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Updating the option implied probability of default methodology

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  • 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.

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

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    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.
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    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

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