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The Option-Ipod. the Probability of Default Implied by Option Prices Basedon Entropy

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  • Christian Capuano

Abstract

We present a framework to derive the probability of default implied by the price of equity options. The framework does not require any strong statistical assumption, and provide results that are informative on the expected developments of balance sheet variables, such as assets, equity and leverage, and on the Greek letters (delta, gamma and vega). We show how to extend the framework by using information from the price of a zero-coupon bond and CDS-spreads. In the episode of the collapse of Bear Stearns, option-iPoD was able to early signal market sentiment.

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Bibliographic Info

Paper provided by International Monetary Fund in its series IMF Working Papers with number 08/194.

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Length: 29
Date of creation: 01 Aug 2008
Date of revision:
Handle: RePEc:imf:imfwpa:08/194

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Keywords: Credit; Risk management; Financial risk; Financial institutions; probability; probability density function; probability density; bond; bonds; equation; coupon bond; optimization; present value; stock price; probability distribution; zero-coupon bonds; credit derivatives; random variable; free parameter; lognormal distribution; coupon bonds; cumulative distribution function; empirical validity; distributional assumption; normal density; statistics; convertible bonds; mathematical statistics; probabilities; mathematica; polynomial; operations research; econometrics; financial stability; derivative; bond markets; financial market; equations; skewness; standard deviation; bond holder;

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References

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  1. Miller, Douglas J. & Liu, Wei-han, 2002. "On the recovery of joint distributions from limited information," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 259-274, March.
  2. 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(01), pages 143-159, March.
  3. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  4. Manmohan Singh & Jochen R. Andritzky, 2006. "The Pricing of Credit Default Swaps During Distress," IMF Working Papers 06/254, International Monetary Fund.
  5. Jorge A. Chan-Lau, 2006. "Market-Based Estimation of Default Probabilities and its Application to Financial Market Surveillance," IMF Working Papers 06/104, International Monetary Fund.
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Citations

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Cited by:
  1. Madan, Dilip B. & Schoutens, Wim, 2013. "Systemic risk tradeoffs and option prices," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 222-230.
  2. 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, Research Centre.
  3. Stefano Fenoaltea, 2010. "The reconstruction of historical national accounts: the case of Italy," PSL Quarterly Review, Economia civile, vol. 63(252), pages 77-96.
  4. Jose Giancarlo Gasha & Andre Santos & Jorge A. Chan-Lau & Carlos I. Medeiros & Marcos Souto & Christian Capuano, 2009. "Recent Advances in Credit Risk Modeling," IMF Working Papers 09/162, International Monetary Fund.
  5. Martin Saldías Zambrana, 2010. "Systemic risk analysis using forward-looking distance-to-default series," Working Paper 1005, Federal Reserve Bank of Cleveland.
  6. Dicembrino, Claudio & Scandizzo, Pasquale Lucio, 2011. "Can portfolio diversification increase systemic risk? evidence from the U.S and European mutual funds market," MPRA Paper 33715, University Library of Munich, Germany.
  7. Rainer Masera, 2010. "Reforming financial systems after the crisis: a comparison of EU and USA," PSL Quarterly Review, Economia civile, vol. 63(255), pages 299-362.
  8. Vilsmeier, Johannes, 2011. "Updating the Option Implied Probability of Default Methodology," University of Regensburg Working Papers in Business, Economics and Management Information Systems 22326, University of Regensburg, Department of Economics.
  9. Sessi Tokpavi, 2013. "Testing for the Systemically Important Financial Institutions: a Conditional Approach," EconomiX Working Papers 2013-27, University of Paris West - Nanterre la Défense, EconomiX.
  10. Dimitrios Bisias & Mark Flood & Andrew W. Lo & Stavros Valavanis, 2012. "A Survey of Systemic Risk Analytics," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 255-296, October.
  11. Rainer Masera, 2011. "Taking the moral hazard out of banking: the next fundamental step in financial reform," PSL Quarterly Review, Economia civile, vol. 64(257), pages 105-142.

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