A Simple Robust Link between American Puts and Credit Protection

We develop a simple robust link between deep out-of-the-money American put options on a company's stock and a credit insurance contract on the company's bond. We assume that the stock price stays above a barrier B before default but drops below a lower barrier A after default, thus generating a default corridor [A,B] that the stock price can never enter. Given the presence of this default corridor, a spread between two co-terminal American put options struck within the corridor replicates a pure credit contract, paying off when and only when default occurs prior to the option expiry. The Author 2011. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

[1]  P. Carr,et al.  Theory and Evidence on the Dynamic Interactions between Sovereign Credit Default Swaps and Currency Options , 2006 .

[2]  H. Leland. Agency Costs, Risk Management, and Capital Structure , 1998 .

[3]  Jens Hilscher,et al.  Is the Corporate Bond Market Forward Looking? , 2007 .

[4]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[5]  Liuren Wu,et al.  A No-Arbitrage Analysis of Economic Determinants of the Credit Spread Term Structure , 2005 .

[6]  M. Rubinstein. Displaced Diffusion Option Pricing , 1983 .

[7]  R. Geske The Valuation of Corporate Liabilities as Compound Options , 1977, Journal of Financial and Quantitative Analysis.

[8]  Andrea Resti,et al.  The Link between Default and Recovery Rates: Theory, Empirical Evidence and Implications , 2003 .

[9]  Alan G. White,et al.  Merton's model, credit risk and volatility skews , 2005 .

[10]  C. Cao,et al.  The Information Content of Option-Implied Volatility for Credit Default Swap Valuation , 2007 .

[11]  R. C. Merton,et al.  Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk , 2007, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[12]  Andrew Bevan,et al.  Corporate Bond Spreads and the Business Cycle , 2000 .

[13]  Mohamed El Babsiri,et al.  Simulating Path-Dependent Options , 1998 .

[14]  Louis Guttman,et al.  Statistical Adjustment of Data , 1944 .

[15]  Kenneth D. Garbade,et al.  Managerial Discretion and the Contingent Valuation of Corporate Securities , 1999 .

[16]  D. Hendry,et al.  Co-Integration and Error Correction : Representation , Estimation , and Testing , 2007 .

[17]  P. Carr,et al.  Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation , 2006 .

[18]  Richard Roll,et al.  Systematic Risk in Corporate Bond Credit Spreads , 1998 .

[19]  Suresh M. Sundaresan,et al.  Does Default Risk in Coupons Affect the Valuation of Corporate Bonds?: A Contingent Claims Model , 1993 .

[20]  Suresh M. Sundaresan,et al.  Debt Valuation, Renegotiation, and Optimal Dividend Policy , 2000 .

[21]  G. Consigli,et al.  CDS and equity volatility: theoretical modelling and ..._Giorgio CONSIGLI CREDIT DEFAULT SWAPS AND EQUITY VOLATILITY: THEORETICAL MODELLING AND MARKET EVIDENCE , 2004 .

[22]  Harjoat S. Bhamra,et al.  The Levered Equity Risk Premium and Credit Spreads: A Unified Framework , 2009 .

[23]  Zhiwei Zhang Corporate Bond Spreads and the Business Cycle , 2002 .

[24]  F. Black,et al.  VALUING CORPORATE SECURITIES: SOME EFFECTS OF BOND INDENTURE PROVISIONS , 1976 .

[25]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[26]  R. Geske,et al.  The Components of Corporate Credit Spreads: Default, Recovery, Taxes, Jumps, Liquidity, and Market Factors , 2001 .

[27]  Liuren Wu,et al.  A No-Arbitrage Analysis of Macroeconomic Determinants of the Credit Spread Term Structure , 2008, Manag. Sci..

[28]  D. Gray Modeling Financial Crises and Sovereign Risks , 2009 .

[29]  Michael B. Gordy,et al.  The Bank as Grim Reaper: Debt Composition and Recoveries on Defaulted Debt , 2007 .

[30]  Mark S. Carey,et al.  Credit Risk in Private Debt Portfolios , 1998 .

[31]  R. Engle,et al.  COINTEGRATION AND ERROR CORRECTION: REPRESENTATION , 1987 .

[32]  Mark Broadie,et al.  Optimal Debt and Equity Values in the Presence of Chapter 7 and Chapter 11 , 2005 .

[33]  A. Le Separating the Components of Default Risk:A Derivative-Based Approach , 2007 .

[34]  H. Leland. Corporate Debt Value, Bond Covenants, and Optimal Capital Structure , 1994, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[35]  E. Elton,et al.  Explaining the Rate Spread on Corporate Bonds , 1999 .

[36]  Chunsheng Zhou,et al.  The term structure of credit spreads with jump risk , 2001 .

[37]  Merton H. Miller The Cost of Capital, Corporation Finance and the Theory of Investment , 1958 .

[38]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[39]  R. Rifkin Information content. , 1981, Circulation.

[40]  Ming Huang,et al.  How Much of Corporate-Treasury Yield Spread is Due to Credit Risk? , 2002 .

[41]  M. Eriksson,et al.  Optimal capital structure , 2000 .

[42]  Eduardo S. Schwartz,et al.  A Simple Approach to Valuing Risky Fixed and Floating Rate Debt , 1995 .

[43]  Sheridan Titman,et al.  Valuing Commercial Mortgages: An Empirical Investigation of the Contingent‐Claims Approach to Pricing Risky Debt , 1989 .

[44]  The Determinants of Credit Default Swap Premia , 2005 .

[45]  Francis X. Diebold,et al.  Ratings Migration and the Business Cycle, With Application to Credit Portfolio Stress Testing , 2002 .

[46]  Ronald W. Anderson,et al.  Strategic analysis of contingent claims , 1996 .

[47]  Nengjiu Ju,et al.  An Ebit-Based Model of Dynamic Capital Structure , 2001 .

[48]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[49]  John Y. Campbell,et al.  Equity Volatility and Corporate Bond Yields , 2002 .

[50]  Kris Jacobs,et al.  The Determinants of Credit Default Swap Premia , 2005, Journal of Financial and Quantitative Analysis.

[51]  Vadim Linetsky,et al.  A jump to default extended CEV model: an application of Bessel processes , 2006, Finance Stochastics.

[52]  Eric Briys,et al.  Valuing Risky Fixed Rate Debt: An Extension , 1997, Journal of Financial and Quantitative Analysis.

[53]  Long Chen,et al.  On the Relation between the Credit Spread Puzzle and the Equity Premium Puzzle , 2008 .

[54]  V. Acharya,et al.  Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy , 2001 .

[55]  R. C. Merton,et al.  On the Pricing of Corporate Debt: The Risk Structure of Interest Rates , 1974, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[56]  Pascal J. Maenhout,et al.  Individual Stock-Option Prices and Credit Spreads , 2004 .

[57]  Didier Cossin,et al.  Exploring for the Determinants of Credit Risk in Credit Default Swap Transaction Data: Is Fixed-Income Markets' Information Sufficient to Evaluate Credit Risk? , 2002 .

[58]  Robust Replication of Default Contingent Claims , 2008 .

[59]  Yuhang Xing,et al.  Default Risk in Equity Returns , 2004 .

[60]  H. Leland.,et al.  Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads , 1996, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[61]  L. Martellini,et al.  EXPLORING FOR THE DETERMINANTS OF CREDIT RISK IN CREDIT DEFAULT SWAP TRANSACTION DATA : IS FIXED-INCOME MARKETS ’ INFORMATION SUFFICIENT TO EVALUATE CREDIT RISK ? , 2002 .

[62]  Hayne E. Leland,et al.  Can the Trade-off Theory Explain Debt Structure? , 2007 .

[63]  Pierre Mella-Barral,et al.  Strategic Debt Service , 1997, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[64]  Hao Zhou,et al.  Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms , 2005 .

[65]  Hao Zhou,et al.  Explaining Credit Default Swap Spreads With the Equity Volatility and Jump Risks of Individual Firms , 2005 .

[66]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[67]  P. Collin‐Dufresne,et al.  The Determinants of Credit Spread Changes , 2001 .

[68]  Suresh M. Sundaresan,et al.  Design and Valuation of Debt Contracts , 1994 .

[69]  John H. Frye,et al.  Depressing Recoveries , 2001 .

[70]  Gurdip Bakshi,et al.  Investigating the Role of Systematic and Firm-Specific Factors in Default Risk: Lessons from Empirically Evaluating Credit Risk Models , 2006 .

[71]  T. Ho,et al.  Bond indenture provisions and the risk of corporate debt , 1982 .

[72]  Ehud I. Ronn,et al.  Pricing Risk‐Adjusted Deposit Insurance: An Option‐Based Model , 1986 .

[73]  Pascal J. Maenhout,et al.  Explaining the Level of Credit Spreads: Option-Implied Jump Risk Premia in a Firm Value Model , 2005 .

[74]  D. Duffie,et al.  Term Structures of Credit Spreads with Incomplete Accounting Information , 2001, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.