Hedging of Defaultable Claims

The goal of this chapter is to present a survey of recent developments in the practically important and challenging area of hedging credit risk. In a companion work, Bielecki et al. (2004a), we presented techniques and results related to the valuation of defaultable claims. It should be emphasized that in most existing papers on credit risk, the risk-neutral valuation of defaultable claims is not supported by any other argument than the desire to produce an arbitrage-free model of default-free and defaultable assets. Here, we focus on the possibility of a perfect replication of defaultable claims and, if the latter is not feasible, on various approaches to hedging in an incomplete setting.

[1]  N. Karoui,et al.  Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market , 1995 .

[2]  Kenneth J. Singleton,et al.  Credit Risk: Pricing, Measurement, and Management , 2003 .

[3]  Robert J. Elliott,et al.  On Models of Default Risk , 2000 .

[4]  Andrew E. B. Lim,et al.  Dynamic Mean-Variance Portfolio Selection with No-Shorting Constraints , 2001, SIAM J. Control. Optim..

[5]  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.

[6]  Marek Musiela,et al.  An example of indifference prices under exponential preferences , 2004, Finance Stochastics.

[7]  S. Peng,et al.  Backward Stochastic Differential Equations in Finance , 1997 .

[8]  Xun Yu Zhou,et al.  Constrained Stochastic LQ Control with Random Coefficients, and Application to Portfolio Selection , 2005, SIAM J. Control. Optim..

[9]  Situ Rong.  On solutions of backward stochastic differential equations with jumps and applications , 1997 .

[10]  Martin Schweizer,et al.  Mean-variance hedging and stochastic control: beyond the Brownian setting , 2004, IEEE Transactions on Automatic Control.

[11]  PRICING CREDIT RISK DERIVATIVES , 1999 .

[12]  T. Bielecki,et al.  Modeling and Valuation of Credit Risk , 2004 .

[13]  D. Kramkov.  Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets , 1996 .

[14]  G. Barles,et al.  Backward stochastic differential equations and integral-partial differential equations , 1997 .

[15]  P. J. Schonbucher.  Credit Derivatives Pricing Models , 2003 .

[16]  M. Kobylanski.  Backward stochastic differential equations and partial differential equations with quadratic growth , 2000 .

[17]  Didier Cossin,et al.  Advanced Credit Risk Analysis , 2000 .

[18]  A. Jankunas.  Optimal contingent claims , 2001 .

[19]  Farshid Jamshidian,et al.  Valuation of credit default swaps and swaptions , 2004, Finance Stochastics.

[20]  N. Karoui,et al.  Backward Stochastic Differential Equations , 1997 .

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

[22]  Xun Yu Zhou,et al.  Markowitz’s World in Continuous Time, and Beyond , 2003 .

[23]  M. Mania,et al.  BACKWARD STOCHASTIC PDE AND IMPERFECT HEDGING , 2003 .

[24]  J. Gregory,et al.  Credit: The Complete Guide to Pricing, Hedging and Risk Management , 2001 .

[25]  Walter Schachermayer,et al.  ON UTILITY‐BASED PRICING OF CONTINGENT CLAIMS IN INCOMPLETE MARKETS , 2005 .

[26]  M. C. Quenez,et al.  Numerical Methods in Finance: Imperfect Markets and Backward Stochastic Differential Equations , 1997 .

[27]  Gang George Yin,et al.  Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model , 2003, SIAM J. Control. Optim..

[28]  F. Delbaen,et al.  Exponential Hedging and Entropic Penalties , 2002 .

[29]  P. Protter.  Stochastic integration and differential equations , 1990 .

[30]  X. Zhou,et al.  Stochastic Controls: Hamiltonian Systems and HJB Equations , 1999 .

[31]  Monique Jeanblanc,et al.  Hazard rate for credit risk and hedging defaultable contingent claims , 2004, Finance Stochastics.

[32]  Michael Mania.  A general problem of an optimal equivalent change of measure and contingent claim pricing in an incomplete market , 2000 .

[33]  Xun Yu Zhou,et al.  Relationship Between Backward Stochastic Differential Equations and Stochastic Controls: A Linear-Quadratic Approach , 2000, SIAM J. Control. Optim..

[34]  Shigeo Kusuoka,et al.  A Remark on default risk models , 1999 .

[35]  Andreas Brandt,et al.  Marked Point Processes on the Real Line: The Dynamical Approach , 1995 .

[36]  Nicole El Karoui,et al.  Pricing Via Utility Maximization and Entropy , 2000 .

[37]  K. Jordan,et al.  I Will Survive: Lesbian, Gay, and Bisexual Youths' Experience of High School , 1997 .

[38]  P. Collin‐Dufresne,et al.  A General Formula for Valuing Defaultable Securities , 2003 .

[39]  T. Bielecki,et al.  Dependent defaults and credit migrations , 2003 .

[40]  J. Ma,et al.  Forward-Backward Stochastic Differential Equations and their Applications , 2007 .

[41]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[42]  R. Jarrow,et al.  Counterparty Risk and the Pricing of Defaultable Securities , 1999 .

[43]  X. Zhou,et al.  Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework , 2000 .

[44]  M. Schweizer.  A guided tour through quadratic hedging approaches , 1999 .

[45]  D. Duffie.  Dynamic Asset Pricing Theory , 1992 .

[46]  M. Musiela,et al.  Martingale Methods in Financial Modelling , 2002 .

[47]  Julien Hugonnier,et al.  Event risk, contingent claims and the temporal resolution of uncertainty , 2001 .

[48]  Thorsten Rheinländer,et al.  On L2-projections on a space of stochastic integrals , 1997 .

[49]  David Lando,et al.  On cox processes and credit risky securities , 1998 .