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Abstract:
No consensus has yet emerged from the existing credit risk literature on how much of the observed corporate-Treasury yield spreads can be explained by credit risk. In this paper, we propose a new calibration approach based on historical default data and show that one can indeed obtain consistent estimate of the credit spread across many different economic considerations within the structural framework of credit risk valuation. We find that credit risk accounts for only a small fraction of the observed corporate-Treasury yield spreads for investment grade bonds of all maturities, with the fraction smaller for bonds of shorter maturities; and that it accounts for a much higher fraction of yield spreads for junk bonds. We obtain these results by calibrating each of the models - both existing and new ones - to be consistent with data on historical default loss experience. Different structural models, which in theory can still generate a very large range of credit spreads, are shown to predict fairly similar credit spreads under empirically reasonable parameter choices, resulting in the robustness of our conclusion.

Abstract:
This paper empirically tests five structural models of corporate bond pricing: Those of Merton (1974), Geske (1977), Leland and Toft (1996), Longstaff and Schwartz (1995), and Collin-Dufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capital structures during the period 1986-1997. The conventional wisdom is that structural models do not generate spreads as high as those seen in the bond market, and true to expectations we find that the predicted spreads in our implementation of the Merton model are too low. The compound option approach of Geske comes much closer to the spreads observed in the market, on average, but still underpredicts spreads. In contrast, the Leland and Toft model substantially overestimates credit risk on most bonds, and especially so for high coupon bonds. The Longstaff and Schwartz model modifies Merton to incorporate a stochastic interest rate and a correlation between interest rates and firm value. While the correlation and the level of interest rates have little effect, higher interest rate volatility leads to higher predicted spreads. However, this and other features of this model result in spreads that are often too high for risky bonds and too low for safe bonds. The target leverage ratio model of Collin-Dufresne and Goldstein helps to raise the spreads on the bonds that were considered very safe by the Longstaff and Schwartz model, but overall tends toward overestimation of credit risk. We conclude that structural models do not systematically underpredict spreads, as the previous literature implies, but accuracy is a problem. Moreover, some of the simplifications made to date lead to overestimation of credit risk on the riskier bonds while scarcely affecting the spreads of the safest bonds.

Credit risk, structural models

Abstract:
In this paper, we propose a general method for pricing and hedging non-standard American options. The proposed method applies to any kind of American-style contract for which the payoff function has a Markovian representation in the state space. Specifically, we obtain an analytic solution for the value and hedge parameters of path-dependent American options such as barrier options. The solution includes standard American options as a special case. The analytic formula also allows us to identify and exploit two key properties of the optimal exercise boundary - homogeneity in price parameters and time-invariance - for American options. In addition, some new put-call "symmetry" relations are also derived. These properties suggest a new, efficient and integrated approach to pricing and hedging a variety of standard and non-standard American options. From an implementation perspective, this approach avoids the current practice of repetitive computation of option prices and hedge ratios. Our implementation of the analytic formula for barrier options indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. In some cases, our method is faster by about four orders of magnitude than existing numerical methods with equal accuracy. In particular, the method overcomes the difficulty that existing numerical methods have in dealing with prices close to the barrier, the case where the barrier matters most.

Abstract:
We examine the question of the determinants of corporate bond credit spreads using both weekly and monthly option-adjusted spreads for nine corporate bond indices from Merrill Lynch from January 1997 to July 2002. We find that the Russell 2000 index historical return volatility and Conference Board composite leading and coincident economic indicators have significant power in explaining credit spread changes, especially for high yield indices. Furthermore, these three variables plus the interest rate level, the historical interest rate volatility, the yield curve slope, the Russell 2000 index return, and the Fama-French [1996] high-minus-low factor can explain more than 40% of credit spread changes for five bond indexes. In particular, these eight variables can explain 67.68% and 60.82% of credit spread changes for the B- and BB rated indexes, respectively. Our analysis confirms that credit spread changes for high-yield bonds are more closely related to equity market factors and also provides evidence in favor of incorporating macroeconomic factors into credit risk models.

Abstract:
This paper revisits the question of the determinants of corporate bond credit spreads using some new explanatory variables with both weekly and monthly option-adjusted credit spreads of corporate bond indices from Merrill Lynch. We find that among the new variables, the interest rate historical volatility, the Russell 2000 index historical return volatility and Conference Board leading and coincident economic indices have significant power in explaining credit spread changes, especially for high yield bond indices. Furthermore, these four variables plus the interest rate level, the yield curve slope, the Russell 2000 index return, and the Fama-French [1996] high-minus-low factor return could explain more than 40% of credit spread changes in 5 out of 9 rating/maturity indices. In particular, these variables could explain 67.68% of the variation in B rated index credit spreads and 60.82% of the variation in BB rated index credit spreads. The overall explanatory power on credit spread changes achieved here is a notable improvement over most previous studies using either option-adjusted index spreads or individual corporate bond spreads. Our analysis confirms that high-yield credit spread changes are more closely related with equity market factors and also provides evidence in favor of incorporating macroeconomic risk factors into credit risk models.

Abstract:
We present a cash-flow based model of corporate debt valuation that incorporates two novel features. First, we allow for the separation and optimal determination of the firm's debt-service and dividend policies; in particular, the firm is allowed to maintain cash reserves to meet future debt obligations. Second, our model admits the possibility that raising resources through issuance of new equity could be a costly procedure. In contrast, much of the previous literature has considered only dividend policies that are the residual consequences of debt-service policy, and has assumed new equity issuance costs are either zero or infinite.

We provide an analytical characterization of equilibrium behavior in our model. Numerical analysis of the equilibrium reveals that our model predicts substantially higher yield spreads than the canonical Merton-type model. More importantly, we find that the two novel features of our model are crucial determinants of not only the overall spreads that result but also of the marginal impact of allowing for debt-service to be strategic. Specifically: (a) assuming residual rather than optimal dividend policies can result in a significant upward bias in the yield spreads predicted by the model; (b) the size of this bias depends in a central way on the costs of equity issuance; (c) the marginal impact of strategic debt-service is substantial, in general, only for low equity-issuance costs, and (d) under optimally-determined dividends, strategic debt-service can actually result in a narrowing of yield spreads. In summary, our results indicate that endogenizing dividend policy and allowing for equity-issuance costs can enhance the model's content substantially, while ignoring these factors could introduce non-trivial biases into the valuation.

Abstract:
A basic requirement for a credit risk model is that it should not imply negative default probabilities. In this paper, we explore the implications of this condition for credit risk modeling. More specifically, we use the condition as a diagnostic tool to investigate if a particular model is consistent with a given set of credit spreads. We show that under this condition, each model has two credit spread boundaries which can be calculated analytically, and the model is correctly specified if and only if the observed credit spread curve lies within the two boundaries. These analytical formulas for the boundaries also allow us to derive some general properties of a large class of credit risk models.

Our study also adds to the literature on pricing defaultable claims off the default probability curve, a method widely used in practice. It is well-known that negative default probabilities frequently occur in constructions of default probability curves. Our analysis provides one possible explanation of why this problem happens and also suggests how the problem may be solved (or at least alleviated).

Credit risk modeling, Credit spread bounds

Abstract:
In this paper, we examine the dynamic behavior of credit spreads on corporate bond portfolios. We propose an econometric model of credit spreads that incorporates portfolio rebalancing, the near unit root property of spreads, the autocorrelation in spread changes, the ARCH conditional heteroscedasticity, jumps, and lagged market factors. In particular, our model is the first that takes into account explicitly the impact of rebalancing and yields estimates of the absorbing bounds on credit spreads induced by such rebalancing. We apply our model to nine Merrill Lynch daily series of option-adjusted spreads with ratings from AAA to C for the period January, 1997 through August, 2002. We find no evidence of mean reversion in these credit spread series over our sample period. However, we find ample evidence of both the ARCH effect and jumps in the data especially in the investment-grade credit spread indices. Incorporating jumps into the ARCH type conditional variance results in significant improvements in model diagnostic tests. We also find that while log spread variations depend on both the lagged Russell 2000 index return and lagged changes in the slope of the yield curve, the time-varying jump intensity of log credit spreads is correlated with the lagged stock market volatility. Finally, our results indicate the ARCH-jump specification outperforms the ARCH specification in the out-of-sample, one-step-ahead forecast of credit spreads.

Credit risk, corporate bonds, credit spread index, index rebalancing, jumps

Abstract:
"Inflation-indexed securities would appear to be the most direct source of information about inflation expectations and real interest rates" (Bernanke, 2004). In this paper we study the term structure of real interest rates, expected inflation and inflation risk premia using data on prices of Treasury Inflation Protected Securities (TIPS) over the period 2000-2007. The estimates of the 10-year inflation risk premium are between 11 and 22 basis points for 2000-2007 depending on the proxy used for the expected inflation. Furthermore, we find that the inflation risk premium is time varying and, specifically, negative in the first half (which might be due to either concerns of deflation or low liquidity of the TIPS market), but positive in the second half of the sample.

Abstract:
"Inflation-indexed securities would appear to be the most direct source of information about inflation expectations and real interest rates." (Bernanke, 2004). In this paper we study the term structure of real interest rates, expected inflation, and inflation risk premia using data on prices of Treasury Inflation Protected Securities (TIPS) over the period 2000-2007. The estimates of the 10-year inflation risk premium are between 11 and 22 basis points for 2000-2007 depending on the proxy used for the expected inflation. Furthermore, we find that the inflation risk premium is time varying and, specifically, negative in the first half (which might be due to either concerns of deflation or low liquidity of the TIPS market), but positive in the second half of the sample.

TIPS market, inflation risk premium, expected inflation

Abstract:
"Inflation-indexed securities would appear to be the most direct source of information about inflation expectations and real interest rates" (Bernanke, 2004). In this paper we study the term structure of real interest rates, expected inflation and inflation risk premia using data on prices of Treasury Inflation Protected Securities (TIPS) over the period 2000-2007. The estimates of the 10-year inflation risk premium are between 11 and 22 basis points for 2000-2007 depending on the proxy used for the expected inflation. Furthermore, we find that the inflation risk premium is time varying and, specifically, negative in the first half (which might be due to either concerns of deflation or low liquidity of the TIPS market), but positive in the second half of the sample.

TIPS market, inflation risk premium, expected inflation, term structure of real rates

Abstract:
In this paper we conduct a specification analysis of structural credit risk models, using term structure of credit default swap (CDS) spreads and equity volatility from high-frequency return data. Our study provides consistent econometric estimation of the pricing model parameters and specification tests based on the joint behavior of time-series asset dynamics and cross-sectional pricing errors. Our empirical tests reject strongly the standard Merton (1974) model, the Black and Cox (1976) barrier model, and the Longstaff and Schwartz (1995) model with stochastic interest rates. The double exponential jump-diffusion barrier model (Huang and Huang, 2003) improves significantly over the three models. The best one among the five models considered is the stationary leverage model of Collin-Dufresne and Goldstein (2001), which we cannot reject in more than half of our sample firms. However, our empirical results document the inability of the existing structural models to capture the dynamic behavior of CDS spreads and equity volatility, especially for investment grade names. This points to a potential role of time-varying asset volatility, a feature that is missing in the standard structural models.

Structural Credit Risk Models, Credit Default Swap Spreads, High Frequency Equity Volatility, Consistent Specification Analysis, Pricing Error Diagnostics

Abstract:
We investigate the impact of scheduled macroeconomic news announcements on the corporate bond market using daily credit spreads from January 1997 through June 2003. We find that macroeconomic announcements mainly affect high-yield bonds. In particular, the announcement surprises in leading economic indicators and employment reports have significant impact on credit spreads of high-yield bonds. We also find that the conditional volatility of credit spreads on high-yield bonds increases on announcement days for the advance monthly retail sales. Finally, we find that the VIX volatility index, not macroeconomic announcements, has significant impact on jumps in daily credit spreads.

Abstract:
Recent work has suggested that strategic underperformance of debt-service obligations by equity holders can resolve the gap between observed yield spreads and those generated by Merton (1974)-style models. We show that this is not quite correct. The value of the option to underperform on debt-service obligations depends on two other optionalities available to equity holders, namely, the option to carry cash reserves within the firm and the option to raise new external financing.

We disentangle the effects of the three factors, and characterize the impact of each in isolation as well as their interaction. We find, among other things, that while strategic behavior can increase spreads significantly under some conditions, its impact is negligible in others, and in some cases it even leads to a decline in equilibrium spreads. We show that this last apparently paradoxical result is a consequence of an interaction of optionalities that results in a trade-off between strategic and liquidity-driven defaults.

Strategic debt-service, interaction of optionalities, liquidity default, strategic default, cash-management

Abstract:
Recent work has suggested that strategic underperformance of debt-service obligations by equity holders can resolve the gap between observed yield spreads and those generated by Merton (1974)-style models. We show that this is not quite correct. The value of the option to underperform on debt-service obligations depends on two other optionalities available to equity holders, namely, the option to carry cash reserves within the firm and the option to raise new external financing.

We disentangle the effects of the three factors, and characterize the impact of each in isolation as well as their interaction. We find, among other things, that while strategic behavior can increase spreads significantly under some conditions, its impact is negligible in others, and in some cases it even leads to a decline in equilibrium spreads. We show that this last apparently paradoxical result is a consequence of an interaction of optionalities that results in a trade-off between strategic and liquidity-driven defaults.

strategic debt-service, interaction of optionalities, liquidity default, strategic default, cash-management

Abstract:
We analyze the specifications of option pricing models based on time-changed Levy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process itself. Our estimation of a variety of model specifications indicates that to better capture the behavior of the S&P 500 index options, we must incorporate a high frequency jump component in the return process and generate stochastic volatilities from two different sources, the jump component and the diffusion component.

Abstract:
This paper examines the ability of government bond fund managers to time the market, based on their holdings of Treasury securities during the period 1997-2006. We find that, on average, government bond fund managers exhibit significant and positive timing ability at the one-month horizon, under a holdings-based timing measure. In particular, fund managers specializing in Treasury securities are more likely to better time the market than general government bond fund managers. We also find that more successful market timers tend to have relatively higher Morningstar ratings, larger fund flows, lower expense ratios, higher Sharpe ratios, and higher concentrations of holdings of Treasury securities.

Market Timing, Government Bond Fund, Holdings-based Timing Measure

Abstract:
Hedge funds often hold illiquid assets whose true value is slowly reflected in reported returns. As a result, reported returns of a hedge fund can become a smoothed version of its true realized returns and, thus, can bias the evaluation of hedge fund performance. To address this problem, we provide a Bayesian framework for the performance evaluation of managed portfolios that accounts for three features of such portfolios: return smoothing; time-variation in performance and factor loadings; and the often short-lived nature of such portfolios. Using simulated data, we estimate several restricted versions of our model and find that return smoothing affects performance evaluation more than the other two features do. We apply the model to a sample of US equity hedge funds over the period January 1994 - December 2005, and find that, even for these relatively liquid strategies, smoothing causes an upward bias in excess performance measures, e.g. the fund's alpha, and a downward bias in risk measures. In particular, we show that a moderate level of smoothing can cause the standard OLS alpha to over-estimate equity funds' abnormal performance by more than 1% annually.

Hedge funds, return smoothing, performance persistence, Bayesian analysis

Abstract:
Recent work has suggested that strategic under performance of debt service obligations by equity holders can resolve the gap between observed yield spreads and those generated Merton (41) style models. We show that it is not quite correct. The value of the option to under perform on debt-service obligations depend on two other optionality's available to equity holders, namely, the option to carry cash reserves within the firm and the option to raise new external financing.

Abstract:
Recent work has suggested that strategic under performance of debt service obligations by equity holders can resolve the gap between observed yield spreads and those generated Merton (41) style models. We show that it is not quite correct. The value of the option to under perform on debt-service obligations depend on two other optionality's available to equity holders, namely, the option to carry cash reserves within the firm and the option to raise new external financing.

Abstract:
Recent work in corporate finance has suggested that strategic debt-service by equityholders works to lower debt values and raise yield spreads substantially. We show that this is not quite correct. With optimal cash management, defaults occasioned by deliberate underperformance (strategic defaults) and those forced by inadequate cash (liquidity defaults) work as substitutes: allowing for strategic debt-service leads to a decline in the equilibrium likelihood of liquidity defaults. In some cases, this decline is sufficiently sharp that equilibrium debt values actually increase and yield spreads decline. We provide an intuitive explanation for these results in terms of an interaction of optionalities.

Strategic debt-service, optimal cash management, liquidity defaults, strategic defaults, yield spreads

Abstract:
In this paper, we propose an alternative approach for pricing and hedging American barrier options. Specifically, we obtain an analytic representation for the value and hedge parameters of barrier options, using the decomposition technique of separating the European option value from the early exercise premium. This allows us to identify some new put-call "symmetry" relations and the homogeneity in price parameters of the optimal exercise boundary. These properties can be utilized to increase the computational efficiency of our method in pricing and hedging American options.

Our implementation of the obtained solution indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. Our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and efficiency. In particular, the method is free of the difficulty that existing numerical methods have in dealing with spot prices in the proximity of the barrier, the case where the barrier options are most problematic.

Abstract:
In this paper, we present a new method for pricing and hedging American options along with an efficient implementation procedure. The proposed method is efficient and accurate in computing both option values and various option hedge parameters. We demonstrate the computational accuracy and efficiency of this numerical procedure in relation to other competing approaches. We also show how the method can be applied to the case of any American option for which a closed-form solution exists for the corresponding European option.