Specification Analysis of Structural Credit Risk Model with Stochastic Volatility (original) (raw)
Related papers
Specification Analysis of Structural Credit Risk Models
SSRN Electronic Journal, 2008
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.
SSRN Electronic Journal, 2000
We develop a structural credit risk model in which the unobserved asset volatility of the firm follows a GARCH process, as in . We estimate our model using an Expectation Maximization algorithm, and benchmark it using simulated data against the Merton (1974) model, both when the latter is calibrated, and when its parameters are estimated using maximum likelihood techniques as in . The Duan method slightly outperforms GARCH when asset volatility is constant, and GARCH significantly outperforms both the Merton and Duan models when the asset follows a GARCH process. An application of the three models studied to the CDS market for the debt of US banks and financial corporations during the period 2007-2008 indicates high levels of asset volatility and financial leverage for many major banks during this period, although only moderate evidence of stochastic volatility. The GARCH model outperforms both the Duan and Merton models in out-of-sample CDS spread prediction. We document a wide incidence of inversion of the spread term structure in the CDS market, both in 2007 and 2008, and all three models exhibit an inverted spread term structure for all banks studied. The group of banks in which the models are able to generate nontrivial spreads is characterized by significantly higher equity time series volatility, higher average CDS spreads across all maturities, and a higher incidence of spread term structure inversion.
SSRN Electronic Journal, 2011
The aim of this paper is to define a model which allows traders to assess the value of equity and credit derivatives in a unified framework. We propose closed-form formulas which traders could use to evaluate equity, equity options and credit default swaps (CDSs) in a consistent way. The model can also be used to solve the inverse problem, that is to extract credit-risk sensitive information from market quotes of equity/credit derivatives. In particular, we wish to estimate the firm's leverage, as it is perceived by traders. This goal is achieved within a model à la Leland (1994), where stockholders have a perpetual American option to default. After making the case for modeling debt in terms of a single perpetual-bond equivalent issue, we define leverage, show the stochastic nature of equity volatility and derive the term structures of default probabilities and credit spreads by making use of the first-passage time distribution function. Then, we give new formulas for call and put options written on stockholders' equity. The formulas, which depend on the leverage parameter L and make use of the univariate normal distribution function, are consistent with the volatility skew observed in the equity options market and converge to the Black-Scholes-Merton (BSM) equations for L → 1. All the Greeks are simple functions of the standard corresponding letters of the BSM model. The paper concludes with an application of the model to the case of Lehman Brothers and General Motors.
On the single name CDS price under structural modeling
Journal of Computational and Applied Mathematics, 2014
Regulators, banks and other market participants realized that true assessment of the credit risk is more critical and complex than their ex-ante appraisals after the US Credit Crunch. They have turned their attention to complex credit risk models and credit instruments such as credit derivatives. Credit default swap contracts (CDSs) are the most common credit derivatives used for speculation and hedging purposes in the credit markets. Thus, in this paper we fundamentally study the pricing of a single name CDS via the discounted cash flow method with survival probability functions of two pioneer structural credit risk models, Merton model and Black-Cox model with constant barrier. Hence, this approach is not only a new one, but also provides a practical technique to price CDSs using publicly available data of equity returns.
The GARCH Structural Credit Risk Model
We develop a structural credit risk model in which the unobserved asset volatility of the firm follows a GARCH process, as in . We estimate our model using an Expectation Maximization algorithm, and benchmark it using simulated data against the Merton (1974) model, both when the latter is calibrated, and when its parameters are estimated using maximum likelihood techniques as in . The Duan method slightly outperforms GARCH when asset volatility is constant, and GARCH significantly outperforms both the Merton and Duan models when the asset follows a GARCH process. An application of the three models studied to the CDS market for the debt of US banks and financial corporations during the period 2007-2008 indicates high levels of asset volatility and financial leverage for many major banks during this period, although only moderate evidence of stochastic volatility. The GARCH model outperforms both the Duan and Merton models in out-of-sample CDS spread prediction. We document a wide incidence of inversion of the spread term structure in the CDS market, both in 2007 and 2008, and all three models exhibit an inverted spread term structure for all banks studied. The group of banks in which the models are able to generate nontrivial spreads is characterized by significantly higher equity time series volatility, higher average CDS spreads across all maturities, and a higher incidence of spread term structure inversion.
Can structural models price default risk? New evidence from bond and credit derivative markets
2005
Abstract: Using a set of structural models, we evaluate bond yield spreads and the price of default protection for a sample of US corporations. Theory predicts that if credit risk alone explains these two quantities, their magnitudes should be similar. Our findings concur with previous results that bond yield spreads are underestimated. However, this is not systematically the case for CDS premia, which in our dataset are much lower than bond spreads.
Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms
Review of Financial Studies, 2009
A structural model with stochastic volatility and jumps implies particular relationships between observed equity returns and credit spreads. This paper explores such effects in the credit default swap (CDS) market. We use a novel approach to identify the realized jumps of individual equity from high frequency data. Our empirical results suggest that volatility risk alone predicts 50% of CDS spread variation, while jump risk alone forecasts 19%. After controlling for credit ratings, macroeconomic conditions, and firms' balance sheet information, we can explain 77% of the total variation. Moreover, the marginal impacts of volatility and jump measures increase dramatically from investment grade to high-yield entities. The estimated nonlinear effects of volatility and jumps are in line with the model impliedrelationships between equity returns and credit spreads.
2004
The joint behaviour of equity premiums and credit spreads on securities issued by the same company provides a direct statistical evidence of the degree of efficiency of equity and fixed income markets, whose participants are expected in the long term to provide a common risk assessment. Increasing interest in the financial industry is attracted both for financial engineering and trading purposes, by the potentials offered by contracts with equity and fixed income components. Increased liquidity in the credit default swaps (CDS) market, on the other hand, provides new grounds for fixed income analysis based on the statistical study of theoretical versus actual spread movements. In the paper we analyse the statistical relationship between CDS spreads, stocks implied volatility and theoretical spreads generated by an application of Merton seminal structural default model. A measure of price discrepancies is also proposed, based on the difference between theoretical and actual spread be...
Structural Credit Modeling Under Stochastic Volatility
International Journal of Statistics and Probability, 2012
This paper presents a structural credit model with underlying stochastic volatility, a CIR process, combining the Black/Cox framework with the Heston Model. We allow to calibrate a Heston Model for a non-observable process as underlying of the Black/Cox Model. A closed-form solution for the price of a down-and-out call option on the assets with the debt as barrier and strike price is derived using the concept of optional sampling. Furthermore, estimators are derived with the Method of Moments for Hidden Markov Chains. As an application in Statistical Finance, the default probabilities of Merrill Lynch during the financial crisis are examined.
An empirical analysis of structural models of corporate debt pricing
Applied Financial Economics, 2007
This paper tests empirically the performance of three structural models of corporate bond pricing, namely Merton (1974), Leland (1994) and Fan and Sundaresan (2000). While the first two models overestimate bond prices, the Fan and Sundaresan model reveals an extremely good performance. When considering the prediction of credit spreads, the three models underestimate market spreads but, again, Fan and Sundaresan has a better performance. We find rating, maturity and asset volatility effects in the prediction power, as the models underestimate less the spreads of riskier firms and of bonds with better rating quality and longer maturity. Moreover, our results reveal the existence of a new industry effect. Spread errors are systematically related to some bond-and firm-specific variables, as well as term structure variables.