term structure model to the pricing of credit default options," International Review of Financial Analysis, Elsevier, vol. 11(2), pages 139-158.
    17. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    18. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    19. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlögl, 2007. "A Markovian Defaultable Term Structure Model With State Dependent Volatilities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 155-202.
    20. Carl Chiarella & Christina Sklibosios, 2003. "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 10(2), pages 87-127, September.
    21. Bollen, Nicolas P. B. & Gray, Stephen F. & Whaley, Robert E., 2000. "Regime switching in foreign exchange rates: Evidence from currency option prices," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 239-276.
    22. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    23. Robert Elliott & Tak Kuen Siu, 2009. "On Markov-modulated Exponential-affine Bond Price Formulae," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 1-15.
    24. Choi, Kyongwook & Hammoudeh, Shawkat, 2010. "Volatility behavior of oil, industrial commodity and stock markets in a regime-switching environment," Energy Policy, Elsevier, vol. 38(8), pages 4388-4399, August.
    25. Chang, Charles & Fuh, Cheng-Der & Lin, Shih-Kuei, 2013. "A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3204-3217.
    26. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    27. Stoyan Valchev, 2004. "Stochastic volatility Gaussian Heath-Jarrow-Morton models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(4), pages 347-368.
    28. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson‐Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94, October.
    29. Rabinovitch, Ramon, 1989. "Pricing Stock and Bond Options when the Default-Free Rate is Stochastic," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(4), pages 447-457, December.
    30. L. Z.J. Liang & D. Lemmens & J. Tempere, 2010. "Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 75(3), pages 335-342, June.
    31. A'Hearn, Brian & Woitek, Ulrich, 2001. "More international evidence on the historical properties of business cycles," Journal of Monetary Economics, Elsevier, vol. 47(2), pages 321-346, April.
    32. L. Z. J. Liang & D. Lemmens & J. Tempere, 2010. "Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model," Papers 1011.1175, arXiv.org.
    33. Bo, Lijun & Wang, Yongjin & Yang, Xuewei, 2010. "Markov-modulated jump-diffusions for currency option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 461-469, June.
    34. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
    35. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
    36. Thomas, Lyn C. & Allen, David E. & Morkel-Kingsbury, Nigel, 2002. "A hidden Markov chain model for the term structure of bond credit risk spreads," International Review of Financial Analysis, Elsevier, vol. 11(3), pages 311-329.
    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. Chen, Son-Nan & Hsu, Pao-Peng, 2018. "Pricing and hedging barrier options under a Markov-modulated double exponential jump diffusion-CIR model," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 330-346.

    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. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011.
    2. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    3. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2005.
    4. 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.
    5. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    6. Batten, Jonathan & Hogan, Warren, 2002. "A perspective on credit derivatives," International Review of Financial Analysis, Elsevier, vol. 11(3), pages 251-278.
    7. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    8. Moraux, Franck, 2004. "Modeling the business risk of financially weakened firms: A new approach for corporate bond pricing," International Review of Financial Analysis, Elsevier, vol. 13(1), pages 47-61.
    9. 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.
    10. Carl Chiarella & Thuy-Duong Tô, 2006. "The Multifactor Nature of the Volatility of Futures Markets," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 163-183, May.
    11. Hsu, Yuan-Lin & Lin, Shih-Kuei & Hung, Ming-Chin & Huang, Tzu-Hui, 2016. "Empirical analysis of stock indices under a regime-switching model with dependent jump size risks," Economic Modelling, Elsevier, vol. 54(C), pages 260-275.
    12. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    13. Lian, Yu-Min & Chen, Jun-Home, 2021. "Pricing virtual currency-linked derivatives with time-inhomogeneity," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 424-439.
    14. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlögl, 2007. "A Markovian Defaultable Term Structure Model With State Dependent Volatilities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 155-202.
    15. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    16. Mi-Hsiu Chiang & Chang-Yi Li & Son-Nan Chen, 2016. "Pricing currency options under double exponential jump diffusion in a Markov-modulated HJM economy," Review of Quantitative Finance and Accounting, Springer, vol. 46(3), pages 459-482, April.
    17. Carl Chiarella & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2005. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton with Jumps," Research Paper Series 167, Quantitative Finance Research Centre, University of Technology, Sydney.
    18. Carl Chiarella & Thuy-Duong To, 2005. "The Multifactor Nature of the Volatility of the Eurodollar Futures Market," Research Paper Series 150, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Lian, Yu-Min & Chen, Jun-Home, 2022. "Foreign exchange option pricing under regime switching with asymmetrical jumps," Finance Research Letters, Elsevier, vol. 46(PA).
    20. Lian, Yu-Min & Chen, Jun-Home & Liao, Szu-Lang, 2016. "Option pricing on foreign exchange in a Markov-modulated, incomplete-market economy," Finance Research Letters, Elsevier, vol. 16(C), pages 208-219.

    More about this item

    Statistics

    Access and download statistics

    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:taf:quantf:v:16:y:2016:i:4:p:573-592. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.