IDEAS home Printed from https://ideas.repec.org/p/zbw/bubdps/432014.html
   My bibliography  Save this paper

Updating the option implied probability of default methodology

Author

Listed:
  • Vilsmeier, Johannes

Abstract

In this paper we 'update' the option implied probability of default (option iPoD) approach recently suggested in the literature. First, a numerically more stable objective function for the estimation of the risk neutral density is derived whose integrals can be solved analytically. Second, it is reasoned that the originally proposed approach for the estimation of the PoD produces arbitrary results and hence an alternative procedure is suggested that is based on the Lagrange multipliers. Based on numerical evaluations and an illustrative empirical application we conclude that the framework provides very promising results.

Suggested Citation

  • Vilsmeier, Johannes, 2014. "Updating the option implied probability of default methodology," Discussion Papers 43/2014, Deutsche Bundesbank.
    • Handle: RePEc:zbw:bubdps:432014
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/106792/1/817008713.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zellner, Arnold & Highfield, Richard A., 1988. "Calculation of maximum entropy distributions and approximation of marginalposterior distributions," Journal of Econometrics, Elsevier, vol. 37(2), pages 195-209, February.
    2. Philipp Matros & Johannes Vilsmeier, 2012. "Measuring Option Implied Degree of Distress in the US Financial Sector Using the Entropy Principle," Working Papers 123, Bavarian Graduate Program in Economics (BGPE).
    3. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    4. D. Ormoneit & H. White, 1999. "An efficient algorithm to compute maximum entropy densities," Econometric Reviews, Taylor & Francis Journals, vol. 18(2), pages 127-140.
    5. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    6. Cassio Neri & Lorenz Schneider, 2012. "Maximum entropy distributions inferred from option portfolios on an asset," Finance and Stochastics, Springer, vol. 16(2), pages 293-318, April.
    7. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(1), pages 143-159, March.
    8. Matros, Philipp & Vilsmeier, Johannes, 2012. "Measuring option implied degree of distress in the US financial sector using the entropy principle," Discussion Papers 30/2012, Deutsche Bundesbank.
    9. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    10. Mr. Jorge A Chan-Lau, 2006. "Market-Based Estimation of Default Probabilities and its Application to Financial Market Surveillance," IMF Working Papers 2006/104, International Monetary Fund.
    11. Christian Capuano, 2008. "The Option-iPoD," IMF Working Papers 2008/194, International Monetary Fund.
    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. Philipp Matros & Johannes Vilsmeier, 2013. "The Multivariate Option iPoD Framework - Assessing Systemic Financial Risk," Working Papers 143, Bavarian Graduate Program in Economics (BGPE).
    2. Matros, Philipp & Vilsmeier, Johannes, 2014. "The multivariate option iPoD framework: assessing systemic financial risk," Discussion Papers 20/2014, Deutsche Bundesbank.
    3. Rockinger, Michael & Jondeau, Eric, 2002. "Entropy densities with an application to autoregressive conditional skewness and kurtosis," Journal of Econometrics, Elsevier, vol. 106(1), pages 119-142, January.
    4. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    5. Johannes Vilsmeier, 2011. "Updating the Option Implied Probability of Default Methodology," Working Papers 107, Bavarian Graduate Program in Economics (BGPE).
    6. Omid M. Ardakani, 2022. "Option pricing with maximum entropy densities: The inclusion of higher‐order moments," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1821-1836, October.
    7. Monteiro, Ana Margarida & Tutuncu, Reha H. & Vicente, Luis N., 2008. "Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity," European Journal of Operational Research, Elsevier, vol. 187(2), pages 525-542, June.
    8. Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
    9. Malhotra, Gifty & Srivastava, R. & Taneja, H.C., 2019. "Calibration of the risk-neutral density function by maximization of a two-parameter entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 45-54.
    10. Vilsmeier, Johannes, 2011. "Updating the Option Implied Probability of Default Methodology," University of Regensburg Working Papers in Business, Economics and Management Information Systems 462, University of Regensburg, Department of Economics.
    11. Jean-Baptiste Monnier, 2013. "Technical report : Risk-neutral density recovery via spectral analysis," Papers 1302.2567, arXiv.org.
    12. Christian Capuano, 2008. "The Option-iPoD," IMF Working Papers 2008/194, International Monetary Fund.
    13. Gottschalk, Sylvia, 2017. "Entropy measure of credit risk in highly correlated markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 11-19.
    14. Chipeniuk, Karsten O. & Walker, Todd B., 2021. "Forward inflation expectations: Evidence from inflation caps and floors," Journal of Macroeconomics, Elsevier, vol. 70(C).
    15. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    16. A. Monteiro & R. Tütüncü & L. Vicente, 2011. "Estimation of risk-neutral density surfaces," Computational Management Science, Springer, vol. 8(4), pages 387-414, November.
    17. Sylvia Gottschalk, 2016. "Entropy and credit risk in highly correlated markets," Papers 1604.07042, arXiv.org.
    18. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Revisited Multi-moment Approximate Option," FMG Discussion Papers dp430, Financial Markets Group.
    19. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    20. D. Ormoneit & H. White, 1999. "An efficient algorithm to compute maximum entropy densities," Econometric Reviews, Taylor & Francis Journals, vol. 18(2), pages 127-140.

    More about this item

    Keywords

    Option Implied Probability of Default; Risk Neutral Density; Cross Entropy;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:zbw:bubdps:432014. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/dbbgvde.html .

    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.