Mar
28

## Paper to Understand Credit Default Swap Valuation

Credit Default Swap (CDS) has existed since the early 1990s, and the market increased tremendously starting in 2003, the outstanding amount was $62.2 trillion by the end of 2007.

You can download the ISDA CDS Standard Model source code at ISDA. Should you like to dig further, here is a list of CDS paper I personally feel useful to understand the pricing methodology:

Longstaff, Mithal et al. (2005) assume premium is paid continuously, set the values of the premium leg and protection leg equal to each other.

Pan and Singleton (2008) apply a reduced form model to Mexico, Turkey, and Korea sovereign CDS, show that a single-factor model for default spread following a lognormal process captures most of the variation in the term structures of spreads.

Nashikkar, Subrahmanyam et al. (2011) assume default process be constant and calculate CDS par yield in reduced-form framework.

Ren-Raw Chen (2008) assume risk-free rates and default rates are correlated and solve the CDS pricing model explicitly used reduced-form.

Hai Lin (2011) value corporate bonds and CDS simultaneously using reduced form model, for CDS part, the authors assume there are both default and non-default part, and solve the model by assuming the two parts are independent.

Jankowitsch, Pullirsch et al. (2008) attribute the difference between corporate bond yields and CDS premium to one covenant of CDS: cheapest-to-delivery option, and solve the covenant by relating it to recovery rate. Their empirical analysis doesn’t support liquidity premium.

Carr and Wu (2010) propose a dynamically consistent framework that allows joint valuation and estimation of stock options and credit default swaps written on the same reference company. By assuming the stock price follows a jump-diffusion process with stochastic volatility, the instantaneous default rate and variance rate follow a bivariate continuous process, the authors solve the reduced form model analytically.

Brigo and Alfonsi (2005) introduce two-dimensional correlated square-root diffusion (SSRD) model for interest-rate and default process, then price CDS with Monte Carlo simulation.

Zhang (2008) use a three-factor model, namely interest rates, firm-specific distress variable, and hazard rate. The author is able to link hazard rate with interest rates by assuming the former is a function of the latter, then he solves the model analytically and applies to Argentina sovereign CDS.

Merton (1974), Black and Cox (1976), RiskMetrics (2002)

Zhong, Cao et al. (2010) argue CDS is similar to out-of-the-money put options in that both offer a low cost and effective protection against downside risk. They then investigates that put option-implied volatility is an important determinant of CDS spreads.

Bedendo, Cathcart et al. (2009) use an extended version of RiskMetrics (2002) to find the gap between the model CDS premium and market premium is time varying and widens substantially in times of financial turbulence. The author notice that CDS liquidity shows a significant impact on the gap, and should therefore be included when pricing CDS contracts.

Bongaerts, de Jong et al. (2011) imply that the equilibrium expected returns on the hedge assets can be decomposed in several components: priced exposure to the non-hedge asset returns, hedging demand effects, an expected illiquidity component, liquidity risk premium and hedge transaction costs.

Bedendo, M., L. Cathcart, et al. (2009). "Market and Model Credit Default Swap Spreads: Mind the Gap!" European Financial Management: no-no.

Black, F. and J. C. Cox (1976). "Valuing Corporate Securities - Some Effects of Bond Indenture Provisions." Journal of Finance 31(2): 351-367.

Bongaerts, D., F. de Jong, et al. (2011). "Derivative Pricing with Liquidity Risk: Theory and Evidence from the Credit Default Swap Market." Journal of Finance 66(1): 203-240.

Brigo, D. and A. Alfonsi (2005). "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model." Finance and Stochastics 9(1): 29-42.

Carr, P. and L. Wu (2010). "Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation." Journal of Financial Econometrics 8(4): 409-449.

Hai Lin, S. L., and Chunchi Wu (2011). "Dissecting Corporate Bond and CDS Spreads." The Journal of Fixed Income 20(3).

Jankowitsch, R., R. Pullirsch, et al. (2008). "The delivery option in credit default swaps." Journal of Banking & Finance 32(7): 1269-1285.

Longstaff, F. A., S. Mithal, et al. (2005). "Corporate yield spreads: Default risk or liquidity ? New evidence from the credit default swap market." Journal of Finance 60(5): 2213-2253.

Merton, R. C. (1974). "Pricing of Corporate Debt - Risk Structure of Interest Rates." Journal of Finance 29(2): 449-470.

Nashikkar, A., M. G. Subrahmanyam, et al. (2011). "Liquidity and Arbitrage in the Market for Credit Risk." Journal of Financial and Quantitative Analysis FirstView: 1-58.

Pan, J. U. N. and K. J. Singleton (2008). "Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads." The Journal of Finance 63(5): 2345-2384.

Ren-Raw Chen, X. C., Frank J. Fabozzi and Bo Liu (2008). "An Explicit, Multi-Factor Credit Default Swap Pricing Model with Correlated Factors." Journal of Financial and Quantitative Analysis 43.

RiskMetrics (2002). "CreditGrades™ Technical Document."

Zhang, F. X. (2008). "Market Expectations and Default Risk Premium in Credit Default Swap Prices: A Study of Argentine Default." Journal of Fixed Income 18(1).

Zhong, Z. D., C. Cao, et al. (2010). "The information content of option-implied volatility for credit default swap valuation." Journal of Financial Markets 13(3): 321-343.

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CONVERTIBLE BOND PRICING MODEL

You can download the ISDA CDS Standard Model source code at ISDA. Should you like to dig further, here is a list of CDS paper I personally feel useful to understand the pricing methodology:

**Reduced form**Longstaff, Mithal et al. (2005) assume premium is paid continuously, set the values of the premium leg and protection leg equal to each other.

Pan and Singleton (2008) apply a reduced form model to Mexico, Turkey, and Korea sovereign CDS, show that a single-factor model for default spread following a lognormal process captures most of the variation in the term structures of spreads.

Nashikkar, Subrahmanyam et al. (2011) assume default process be constant and calculate CDS par yield in reduced-form framework.

Ren-Raw Chen (2008) assume risk-free rates and default rates are correlated and solve the CDS pricing model explicitly used reduced-form.

Hai Lin (2011) value corporate bonds and CDS simultaneously using reduced form model, for CDS part, the authors assume there are both default and non-default part, and solve the model by assuming the two parts are independent.

Jankowitsch, Pullirsch et al. (2008) attribute the difference between corporate bond yields and CDS premium to one covenant of CDS: cheapest-to-delivery option, and solve the covenant by relating it to recovery rate. Their empirical analysis doesn’t support liquidity premium.

Carr and Wu (2010) propose a dynamically consistent framework that allows joint valuation and estimation of stock options and credit default swaps written on the same reference company. By assuming the stock price follows a jump-diffusion process with stochastic volatility, the instantaneous default rate and variance rate follow a bivariate continuous process, the authors solve the reduced form model analytically.

Brigo and Alfonsi (2005) introduce two-dimensional correlated square-root diffusion (SSRD) model for interest-rate and default process, then price CDS with Monte Carlo simulation.

Zhang (2008) use a three-factor model, namely interest rates, firm-specific distress variable, and hazard rate. The author is able to link hazard rate with interest rates by assuming the former is a function of the latter, then he solves the model analytically and applies to Argentina sovereign CDS.

**Structural model**Merton (1974), Black and Cox (1976), RiskMetrics (2002)

Zhong, Cao et al. (2010) argue CDS is similar to out-of-the-money put options in that both offer a low cost and effective protection against downside risk. They then investigates that put option-implied volatility is an important determinant of CDS spreads.

Bedendo, Cathcart et al. (2009) use an extended version of RiskMetrics (2002) to find the gap between the model CDS premium and market premium is time varying and widens substantially in times of financial turbulence. The author notice that CDS liquidity shows a significant impact on the gap, and should therefore be included when pricing CDS contracts.

**CAPM framework**Bongaerts, de Jong et al. (2011) imply that the equilibrium expected returns on the hedge assets can be decomposed in several components: priced exposure to the non-hedge asset returns, hedging demand effects, an expected illiquidity component, liquidity risk premium and hedge transaction costs.

**Reference:**Bedendo, M., L. Cathcart, et al. (2009). "Market and Model Credit Default Swap Spreads: Mind the Gap!" European Financial Management: no-no.

Black, F. and J. C. Cox (1976). "Valuing Corporate Securities - Some Effects of Bond Indenture Provisions." Journal of Finance 31(2): 351-367.

Bongaerts, D., F. de Jong, et al. (2011). "Derivative Pricing with Liquidity Risk: Theory and Evidence from the Credit Default Swap Market." Journal of Finance 66(1): 203-240.

Brigo, D. and A. Alfonsi (2005). "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model." Finance and Stochastics 9(1): 29-42.

Carr, P. and L. Wu (2010). "Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation." Journal of Financial Econometrics 8(4): 409-449.

Hai Lin, S. L., and Chunchi Wu (2011). "Dissecting Corporate Bond and CDS Spreads." The Journal of Fixed Income 20(3).

Jankowitsch, R., R. Pullirsch, et al. (2008). "The delivery option in credit default swaps." Journal of Banking & Finance 32(7): 1269-1285.

Longstaff, F. A., S. Mithal, et al. (2005). "Corporate yield spreads: Default risk or liquidity ? New evidence from the credit default swap market." Journal of Finance 60(5): 2213-2253.

Merton, R. C. (1974). "Pricing of Corporate Debt - Risk Structure of Interest Rates." Journal of Finance 29(2): 449-470.

Nashikkar, A., M. G. Subrahmanyam, et al. (2011). "Liquidity and Arbitrage in the Market for Credit Risk." Journal of Financial and Quantitative Analysis FirstView: 1-58.

Pan, J. U. N. and K. J. Singleton (2008). "Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads." The Journal of Finance 63(5): 2345-2384.

Ren-Raw Chen, X. C., Frank J. Fabozzi and Bo Liu (2008). "An Explicit, Multi-Factor Credit Default Swap Pricing Model with Correlated Factors." Journal of Financial and Quantitative Analysis 43.

RiskMetrics (2002). "CreditGrades™ Technical Document."

Zhang, F. X. (2008). "Market Expectations and Default Risk Premium in Credit Default Swap Prices: A Study of Argentine Default." Journal of Fixed Income 18(1).

Zhong, Z. D., C. Cao, et al. (2010). "The information content of option-implied volatility for credit default swap valuation." Journal of Financial Markets 13(3): 321-343.

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