IDEAS home Printed from https://ideas.repec.org/a/wly/apsmbi/v25y2009i5p565-582.html
   My bibliography  Save this article

First passage time for multivariate jump‐diffusion processes in finance and other areas of applications

Author

Listed:
  • Di Zhang
  • Roderick V. N. Melnik

Abstract

The first passage time (FPT) problem is an important problem with a wide range of applications in science, engineering, economics, and industry. Mathematically, such a problem can be reduced to estimating the probability of a stochastic process first to reach a boundary level. In most important applications in the financial industry, the FPT problem does not have an analytical solution and the development of efficient numerical methods becomes the only practical avenue for its solution. Most of our examples in this contribution are centered around the evaluation of default correlations in credit risk analysis, where we are concerned with the joint defaults of several correlated firms, the task that is reducible to a FPT problem. This task represents a great challenge for jump‐diffusion processes (JDP). In this contribution, we develop further our previous fast Monte Carlo method in the case of multivariate (and correlated) JDP. This generalization allows us, among other things, to evaluate the default events of several correlated assets based on a set of empirical data. The developed technique is an efficient tool for a number of financial, economic, and business applications, such as credit analysis, barrier option pricing, macroeconomic dynamics, and the evaluation of risk, as well as for a number of other areas of applications in science and engineering, where the FPT problem arises. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Di Zhang & Roderick V. N. Melnik, 2009. "First passage time for multivariate jump‐diffusion processes in finance and other areas of applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(5), pages 565-582, September.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:5:p:565-582
    DOI: 10.1002/asmb.745
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/asmb.745
    Download Restriction: no
    File URL: https://libkey.io/10.1002/asmb.745?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
    ---><---

    References listed on IDEAS

    as
    1. Pesaran, M. Hashem & Schuermann, Til & Treutler, Bjorn-Jakob & Weiner, Scott M., 2006. "Macroeconomic Dynamics and Credit Risk: A Global Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(5), pages 1211-1261, August.
    2. Wang, Jun & Zhang, Wen-Jun & Liang, Jin-Rong & Xiao, Jian-Bin & Ren, Fu-Yao, 2008. "Fractional nonlinear diffusion equation and first passage time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 764-772.
    3. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    4. Chen, Ren-Raw & Sopranzetti, Ben J., 2003. "The Valuation of Default-Triggered Credit Derivatives," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(2), pages 359-382, June.
    5. Robert A. Jarrow & David Lando & Fan Yu, 2008. "Default Risk And Diversification: Theory And Empirical Implications," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 19, pages 455-480, World Scientific Publishing Co. Pte. Ltd..
    6. Giesecke, Kay, 2004. "Correlated default with incomplete information," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1521-1545, July.
    7. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    8. Yu, Jialin, 2007. "Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan," Journal of Econometrics, Elsevier, vol. 141(2), pages 1245-1280, December.
    9. Sanjiv Ranjan Das & Raman Uppal, 2004. "Systemic Risk and International Portfolio Choice," Journal of Finance, American Finance Association, vol. 59(6), pages 2809-2834, December.
    10. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-576.
    11. Roy Mahapatra, D. & Melnik, R.V.N., 2007. "Finite element approach to modelling evolution of 3D shape memory materials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 141-148.
    12. Giesecke, Kay, 2006. "Default and information," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 2281-2303, November.
    13. Melnik, Roderick V.N & Povitsky, Alex, 2004. "Wave phenomena in physics and engineering: new models, algorithms, and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(4), pages 299-302.
    14. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2006. "Portfolio implications of systemic crises," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2347-2369, August.
    15. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
    16. Ngwira, Bernard & Gerrard, Russell, 2007. "Stochastic pension fund control in the presence of Poisson jumps," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 283-292, March.
    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. Hongda Gao & Dejing Kong & Yixin Sun, 2022. "Reliability modeling and analysis for systems governed by multiple competing failures processes," Journal of Risk and Reliability, , vol. 236(2), pages 256-265, April.

    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. Wan†Chien Chiu & Juan Ignacio Peña & Chih†Wei Wang, 2015. "Measuring Systemic Risk: Common Factor Exposures and Tail Dependence Effects," European Financial Management, European Financial Management Association, vol. 21(5), pages 833-866, November.
    2. Hanson, Samuel G. & Pesaran, M. Hashem & Schuermann, Til, 2008. "Firm heterogeneity and credit risk diversification," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 583-612, September.
    3. Pierre Collin-Dufresne & Robert S. Goldstein & Jean Helwege, 2010. "Is Credit Event Risk Priced? Modeling Contagion via the Updating of Beliefs," NBER Working Papers 15733, National Bureau of Economic Research, Inc.
    4. Azizpour, S & Giesecke, K. & Schwenkler, G., 2018. "Exploring the sources of default clustering," Journal of Financial Economics, Elsevier, vol. 129(1), pages 154-183.
    5. Nystrom, Kaj & Skoglund, Jimmy, 2006. "A credit risk model for large dimensional portfolios with application to economic capital," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2163-2197, August.
    6. Gunter Meissner & Seth Rooder & Kristofor Fan, 2013. "The impact of different correlation approaches on valuing credit default swaps with counterparty risk," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1903-1913, December.
    7. Jennie Bai & Pierre Collin-Dufresne & Robert S. Goldstein & Jean Helwege, 2012. "On bounding credit event risk premia," Staff Reports 577, Federal Reserve Bank of New York.
    8. Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein & Jean Helwege, 2015. "Modeling Credit Contagion via the Updating of Fragile Beliefs," The Review of Financial Studies, Society for Financial Studies, vol. 28(7), pages 1960-2008.
    9. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    10. Zhu, Haibin & Tarashev, Nikola A., 2008. "The pricing of correlated default risk: evidence from the credit derivatives market," Discussion Paper Series 2: Banking and Financial Studies 2008,09, Deutsche Bundesbank.
    11. Diogo Duarte & Rodolfo Prieto & Marcel Rindisbacher & Yuri F. Saporito, 2022. "Vanishing Contagion Spreads," Management Science, INFORMS, vol. 68(1), pages 740-772, January.
    12. Wagner, Stephan M. & Bode, Christoph & Koziol, Philipp, 2011. "Negative default dependence in supplier networks," International Journal of Production Economics, Elsevier, vol. 134(2), pages 398-406, December.
    13. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.
    14. Rosenthal, Dale W.R., 2008. "Approximating correlated defaults," MPRA Paper 36788, University Library of Munich, Germany, revised 15 Feb 2012.
    15. Murphy, Austin & Headley, Adrian, 2022. "An empirical evaluation of alternative fundamental models of credit spreads," International Review of Financial Analysis, Elsevier, vol. 81(C).
    16. Jorion, Philippe & Zhang, Gaiyan, 2007. "Good and bad credit contagion: Evidence from credit default swaps," Journal of Financial Economics, Elsevier, vol. 84(3), pages 860-883, June.
    17. Nan Chen & S. G. Kou, 2009. "Credit Spreads, Optimal Capital Structure, And Implied Volatility With Endogenous Default And Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 343-378, July.
    18. Xiao, Tim, 2018. "The Valuation of Credit Default Swap with Counterparty Risk and Collateralization," EconStor Preprints 203447, ZBW - Leibniz Information Centre for Economics.
    19. Linda Allen & Anthony Saunders, 2004. "Incorporating Systemic Influences Into Risk Measurements: A Survey of the Literature," Journal of Financial Services Research, Springer;Western Finance Association, vol. 26(2), pages 161-191, October.
    20. Luca Benzoni & Lorenzo Garlappi & Robert S. Goldstein, 2019. "Asymmetric Information, Dynamic Debt Issuance, and the Term Structure of Credit Spreads," Working Paper Series WP-2019-8, Federal Reserve Bank of Chicago.

    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:wly:apsmbi:v:25:y:2009:i:5:p:565-582. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1526-4025 .

    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.