IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v10y2018i4p1027-d138895.html
   My bibliography  Save this article

The Study of Utility Valuation of Single-Name Credit Derivatives with the Fast-Scale Stochastic Volatility Correction

Author

Listed:
  • Shican Liu

    (Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia)

  • Yanli Zhou

    (School of Finance, Zhongnan University of Economics and Law, Wuhan 430073, China)

  • Benchawan Wiwatanapataphee

    (Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia)

  • Yonghong Wu

    (Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia)

  • Xiangyu Ge

    (Department of Finance, Wuhan Technology and Business University, Wuhan 430065, China)

Abstract

In this paper, we study the risk aversion on valuing the single-name credit derivatives with the fast-scale stochastic volatility correction. Two specific utility forms, including the exponential utility and the power utility, are tested as examples in our work. We apply the asymptotic approximation to obtain the solution of the non-linear PDE, and make a comparison of the utility before and after the stochastic volatility modification, and we find that incorporation of fast-scale volatility will lower down the utility. By using the indifference price, we also give the yield spread impacted by the risk adverse valuation. We find that by considering the default risk, yield spread is sloping in a short period and converge in a long run.

Suggested Citation

  • Shican Liu & Yanli Zhou & Benchawan Wiwatanapataphee & Yonghong Wu & Xiangyu Ge, 2018. "The Study of Utility Valuation of Single-Name Credit Derivatives with the Fast-Scale Stochastic Volatility Correction," Sustainability, MDPI, vol. 10(4), pages 1-21, March.
    • Handle: RePEc:gam:jsusta:v:10:y:2018:i:4:p:1027-:d:138895
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/10/4/1027/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/10/4/1027/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    2. Ronnie Sircar & Thaleia Zariphopoulou, 2010. "Utility valuation of multi-name credit derivatives and application to CDOs," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 195-208.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    5. Tan, Yong & Floros, Christos, 2013. "Risk, capital and efficiency in Chinese banking," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 26(C), pages 378-393.
    6. Darrell Duffie & Thaleia Zariphopoulou, 1993. "Optimal Investment With Undiversifiable Income Risk," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 135-148, April.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. E. Papageorgiou & R. Sircar, 2008. "Multiscale Intensity Models for Single Name Credit Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(1), pages 73-105.
    9. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    10. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    11. Tan, Yong, 2016. "The impacts of risk and competition on bank profitability in China," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 40(C), pages 85-110.
    12. Jean-Pierre Fouque & Ronnie Sircar & Thaleia Zariphopoulou, 2017. "Portfolio Optimization And Stochastic Volatility Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 704-745, July.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    3. Regis Houssou & Olivier Besson, 2010. "Indifference of Defaultable Bonds with Stochastic Intensity models," Papers 1003.4118, arXiv.org.
    4. 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.
    5. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    6. 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, January-A.
    7. Gatzert, Nadine & Martin, Michael, 2012. "Quantifying credit and market risk under Solvency II: Standard approach versus internal model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 649-666.
    8. 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.
    9. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736, December.
    10. Jeremy Leake, 2003. "Credit spreads on sterling corporate bonds and the term structure of UK interest rates," Bank of England working papers 202, Bank of England.
    11. Jacquier, Antoine & Roome, Patrick, 2016. "Large-maturity regimes of the Heston forward smile," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1087-1123.
    12. Augusto Castillo, 2004. "Firm and Corporate Bond Valuation: A Simulation Dynamic Programming Approach," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 41(124), pages 345-360.
    13. John Y. Campbell & Glen B. Taksler, 2003. "Equity Volatility and Corporate Bond Yields," Journal of Finance, American Finance Association, vol. 58(6), pages 2321-2350, December.
    14. Wisniewski, Tomasz Piotr & Lambe, Brendan John, 2015. "Does economic policy uncertainty drive CDS spreads?," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 447-458.
    15. Dassios, Angelos & Li, Luting, 2020. "Explicit asymptotic on first passage times of diffusion processes," LSE Research Online Documents on Economics 103087, London School of Economics and Political Science, LSE Library.
    16. Jean-Pierre Fouque & Ruimeng Hu & Ronnie Sircar, 2021. "Sub- and Super-solution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Market," Papers 2106.11510, arXiv.org, revised Oct 2021.
    17. Cao, Jiling & Kim, Jeong-Hoon & Liu, Wenqiang & Zhang, Wenjun, 2023. "Rescaling the double-mean-reverting 4/2 stochastic volatility model for derivative pricing," Finance Research Letters, Elsevier, vol. 58(PB).
    18. Giesecke, Kay & Longstaff, Francis A. & Schaefer, Stephen & Strebulaev, Ilya, 2011. "Corporate bond default risk: A 150-year perspective," Journal of Financial Economics, Elsevier, vol. 102(2), pages 233-250.
    19. Kim, Seong-Tae & Kim, Jeong-Hoon, 2020. "Stochastic elasticity of vol-of-vol and pricing of variance swaps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 420-440.
    20. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.

    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:gam:jsusta:v:10:y:2018:i:4:p:1027-:d:138895. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.