Risk Structure Of Interest Rates Research Articles

Introducing and testing the Carr model of default

The Merton (On the pricing of corporate debt: The risk structure of interest rates. J. Finance, 1974, 29, 449–470) model is often considered the simplest structural model of default. Its famous modification developed by KMV is also widely used and well understood by both practitioners and academics. However, as the underlying asset process is driven by a diffusion process, the Merton model suffers from the well-known issue of the vanishing of credit spreads for progressively shorter maturities. To overcome such shortfall, several modifications have been proposed in the literature; however, none of these, despite succeeding at better pricing spreads and explaining default dynamics, are able to retain the simplicity of the Merton model. In this paper, we propose a new structural model of default driven by an additive process whose pricing formulas are as simple as – if not even simpler than – those of the Merton model. We named such model the Carr model of default after Peter Carr, given his recent passing and the fact that the underlying asset distribution is the one introduced in Carr and Torricelli (Additive logistic processes in option pricing. Finance Stoch., 2021, 25, 689–724) and Carr and Maglione (Compound option pricing and the Roll-Geske-Whaley formula under the conjugate-power Dagum distribution. J. Deriv., 2022, 31, 1–32). We first provide pricing formulas for the firm's claims and credit spreads, and then discuss a general theory of change of measure for such processes in order to introduce a distance-to-default version of this newly-introduced model. Finally, we empirically test the Carr versus the Merton model and document the far better ability of the Carr model to reproduce CDS spreads as well as explain their cross-sectional and time-series variation.

Secured Debt, Agency Problems, and the Classic Model of the Firm

In the traditional literature on firm models it is generally accepted that secured debt reduces the agency costs of debt, as it alleviates the underinvestment and overinvestment problems. We demonstrate that secured debt can also produce the opposite effects. Under the [Merton 1974, On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance 29, 442–470] framework, we provide numerical examples where junior secured debt produces underinvestment and senior and all-assets secured debt bring about overinvestment. Project financing and independent-firm financing eliminate these problems but may induce suboptimal decisions for shareholders. We show that shareholders will finance a project as an independent firm if its net present value is sufficiently high. Otherwise, they are better off financing the project with all-assets secured debt.

Foreign capital flows, credit spreads, and the business cycle

Previous studies have found that foreign capital flows into the US Treasury and corporate-bond markets drive US long-term interest rates. In this paper, we extend the literature by showing that (1) foreign capital flows also drive the US risk structure of interest rates (i.e., credit spreads), and (2) the impacts of foreign capital flows through the credit spread on corporate financing and investment as well as aggregate economic activities are significant, even outside of the Global Financial Crisis period.

Credit Ratings and Credit Risk: Is One Measure Enough?

This paper investigates the information in corporate credit ratings. If ratings are to be informative indicators of credit risk, they must reflect what a risk-averse investor cares about: both raw default probability and systematic risk. We find that ratings are relatively inaccurate measures of raw default probability—they are dominated as predictors of failure by a simple model based on publicly available financial information. However, ratings do contain relevant information since they are related to a measure of exposure to common (and undiversifiable) variation in default probability (“failure beta”). Systematic risk is shown to be related to joint default probabilities in the context of the Merton [Merton RC (1974) On the pricing of corporate debt: The risk structure of interest rates. J. Finance 29(2):449–470] model. Empirically, it is related to credit default swap spreads and risk premia. Given the multidimensional nature of credit risk, it is not possible for one measure to capture all the relevant information. This paper was accepted by Gustavo Manso, finance.

Pricing Recovery Risk via a Partial Information Transform

In his seminal paper, Wang ( S. S. Wang, A Universal Framework for Pricing Financial and Insurance Risks, ASTIN Bulletin, Volume 32, Issue 02 November 2002, pp 213-234) proposes a transform method to price both liabilities and contingent claims, whether traded or not. One application of the Wang Transform is in option pricing, which for example can be used in the structural modeling of defaultable bonds. The classical Merton model (R.C. Merton, On the pricing of corporate debt: The risk structure of interest rates, The Journal of Finance 29.2, 449-470, 1974.) assumes that default and post-default recoverable values are driven by a common stochastic factor, that of the firm's asset value. However, a single factor for pricing such bonds assumes that bond and equity returns are perfectly correlated, which need not be true. methods, (A. Cohen and N. Costanzino, Bond and CDS Pricing with Recovery Risk I and II, SSRN preprints) address the entanglement of recovery risk with default risk in the pricing of defaultable bonds. The authors show that this mixture can lead to errors in estimating the total risk that investors in these bonds have undertaken. The taken also considers related instruments such as CDS's and equity as well as solving the related boundary value problems for bond price. The time value of money is another important aspect of bond pricing, and in the same issue that Wang's paper appeared, Buhlmann (H. Buhlmann, New Math for Life Actuaries, ASTIN Bulletin, Volume 32, Issue 02 November 2002, pp 209-211.) proposed a paradigm shift in thinking about this technology. In his editorial, Buhlmann advocated switching to a based approach for teaching financial risk to actuaries. In our short note, we present a transform for a multifactor bond-pricing model that represents the partial information available to firm managers about recoverable value. In the spirit of Buhlmann's proposal, this is dependent on the choice of numeraire as well as the conditions for default. We will recover a version of the Wang Transform in the classical Merton model, and will calculate the transformed default probability in two other related structural models. The effect of this extra uncertainty about post-default recovery, we will see, can be observed through the distortion of the original default risk. Three examples are used to illuminate the approach, including a model that incorporates short-term credit spreads into asset and recovery value evolution.

Tail Dependence of Financial Stocks and CDS Markets – Evidence Using Copula Methods and Simulation-Based Inference

Abstract Using copula methods and simulation-based inference, the authors investigate the association between the performance of a stock index formed by European financial institutions and a basket of CDS contracts of the same sector. Their analysis focuses on (i) assessing the dependence structure of the markets when extreme events occur, and (ii) checking the validity of the conclusion by Merton (On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, 1974) and other similar structural models that there is an intensification of the relationship between stock prices and credit spreads after large negative shocks in the value of firms’ assets. The authors show that there is a large tail dependence between the two portfolios. However, the dependence structure seems to be similar with respect to positive and negative innovations in the indexes. Their findings suggest that credit models’ implications do not apply to financial firms, likely because the implicit subsidies from governments to financial institutions are distorting the dependency structure.

The Cost of Capital in Markets with Opaque Intermediaries and the Risk-Structure of Interest Rates

The demand for cash balances of financial intermediaries that establish contractual liabilities with credit-sensitive customers is characterised. As stated by Merton, the success of the business activities of such firms crucially depends on their credit quality, and hence, they are obliged to rely on deposit insurance and capital cushions in order to assure that their promised payments are free of default. Unlike the Merton’s approach, the optimal guaranteeing contract is formulated in actuarial terms in this paper, because in this way the model can be extended to consider the situation of firms that can only hedge up to a limited extent. Within this framework, the equilibrium in the market determines the rate at which a unit of capital is exchange by a unit of risk, or, in other words, it determines the market price of risk. Episodes of liquidity crises are meaningful in this theoretical setting.

Single and Double Black–Cox: Two approaches for modelling debt restructuring

In this paper we propose two first-passage-time approaches for pricing debt and equity when the firm is able to restructure its debt as an alternative to liquidation. In contrast to other first passage models that account for reorganization, our approaches allow the firm to restructure its debt by changing its maturity and/or its face value. The first approach developed consists of a first-passage model for reorganization together with a Merton approach for default, while the second approach uses first-passage models for both reorganization and default. We also provide a comparison of the proposed approaches with the Merton (Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29, 449–470.) and Black and Cox (Black, F. and Cox, J.C., 1976, Valuing corporate securities: Some effects of bond indenture provisions. Journal of Finance, 31, 351–367.) models.

Accounting-based versus market-based cross-sectional models of CDS spreads

Models of financial distress rely primarily on accounting-based information (e.g. [Altman, E., 1968. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance 23, 589–609; Ohlson, J., 1980. Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research 19, 109–131]) or market-based information (e.g. [Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, 449–470]). In this paper, we provide evidence on the relative performance of these two classes of models. Using a sample of 2860 quarterly CDS spreads we find that a model of distress using accounting metrics performs comparably to market-based structural models of default. Moreover, a model using both sources of information performs better than either of the two models. Overall, our results suggest that both sources of information (accounting- and market-based) are complementary in pricing distress.

Hedging credit: Equity liquidity matters

Abstract We theorize and confirm a new channel by means of which liquidity costs are embedded in CDS spreads. We show that credit default swap (CDS) spreads are directly related to equity market liquidity in the Merton [Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. J. Finance 29, 449–470] model via hedging. We confirm this relationship empirically using a sample of 1452 quarterly CDS spreads over 2001–2005. In the model, this relationship is monotone increasing when credit quality worsens. These results are robust to alternative measures of equity liquidity and other possible determinants of CDS spreads.

Structural models of credit risk are useful: Evidence from hedge ratios on corporate bonds

Structural models of credit risk provide poor predictions of bond prices. We show that, despite this, they provide quite accurate predictions of the sensitivity of corporate bond returns to changes in the value of equity (hedge ratios). This is important since it suggests that the poor performance of structural models may have more to do with the influence of non-credit factors rather than their failure to capture the credit exposure of corporate debt. The main result of this paper is that even the simplest of the structural models [Merton, R., 1974. On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 29, 449–470] produces hedge ratios that are not rejected in time-series tests. However, we find that the Merton model (with or without stochastic interest rates) does not capture the interest rate sensitivity of corporate debt, which is substantially lower than would be expected from conventional duration measures. The paper also shows that corporate bond prices are related to a number of market-wide factors such as the Fama-French SMB (small minus big) factor in a way that is not predicted by structural models.

A market-based framework for bankruptcy prediction

We estimate probabilities of bankruptcy for 5784 industrial firms in the period 1988–2002 in a model where common equity is viewed as a down-and-out barrier option on the firm's assets. Asset values and volatilities as well as firm-specific bankruptcy barriers are simultaneously backed out from the prices of traded equity. Implied barriers are significantly positive and monotonic in the firm's leverage and asset volatility. Our default probabilities display better calibration and discriminatory power than the ones inferred in a standard Black and Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. J. Pol. Econ. 81, 637–659]/Merton [Merton, R.C., 1974. On the pricing of corporate debt: the risk structure of interest rates. J. Finance 29, 449–470] and KMV frameworks. However, accounting-based measures such as Altman Z- and Z″-scores outperform structural models in 1-year-ahead bankruptcy predictions, but lose relevance as the forecast horizon is extended.

A simple continuous measure of credit risk

This paper introduces a simple parameterization for the risk-neutral default probability distributions for risky firms that are easily computed from quoted bond prices. The corresponding expected times to default have a particularly simple form and are proposed as a measure for credit risk. Being continuous in nature, times to default provide a much finer measure of risk than those provided by ratings agencies. Comparison with the ratings provided by Moody's and the distance to default measures calculated using the Merton [Merton, R. (1974). On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance, 2(2), 449–470] model shows that the highest rank correlation is found between the proposed time to default measure and Moody's ratings.

An Empirical Estimation of Default Risk of the UK Real Estate Companies

Based on the Black and Scholes (Black, F., and M. Scholes. (1973). The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81, 637–659) and Merton (Merton, R. C. (1974). On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance 29, 449–470) (BSM) contingent claims model, and KMV Corporation framework, we estimate the distance to default and the “risk neutral” default probabilities for a sample of 112 real estate companies over the period 1980 to 2001. Our empirical results classifies failed and non-failed companies into Type I error, cases that the BSM-type model fails to predict default when it did occur, and Type II error where BSM-type model predicts default when it did not occur. We find that none of the companies belong to the category of Type I error. Type II error is observed in 12 out of 112 companies. These results support the theoretical underpinnings of the BSM-type structural model in that the two driving forces of default are high leverage and high asset volatility.

Default risk, systematic risk and Thai firms before, during and after the Asian crisis

This paper applies the Merton [Merton, R., 1974. On the pricing of corporate debt: the risk structure of interest rates. J. Finance 2 (2), 449–470] default probability model to the firms in the SET50 index at the Stock Exchange of Thailand (SET). It also examines the relationship between a firm's default probability and firm-specific characteristics like size and book-to-market ratio, and whether default risk is systematic or not. We believe this to be the first paper dealing with these issues using data from an emerging country. The study also differs from other studies by dealing with how the default risk of firms in different sectors of the economy changes during a severe crisis. Overall, we find a significant increase in market based default probabilities around the crisis and a fairly slow return to pre-crisis levels. The first sector to suffer a deterioration in creditworthiness was the sector of finance and securities firms and the worst effected sector at the peak of the Asian crisis was the building materials sector. There are further some indications of the most distressed firms being on average somewhat smaller than the least distressed, but only during the crisis. We do not find significant evidence of the book-to-market ratio being related to the default risk in this particular market, though. Finally, if default risk is systematic, one would expect that default risk is rewarded by higher returns. However, in this sample the level of default risk of a firm does not seem to be able to explain the firm's subsequent realized returns at different horizons. We therefore reject the hypothesis that default risk is systematic.

Risk structure of interest rates: an empirical analysis for Deutschemark-denominated bonds

This paper empirically studies the risk structure of interest rates for Deutschemark-denominated bonds. For this purpose, we estimate term structures of interest rates using the parsimonious fitting function of Nelson and Siegel (1987) for virtually risk free Government bonds and five different rating categories classified by Moody’s ratings (Aaa, Aa, A, Baa, Ba). The sample period covers the time interval from July 1990 to December 1996. We investigate the pricing errors resulting from our estimation procedure and analyse credit spreads over the term structure of Government bonds.

Continuous-Time Finance.

Section I: Introductin to Finance and the Mathematics of Continuous-Time Models 1 Modern Finance 2 Introduction to Portfolio Selection and Capital Market Theory: Static Analysis 3 On the Mathematics and Economic Assumptions of Continuous-Time Financial Models Section II: Optimum Consumption and Portfolio Selection in Continuous-Time Models 4. Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case 5. Optimum Consumption and Portfolio Rules in a Continuous-Time Model 6. Further Developments in theory of Optimal Consumption and Portfolio Selection Section III: Warrant and Option Pricing Theory 7. A Complete Model of Warrant Pricing the Maximizes Utility 8. Theory of Rational Option Pricing 9. Option Pricing when Underlying Stock Returns are Discontinuous 10. Further Developments in Option Pricing Theory Section IV: Contingent-Claims Analysis in the Theory of Corporate Finance and Financial Intermediation 11. A Dynamic General Equilibrium Model of the Asset Market and its Application to the Pricing of the Capital Structure of the Firm 12. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates 13. On the Pricing of Contingent Claims and the Modigliani-Miller Theorem 14. Contingent Claims Analysis in the Theory of Corporate Finance and Financial Intermediation Section V: An Intertemporal-Equilibrium Theory of Finance 15. An Intertemporal Capital Asset Pricing Model 16. A General Equilibrium Theory of Finance in Continuous-Time Section VI: Applications of the Continuous-Time Model to Selected Issues in Public Finance 17. An Asymptotic Theory of Growth Under Uncertainty 18. On Consumption-Indexed Public Pension Plans 19. An Analytic Derivation of the Cost of Loan Guarantees and Deposit Insurance 20. On the Cost of Deposit Insurance when there are Surveillance Costs

Some Empirical Estimates of the Risk Structure of Interest Rates

ABSTRACTThis paper investigates the risk structure of interest rates using pure discount bonds. The most striking feature of our estimates of default‐risk premia is the resemblance of their time profile to the theoretical time profile obtained by Merton (1974).

Some Empirical Estimates of the Risk Structure of Interest Rates

Some Empirical Estimates of the Risk Structure of Interest Rates

THE INFORMATIONAL CONTENT OF BOND RATINGS

AbstractThis paper explores the risk structure of interest rates. The focus is on whether yields on industrial bonds indicate that market participants base their evaluations of a bond issue's default risk on agency ratings or on publicly available financial statistics. Using a non‐linear least squares procedure, the yield‐to‐maturity is related to Moody's rating, Standard and Poor's (S&P) rating, and accounting measures of creditworthiness such as coverage and leverage. Market yields are found to be significantly correlated with both the ratings and a set of readily available financial accounting statistics. These results indicate (1) that market participants base their evaluations of an issue's creditworthiness on more than the agencies' ratings and (2) that the ratings bring some information to the market above and beyond that contained in the set of accounting variables. The paper also asks whether the market views Moody's and Standard and Poor's ratings as equally reliable measures of risk or whether the market attaches more weight to one agency's ratings than the other. Finally, the hypothesis that the market pays more attention to the accounting measures and less to the ratings if the rating has not been reviewed recently is tested.