A Reduced Form Model of Default Spreads with Markov-Switching Macroeconomic Factors

An important research area of the corporate yield spread literature seeks to measure the proportion of the spread that can be explained by factors such as the possibility of default, liquidity, tax differentials and market risk. We contribute to this literature by assessing the ability of observed macroeconomic factors and the possibility of changes in regime to explain the proportion of yield spreads caused by the risk of default in the context of a reduced form model. For this purpose, we extend the Markov Switching risk-free term structure model of Bansal and Zhou (2002) to the corporate bond setting and develop recursive formulas for default probabilities, risk-free and risky zero-coupon bond yields as well as credit default swap premia. The model is calibrated with consumption, inflation, risk-free yields and default data for Aa, A and Baa bonds from the 1987-2008 period. We find that our macroeconomic factors are linked with two out of three sharp increases in the spreads during this sample period, indicating that the variations can be related to macroeconomic undiversifiable risk. The estimated default spreads can explain almost half of the 10 years to maturity industrial Baa zero-coupon yields in some regime. Much smaller proportions are found for Aa and A bonds with numbers around 10%. The proportions of default estimated with credit default swaps are higher, in many cases doubling those found with corporate yield spreads.Credit spread, default spread, Markov switching, macroeconomic factors, reduced form model of default, random subjective discount factor, credit default swap, CDS

A Unified Framework for Pricing Credit and Equity Derivatives

We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be calibrated to find a risk neutral model that matches a set of observed market prices. This risk neutral model can then be used to price more exotic, illiquid or over-the-counter derivatives. We observe that the model implied credit default swap (CDS) spread matches the market CDS spread and that our model produces a very desirable CDS spread term structure. This is observation is worth noticing since without calibrating any parameter to the CDS spread data, it is matched by the CDS spread that our model generates using the available information from the equity options and corporate bond markets. We also observe that our model matches the equity option implied volatility surface well since we properly account for the default risk premium in the implied volatility surface. We demonstrate the importance of accounting for the default risk and stochastic interest rate in equity option pricing by comparing our results to Fouque, Papanicolaou, Sircar and Solna (2003), which only accounts for stochastic volatility.Comment: Keywords: Credit Default Swap, Defaultable Bond, Defaultable Stock, Equity Options, Stochastic Interest Rate, Implied Volatility, Multiscale Perturbation Metho

On the term structure of default premia in the Swap and Libor markets

Existing theories of the term structure of swap rates provide an analysis of the Treasury-swap spread based on either a liquidity convenience yield in the Treasury market, or default risk in the swap market. While these models do not focus on the relation between corporate yields and swap rates (the LIBOR-Swap spread), they imply that the term structure of corporate yields and swap rates should be identical. As documented previously (e.g. in Sun, Sundares and Wang (1993)) this is counter-factual. Here, we propose a simple model of the (complex) default risk imbedded in the swap term structure that is able to explain the LIBOR-swap spread. Whereas corporate bonds carry default risk, we argue that swaps should bear less default risk. In fact, we assume that swap contracts are free of default risk. Because swaps are indexed on "refreshed"-credit-quality LIBOR rates, the spread between corporate yields and swap rates should capture the market's expectations of the probability of deterioration in credit quality of a corporate bond issuer. We model this feature and use our model to estimate the likelihood of future deterioration in credit quality from the LIBOR-swap spread. The analysis is important because it shows that the term structure of swap rates does not reflect the borrowing cost of a standard LIBOR credit quality issuer. It also has implications for modeling the dynamics of the swap term structure.Credit risk; asset pricing; international finance

A Reduced Form Model of Default Spreads with Markov Switching Macroeconomic Factors

An important research area of the corporate yield spread literature seeks to measure the proportion of the spread explained by factors such as the possibility of default, liquidity or tax differentials. We contribute to this literature by assessing the ability of observed macroeconomic factors and the possibility of changes in regime to explain the proportion in yield spreads caused by the risk of default in the context of a reduced form model. For this purpose, we extend the Markov Switching risk-free term structure model of Bansal ad Zhou (2002) to the corporate bond setting and develop recursive formulas for default probabilities, risk-free and risky zero-coupon bond yields. The model is calibrated out of sample with consumption, inflation, risk-free yield and default data over the 1987-1996 period. Our results indicate that inflation is a key factor to consider for explaining default spreads during our sample period. We also find that the estimated default spreads can explain up to half of the 10 year to maturity Baa zero-coupon yield in certain regime with different sensitivities to consumption and inflation through time.Credit spread, default spread, Markov Switching, macroeconomic factors, reduced form model of default

An Empirical Analysis of the Pricing of Collateralized Debt Obligations

We study the pricing of collateralized debt obligations (CDOs) using an extensive new data set for the actively-traded CDX credit index and its tranches. We find that a three-factor portfolio credit model allowing for firm-specific, industry, and economywide default events explains virtually all of the time-series and crosssectional variation in CDX index tranche prices. These tranches are priced as if losses of 0.4, 6, and 35 percent of the portfolio occur with expected frequencies of 1.2, 41.5, and 763 years, respectively. On average, 65 percent of the CDX spread is due to firm-specific default risk, 27 percent to clustered industry or sector default risk, and 8 percent to catastrophic or systemic default risk. Recently, however, firm-specific default risk has begun to play a larger role.

Default Risk in Corporate Yield Spreads

An important research question examined in the recent credit risk literature focuses on the proportion of corporate yield spreads which can be attributed to default risk. Past studies have verified that only a small fraction of the spreads can be explained by default risk. In this paper, we reexamine this topic in the light of the different issues associated with the computation of transition and default probabilities obained with historical rating transition data. One significant finding of our research is that the estimated default-risk proportion of corporate yield spreads in highly sensitive to the term structure of the default probabilities estimated for each rating class. Moreover, this proportion can become a large fraction of the yield spread when sensitivity analyses are made with respect to recovery rates, default cycles in the economy, and information considered in the historical rating transition data.Credit risk, default risk, corporate yield spread, transition matrix, default probability, Moody's, Standard and Poor's, recovery rate, data filtration, default cycle

Default risk premium in credit and equity markets

The default risk premium expresses the difference between the actual default risk of a company and the default risk implied by the securities issued by the company. In this paper, we study the simultaneous relationship between the dynamics of the default risk premium and both the dynamics of the stock price and the CDS (Credit Default Swap) spread of a company. We show that an increase in the default risk premium can be associated, at the same time, to either an increase in the stock price and a decrease in the CDS spread, or to a decrease in the stock price and an increase in the CDS spread. We document that the first type of relationship features securities belonging to a consistent risk-return framework, while the second type of relationship describes securities following a counterintuitive risk-return puzzle. We show this result theoretically end empirically, by adopting a contingent claim model. We estimate the model with a non-linear Kalman filter in conjunction with quasimaximum likelihood, and we shed light on the relationship over time between the default risk premium and both the equity value and the CDS spreads for a sample of non-financial firms

A note on the risk management of CDOs

The purpose of this note is to describe a risk management procedure applicable to options on large credit portfolios such as CDO tranches on iTraxx or CDX. Credit spread risk is dynamically hedged using single name defaultable claims such as CDS while default risk is kept under control thanks to diversification. The proposed risk management approach mixes ideas from finance and insurance and departs from standard approaches used in incomplete markets such as mean-variance hedging or expected utility maximisation. In order to ease the analysis and the exposure, default dates follow a multivariate Cox process.CDOs; default risk; credit spread risk; dynamic hedging; diversification, large portfolios; incomplete markets; Cox process; doubly stochastic Poisson process