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Asset pricing
In this section, the reports deal with articles on asset pricing: asset pricing models, stochastic discount factors, equity premium puzzle, consumption-based models, habit-persistence models, multi-factor models, pricing anomalies, asset return predictability, credit spreads, credit models etc...

Measuring Default Risk Premia from Default Swap Rates and EDFs

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This paper estimates recent default risk premia for U.S. corporate debt, based on a close relationship between default probabilities, as estimated by Moody's KMV EDFs, and default swap (CDS) market rates.
The default-swap data, obtained through CIBC from 39 banks and specialty dealers, allow to establish a strong link between actual and risk-neutral default probabilities for firms in the three sectors that the authors analyze: broadcasting and entertainment, healthcare, and oil and gas.
The authors find dramatic variation over time in risk premia, from peaks in the third quarter of 2002, dropping by roughly 50% to late 2003. They run a panel data regression of log CDS on log EDF controlling for month and sectors. The slope is 0.76 and the intercept is positive. There is substantial risk premium. They look at the time-variation and sector variation of risk premium for a constant default probability. They then use a default intensity time-series model.
From the time series of EDF they estimate the default intensities assuming that the log of the default intensity follows an Ornstein-Uhlenbeck process.  From time-series of CDS, they estimate risk-neutral default intensities. They have estimates of the risk premium and comment on the fluctuation of the risk premium due to misestimate of default probabilities, time variation of risk-neutral conditional expectation of loss given default, changes in the supply and demand for risk bearing, whose effects are exaggerated by some limits on capital mobility across segments of the capital market and principal-agent inefficiencies in the asset management industry (risk aversion after recent losses, search for yield when treasury rates decline). Also credit premium might change due to change in correlation as it reduces the effect of diversification.
Berndt, Antje, Douglas, Rohan and Schranz, David, "Measuring Default Risk Premia from Default Swap Rates and EDFs" . BIS Working Paper No. 173 Available at SSRN: http://ssrn.com/abstract=556080 
 

Individual Stock Option Prices and Credit Spreads

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The authors look at the explanatory power of option-implied volatility and volatility skew on credit spreads. They find that implied vol has a higher explanatory power than credit ratings. They look at 69 firms from 1996 to 2002. They use 524 corporate bonds non-callable, non-puttable. End-of-day bid-ask quotes and open interest and volume from January 1996 to September 2002 with over 3 million option observations per month. Optionmetrics also computes implied volatility.  They use options that expire in the month immediately after the current month. The implied volatility skew is the left slope of the implied volatility smirk. It is the difference between the put with 0.92 strike to spot ratio and the implied volatility of the at-the-money put. The cross-sectional correlation between skew and spread is small for individual names. The time series correlation is 25.8%. SPX and skew are highly correlated with credit spreads. They use detrended skew data. Option-implied skews are interpreted as measuring jump risk. They run regression on weekly spread data on historical stock volatility, implied stock volatility and volatility skew. Regression on implied volatility, implied volatility skew and a constant gives positive coefficient. An increase in volatility skew increases credit spreads. Historical volatility has the same effect as implied volatility whereas historical skewness (the third moment, wrong sign in the regression)has less effect than the volatility skew. Historical data use 180 days. They also use aggregate variables, volatility and skewness on S&P options.

Cremers, Martijn , Driessen, Joost, Maenhout, Pascal J. and Weinbaum, David, "Individual Stock-Option Prices and Credit Spreads" (December 2004). Yale ICF Working Paper No. 04-14; EFA 2004 Maastricht Meetings Paper No. 5147. Available at SSRN: http://ssrn.com/abstract=527502

 

 

Is Default Event Risk Priced in Corporate Bonds?

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Driessen separates risk of credit change, if no default occurs and the risk of the default event itself. He uses credit spread data and historical default rates to estimate the size of the default jump premium along with the credit spread change premium. He is testing the conditional diversification hypothesis of JLY.  JLY states that if there is an infinite number of bonds and if default jumps are conditionally independent across firms then default jump risk cannot be priced. Investors take into account multiple defaults. Model follows the Duffie-Singleton framework. At each instant, firm can default. The product of the risk-neutral default intensity and the loss rate equals the instantaneous credit spread. It assumed a constant loss rate and a stochastic default intensity. Each firm’s default intensity is a function of a low number of latent common factors and a firm specific factor. All factors follow square root processes.

Since Collin-Dufresne et al. (2001) show that observable financial and economic variables cannot explain the correlation of credit spread changes across firms, he uses a latent factor model. There is correlation between credit spreads and default-free interest rates, modelled with a two-factor affine model used by Duffie-Perdersen and Singleton (2001). He models the relation between risk-neutral and actual default intensities. The ratio of the risk-neutral default intensity and actual intensity defines the jump risk premium, assumed to be constant over time.

Excess corporate bond returns are generated in four ways:

1. through the dependence of credit spreads on default-free term structure factors

2. risk of common or systematic changes is priced

3. via the risk premium on firm-specific credit spread changes

4. via the risk premium of default jump

He used weekly data of 592 investment-grade bonds from 104 firms from 1991-2000.

He first estimates a two-factor model for the default-free term structure using Quasi-Maximum-Likelihood based on the Kalman filter. He then estimates the common factor processes that influence corporate bond spreads of all firms, again using Quasi-Maximum-Likelihood based on the Kalman filter. He then uses residual bond pricing errors to estimate the firm-specific factor for each firm. As a final step, he uses data on historical default rates to estimate the default jump risk premium. The results are the following:


The two common factor processes that influence corporate bond spreads of all firms have statistically significant risk prices. The risk associated with the firm-specific factors is not priced. There is negative correlation between credit spreads and the default-free term structure. If there is no jump risk premium in the model, the model overestimates observed default rates and thus underestimates expected corporate bond returns.
 
Driessen, Joost, "Is Default Event Risk Priced in Corporate Bonds?" ( 2005). The Review of Financial Studies, Vol. 18, Issue 1, pp. 165-195, 2005 Available at SSRN: http://ssrn.com/abstract=900679 

 

Modeling Expected Return on Defaultable Bonds

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Duffie and Singleton (1999) showed that under certain technical assumptions, defaultable bonds are priced pre-default with an adjusted interest rate that can be modelled as an affine function of diffusion state variables just as in the default-free case. JLY (2001) shows that there are two kinds of default risk premia, one related to systematic variations in default intensity and the other the jump risk premium on the default event (default event premium). Yu shows that the expected return of on defaultable bonds has three components:

1. The first one is the expected return of an otherwise default-free bond,

2. The second component is related to the parameters of the risk-neutral mean loss rate and their adjustment under the physical measure (compensation for variations in credit risk generated by the state variables),

3. The third component is the difference between the risk-neutral and the physical mean-loss rates (compensation for bearing the risk of the systematic default event).
Yu, Fan, "Modeling Expected Return on Defaultable Bonds" (April 4, 2002). Available at SSRN: http://ssrn.com/abstract=291065 or DOI: 10.2139/ssrn.291065 
 


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