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Credit Derivatives: Risk Management, Trading and Investing

ISBN: 978-0-470-02417-1
336 pages
September 2005
Credit Derivatives: Risk Management, Trading and Investing (0470024178) cover image


The credit derivatives market has developed rapidly over the last ten years and is now well established in the banking community and is increasingly making its presence felt in all areas of finance. This book covers the subject from credit bonds, asset swaps and related ‘real world’ issues such as liquidity, poor data, and credit spreads, to the latest innovations in portfolio products, hedging and risk management techniques. The book concentrates on practical issues and develops an understanding of the products through applications and detailed analysis of the risks and alternative means of trading. Credit Derivatives: Risk Management, Trading and Investing provides:
  • A description of the key products, applications, and an analysis of typical trades including basis trading, hedging, and credit structuring
  • Analysis of the industry standard ‘default and recovery’ and Copula models including many examples, and a description of the models’ shortcomings
  • Tools and techniques for the management of a portfolio or book of credit risks including appropriate and inappropriate methods of correlation risk management
  • A thorough analysis of counterparty risk
  • An intuitive understanding of credit correlation in reality and in the Copula model

The CD in the back of this book includes an Evaluation Version of Mathcad® 12 Single User Edition, which is reproduced by permission. This software is a fully-functional trial of Mathcad which will expire 30 days from installation. For technical support or more information see http://www.mathcad.com.

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Table of Contents



Disclaimer and Software Instructions.

Table of Spreadsheet Examples and Software.


1. Credit Debt and Other Traditional Credit Instruments.

1.1 Bonds and loans; LIBOR rates and swaps; 'repo' and general collateral rates.

1.1.1 Bonds and loans.

1.1.2 BBA LIBOR and swaps.

1.1.3 Collateralised lending and repo.

1.1.4 Repo as a credit derivative.

1.2 Credit debt versus 'risk-free' debt.

1.3 Issue documents, seniority and the recovery process.

1.3.1 Issue documents and default.

1.3.2 Claim amount.

1.3.3 The recovery process and recovery amount.

1.3.4 Sovereign versus corporate debt.

1.4 Valuation, yield and spread.

1.5 Buying risk.

1.6 Marking to market, marking to model and reserves.

2. Default and Recovery Data; Transition Matrices; Historical Pricing.

2.1 Recovery: ultimate and market value based recovery.

2.1.1 Ultimate recovery.

2.1.2 Market recovery.

2.1.3 Recovery rates and industry sector.

2.1.4 Recovery and default rates and the economic cycle.

2.1.5 Modelling recovery rates.

2.2 Default rates: rating and other factors.

2.3 Transition matrices.

2.4 Measures' and transition matrix-based pricing.

2.5 Spread jumps and spread volatility derived from transition matrices.

2.6 Adjusting transition matrices.

3. Asset Swaps and Asset Swap Spread; z-Spread.

3.1 'Par-par' asset swap contracts.

3.1.1 Contract description and hedging.

3.1.2 Hedging.

3.1.3 Default of the reference name.

3.2 Asset swap spread.

3.3 Maturity and z-spread.

3.4 Callable asset swaps; 'perfect' asset swaps.

3.4.1 Callable asset swaps.

3.4.2 'Perfect' asset swaps.

3.5 A bond spread model.

4. Liquidity, the Credit Pyramid and Market Data .

4.1 Bond liquidity .

4.2 The Credit Pyramid .

4.3 Survey and engineered spread data.

4.3.1 Survey data.

4.3.2 Engineered data .

4.4 Spread and rating.

5. Traditional Counterparty Risk Management.

5.1 Vetting.

5.2 Collateralisation and netting.

5.3 Additional counterparty requirements for credit derivative counterparties.

5.4 Internal capital charge.

6. Credit Portfolios and Portfolio Risk.

6.1 VaR and counterpartyVaR.

6.2 Distribution of forward values of a credit bond.

6.3 Correlation and the multi-factor Normal (Gaussian) distribution.

6.4 Correlation and the correlation matrix.

7. Introduction to Credit Derivatives.

7.1 Products and users.

7.1.1 'Traditional' credit instruments..

7.1.2 'Single name' credit derivatives.

7.1.3 Credit-linked notes.

7.1.4 Portfolio credit derivatives.

7.2 Market participants and market growth.


8. Credit Default Swaps; Product Description and Simple Applications.

8.1 CDS product definition.

8.1.1 Contract description and example.

8.1.2 Market CDS quotes.

8.1.3 Related products.

8.2 Documentation.

8.2.1 ISDA documentation and insurance contract differences.

8.2.2 Reference obligations and 'Mark-it RED'.

8.3 Credit triggers for credit derivatives.

8.3.1 Credit events.

8.3.2 Restructuring.

8.4 CDS Applications and elementary strategies.

8.4.1 Single names.

8.4.2 Sector/portfolio trades.

8.4.3 Income generation.

8.4.4 Regulatory capital reduction.

8.5 Counterparty risk: PFE for CDS.

8.6 CDS trading desk.

8.6.1 Mechanics of transacting a CDS deal.

8.6.2 Trade monitoring, credit events, unwinds.

8.6.3 CDS desk interactions and organisation.

Addendum: ISDA 2003 CDS confirmation.

9. Valuation and Risk: Basic Concepts and the Default and Recovery Model.

9.1 The fundamental credit arbitrage: repo cost.

9.2 Default and recovery model; claim amount.

9.2.1 Claim amount.

9.2.2 Recovery modelling.

9.2.3 Hazard (default) rate model.

9.2.4 Choice of hazard rate function/interpolation process.

9.3 Deterministic default rate model.

9.3.1 CDS valuation.

9.3.2 Accrued interest and the delivery option

9.3.3 CDS under constant hazard rate

9.3.4 Bond valuation

9.3.5 Bond price under a constant hazard rate

9.3.6 Limiting cases of the bond price.

9.3.7 Risky zero coupon bonds.

9.3.8 CDS and bond sensitivities.

9.4 Stochastic default rate model; hazard and pseudo-hazard rates.

9.5 Calibration to market data.

9.5.1 Calibrating to CDS and to bonds.

9.5.2 Implied hazard rates.

9.5.3 Calibrating to bonds: multiple solutions for the hazard rate.

9.5.4 Calibrating to bonds: implied recovery and hazard rates.

9.5.5 Implied hazard rate curve and no-arbitrage.

9.6 CDS data/sources.

9.6.1 Survey data.

9.6.2 Data engineering.

9.7 Model errors and tests.

9.7.1 Recovery assumption.

9.7.2 Interest and hazard rate correlation.

9.7.3 Reference name and counterparty hazard rate correlation.

9.7.4 Interpolation assumptions, and the pseudo-hazard rate versus stochastic hazard rate.

9.8 CDS risk factors; reserves and model risk.

9.8.1 Captured and hidden risks.

9.8.2 Limits.

9.8.3 Reserves against implementation errors.

9.8.4 Model reserves.

10. CDS Deal Examples.

10.1 A CDS hedged against another CDS.

10.1.1 Cross-currency default swap pricing and hedging.

10.1.2 Back-to-back trades, default event hedges and curve trades.

10.1.3 Hedging both credit event and spread risk simultaneously.

10.1.4 Seniority mismatch.

10.1.5 Trade level hedging and book basis hedging.

10.2 Introduction to bond hedging.

10.2.1 Default event hedging.

10.2.2 Spread hedging.

10.2.3 Convertible bonds and equity risk.

10.3 Hedge and credit event examples.

11. CDS/Bond Basis Trading.

11.1 Bond versus CDS: liquidity.

11.2 Bond repo cost.

11.3 Bond spread measurement: z-spread not asset swap spread.

11.4 Bond price impact.

11.5 Embedded options in bonds.

11.6 Delivery option in CDS.

11.7 Payoff of par.

11.8 Trigger event differences.

11.9 Embedded repo option.

11.10 Putting it all together.

12. Forward CDS; Back-to-Back CDS, Mark-to-Market and CDS Unwind.

12.1 Forward CDS.

12.2 Mark-to-market and back-to-back CDS.

12.3 Unwind calculation; off-market trade valuation and hedging.

12.4 'Double-trigger CDS'.

13. Credit-Linked Notes.

13.1 CLN set-up; counterparty or collateral risk.

13.2 Embedded swaps and options.

13.3 Costs.

13.4 Applications.

13.5 CLN pricing.

13.5.1 Basic pricing.

13.5.2 CLN pricing model.

13.6 Capital guaranteed note.

14. Digital or 'Fixed Recovery' CDS.

14.1 Product description.

14.2 Pricing, hedging, valuation and risk calculations.

14.2.1 Simple pricing.

14.2.2 Recovery assumptions.

14.2.3 Valuation and hedging.

14.3 Trigger event differences.

15. Spread Options, Callable/Puttable Bonds, Callable Asset Swaps, Callable Default Swaps.

15.1 Product definitions.

15.1.1 Vanilla spread options and variations.

15.1.2 Related embedded products.

15.1.3 Bond price options.

15.1.4 Applications.

15.2 Model alternatives and a stochastic default rate model for spread option pricing.

15.2.1 Model approaches.

15.2.2 Hazard rate tree.

15.2.3 Callable high-yield bonds.

15.3 Sensitivities and hedging.

16. Total Return Swaps .

16.1 Product definition and examples.

16.2 Applications

   16.3 Hedging and valuation.

16.3.1 Pricing and hedging.

16.3.2 Valuation.

17. Single Name Book Management.

17.1 Risk aggregation.

17.2 CreditVaR for CDS.

18. CDS and Simulation.

18.1 The Poisson model and default times.

18.2 Valuation by Monte Carlo simulation.

18.2 Sensitivity.


19. Nth-to-Default Baskets.

19.1 Product definition and features.

19.1.1 First-to-default product definition and example.

19.1.2 Documentation and takeovers.

19.1.3 Second (and higher)-to-default.

19.2 Applications.

19.2.1 Correlation trading.

19.2.2 Mergers.

19.2.3 Standard baskets.

19.3 Pricing: zero and 100% correlation.

19.3.1 Zero correlation case: exact pricing from the CDS model.

19.3.2 100% correlation: exact pricing.

20. Collateralised Debt Obligations.

20.1 Static synthetic CDO.

20.1.1 Product definition.

20.1.2 Premium waterfall.

20.1.3 Documentation; CDO set-up.

20.1.4 CDO tranches; funded and unfunded tranches; 'buying' and 'selling'.

20.1.5 Relationship to nth-to-default.

20.1.6 Arbitrage CDOs.

20.2 Index portfolios and Standard CDO structures.

20.2.1 Background and terminology.

20.2.2 Composition of the indices.

20.2.3 Single tranche [0%, 100%] CDO products.

20.2.4 Standard tranched CDO structures: iTraxx and CDX.

20.2.5 Index options and modelling spread.

20.3 CDO terminology and variations.

20.3.1 OC and IC tests; WARF; diversity score.

20.3.2 Cash and cashflow CDOs.

20.3.3 Cashflow waterfall.

20.3.4 Managed CDOs.

20.3.5 High-grade and high-yield CDOs.

20.3.6 Reference assets.

20.4 Tranche ratings and BET.

20.5 SPVs and CDOs.

20.6 Applications.

20.6.1 Balance sheet CDOs.

20.6.2 Diversification and risk reduction trades; a 'credit bank'.

21. Valuation and Hedging.

21.1 Default time correlation.

21.1.1 Generating correlated default times.

21.1.2 Intuitive understanding of default time correlation.

21.1.3 Spread implications of 100% default time correlation.

21.2 The Normal Copula.

21.3 Portfolio product pricing under Monte Carlo simulation.

21.3.1 N2D baskets.

21.3.2 CDO tranches.

21.3.3 The number of simulations.

21.3.4 Variance reduction techniques.

21.3.5 Complex CDO structures.

21.3.6 Summary of the Normal Copula default time simulation and valuation process.

21.4 Valuation examples.

21.4.1 F2D baskets.

21.4.2 CDO pricing: change of correlation.

21.4.3 CDO pricing: change of tranching.

21.4.4 CDO pricing: change of underlying.

21.4.5 CDO pricing: change of maturity.

21.5 Sensitivity calculation and hedging.

21.5.1 Dynamic hedging: spread risk.

21.5.2 Static hedging: default event risk.

21.5.3 Correlation risk.

21.5.4 Recovery risk.

21.5.5 Convexity risks.

21.6 Model errors and tests; alternative models.

21.6.1 Captured and hidden risks.

21.6.2 Spread models.

21.6.3 Reserves.

22. The Correlation Matrix.

22.1 Constraints: what makes a correlation matrix?.

22.2 Implied correlation.

22.2.1 Index CDO deals and implied correlation.

22.2.2 Base correlation.

22.2.3 Interpolating correlation.

22.2.4 Portfolio differences.

22.3 Tag correlation and semi-closed form pricing.

22.4 Spread correlation.

22.5 Asset and equity correlation.

22.6 Calculation techniques.

22.6.1 Pairwise estimation from historical data.

22.6.2 Factor analysis and correlation.

22.6.3 Impact on hedging of using historical or implied correlations.

23. Other Copulae.

23.1 Student's t distribution.

23.2 Copulae in general.

23.3 Archimedean Copulae: Clayton and Gumbel.

23.4 Clayton at θ =0 and ? &theta =.

23.5 Model risk.


24. Correlation Portfolio Management.

24.1 Static and dynamic hedges.

24.2 Correlation book management.

24.3 CreditVaR and CounterpartyVaR.


25. 'Single Name' CDS.

25.1 Non-correlated counterparty.

25.2 100% correlation.

25.3 Correlated counterparty: pricing and hedging.

25.4 Choice of Copula.

25.5 Collateralised deals and CDS book management.

26. Counterparty CDS.

26.1 Pricing.

26.2 Counterparty CDS (CCDS) book management.

27. The Future for Credit Derivatives.

27.1 Development processes.

27.2 Conclusion.

Appendix: iTraxx Indices.



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Author Information

GEOFF CHAPLIN studied mathematics at Cambridge (MA 1972) and Oxford (MSc 1973, DPhil 1975) and qualified as an actuary (FFA 1978) while working in a life insurance company. He moved to the City in 1980 and has worked for major banks (including HSBC, Nomura International, and ABN AMRO) as well as consulting to hedge funds, corporate treasurers, and institutional investment funds. He has been involved in the credit derivatives market since 1996 and has both traded portfolio products and developed risk management systems for these products. In addition to consulting and training for the major financial institutions, Geoff has maintained strong academic interests and was a visiting (emeritus) professor at the University of Waterloo (Canada) from 1987 until 1999. He has also published many articles (in Risk, the Journal of the Institute and Faculty of Actuaries, and others) and speaks regularly at conferences on credit derivatives.
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