In the following, we develop a model for pricing defaultable debt that is capable of reflecting real world phenomena realistically. Before we actually introduce the model, we make some heuristic observations to motivate the theory. Throughout the following sections we examine and extend these considerations further: Since defaults actually happen, a bond pricing model must be able to deal with default events: For example, in August 1999 Ecuador defaulted on interest rate payments of Brady bonds with a total amount of about US$ 6 billions. In October 1999 there was a second default of US$ 500 millions. Figure 6.1 shows the yields to maturity and S&P ratings of an Ecuadorian sovereign bond that was downgraded to the rating D in September 1999. Rating agencies can’t check the ratings on a daily basis or even continuously. Ratings of rating agencies can only be described by discrete time processes. But the quality of an obligor usually changes according to a continuous time process (see, e.g., figure 6.1). Thus, the quality or the distance to default of an obligor should be observed continuously. Very often the quality of obligors shows mean reversion properties. In case of a downgrade the management of a firm usually takes actions to improve the quality again. Figure 6.2 shows this phenomenon for the firm Hertz. The mean reversion level of the rating of Hertz is A- and A3 for S&P’s and Moody’s rating, respectively. Many models for pricing defaultable zero coupon bonds don’t allow for positive short term credit spreads: As time to maturity tends to zero the model credit spreads tend to zero, too. Obviously, these models are far away from describing reality. In figure 6.3 we show observed corporate credit spreads for different maturities. Even bonds with a rating of A and time to maturity of seven days can have credit spreads which are higher than 500 basis points. Hence, a model must be capable of generating high credit spreads even for short term debt. Yields and credit spreads usually depend on the quality of the obligor. The better the quality the smaller the yields (compare to figure 6.4). The time series of the yields show high correlations between the rating classes A and AAA. Gains and losses are — at least to some extend — caused by changes in the quality of the obligor. Credit spread processes often show mean reversion properties. See, e.g., figure 6.5. Non-defaultable interest rates are usually mean reverting. See, e.g., figure 6.6. KeywordsDefault RiskCredit SpreadBond PriceShort RateCredit DerivativeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
11Are Credit Spreads and Interest Rates Co-Integrated? Empirical Analysis in the USD Corporate Bond Market
Are Credit Spreads and Interest Rates Co-Integrated? Empirical Analysis in the USD Corporate Bond Market
4Modelling the Evolution of Credit Spreads using the Cox Process within the HJM Framework: A CDS Option Pricing Model
Modelling the Evolution of Credit Spreads using the Cox Process within the HJM Framework: A CDS Option Pricing Model
19Vulnerable options, risky corporate bond, and credit spread
In the current literature, the focus of credit-risk analysis has been either on the valuation of risky corporate bond and credit spread or on the valuation of vulnerable options, but never both in the same context. There are two main concerns with existing studies. First, corporate bonds and credit spreads are generally analyzed in a context where corporate debt is the only liability of the firm and a firm’s value follows a continuous stochastic process. This setup implies a zero short-term spread, which is strongly rejected by empirical observations. The failure of generating non-zero short-term credit spreads may be attributed to the simplified assumption on corporate liabilities. Because a corporation generally has more than one type of liability, modeling multiple liabilities may help to incorporate discontinuity in a firm’s value and thereby lead to realistic credit term structures. Second, vulnerable options are generally valued under the assumption that a firm can fully pay off the option if the firm’s value is above the default barrier at the option’s maturity. Such an assumption is not realistic because a corporation can find itself in a solvent position at option’s maturity but with assets insufficient to pay off the option. The main contribution of this study is to address these concerns. The proposed framework extends the existing equity-bond capital structure to an equity-bond-derivative setting and encompasses many existing models as special cases. The firm under study has two types of liabilities: a corporate bond and a short position in a call option. The risky corporate bond, credit spreads, and vulnerable options are analyzed and compared with their counterparts from previous models. Numerical results show that adding a derivative type of liability can lead to positive short-term credit spreads and various shapes of credit-spread term structures that were not possible in previous models. In addition, we found that vulnerable options need not always be worth less than their default-free counterparts. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:301–327, 2001
Read more8Economic policy uncertainty and municipal corporate bonds credit spreads: Evidence from China
Economic policy uncertainty and municipal corporate bonds credit spreads: Evidence from China
46Modeling the Dynamics of Credit Spreads with Stochastic Volatility
This paper investigates a two-factor affine model for the credit spreads on corporate bonds. The first factor can be interpreted as the level of the spread and the second factor is the volatility of the spread. The riskless interest rate is modeled using a standard two-factor affine model, thus leading to a four-factor model for corporate yields. This approach allows us to model the volatility of corporate credit spreads as stochastic, and also allows us to capture higher moments of credit spreads. We use an extended Kalman filter approach to estimate our model on corporate bond prices for 108 firms. The model is found to be successful at fitting actual corporate bond credit spreads, resulting in a significantly lower root mean square error than a standard alternative model both in sample and out of sample. In addition, key properties of actual credit spreads such as the stochastic volatility of the credit spreads and the positive skewness of the credit spread distribution are better captured by the model.
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Exchange Rate Dynamics and United States Dollar-Denominated Sovereign Bond Prices in Emerging Markets
The study conducts an empirical test on dollar-denominated sovereign credit spreads in emerging markets, including Brazil, Colombia, Mexico, the Philippines, the Russian Federation, and Turkey to examine their relationship with each country’s exchange rate and the United States (US) Treasury yields. The relationship between each country’s exchange rate and the pricing of each country’s US-dollar denominated sovereign bonds was particularly strong after the global financial crisis of 2008–2009. A two-factor pricing model is developed with closed-form solutions for the sovereign bonds. The correlated factors in the model are foreign exchange rates and US risk-free interest rates that follow a double square-root process relevant in a low interest rate environment. The numerical results and associated error analysis show that the model credit spreads can broadly track market credit spreads.
Read more44Economic determinants of oil futures volatility: A term structure perspective
Economic determinants of oil futures volatility: A term structure perspective
15Corporate yield spreads and real interest rates
Corporate yield spreads and real interest rates
14Interest Rates and Credit Spread Dynamics
Corporate credit spreads narrow when the general level of rates is high, but the effect appears to go well beyond what can be justified by firm-specific and marketwide credit conditions. In this article, the authors argue that the phenomenon is largely a statistical artifact caused by failure to take account of cointegration between Treasury and corporate yields. Using a generalized impulse-response approach and conditioning on the current level of rates, they find that large shocks to the Treasury curve do not produce significant changes in credit spreads, either contemporaneously or out to three years in the future. Among other things, this empirical result calls into question assumptions commonly made in theoretical models of corporate credit risk.
Read more9No-Arbitrage Approach to Pricing Credit Spread Derivatives
Among the new credit-based derivatives are options on the yield spread between a credit-sensitive instrument and a comparable riskless bond. Valuation requires considering the behavior of both the risk-free interest rate and the credit spread, which may be correlated. A challenge in implementing valuation models for such derivatives is the need to match observed market pricing for both riskless and risky securities. In this article, Chu and Kwok show how a pricing model for credit spread options can be constructed and calibrated to the market, while maintaining its ability to produce option prices in closed form. The two correlated processes are assumed to follow the “extended Vasicek” model developed by Hull and White for arbitrage-free modeling of the interest rate. The article also shows how models of the Black-Karasinski and Heath-Jarrow-Morton type may also be fitted, though not in closed form.
Read more4DETERMINANTS OF INTEREST RATES ON CORPORATE DEBT
Abstract. The objective of this article is theoretical and methodological justifying of determining algorithm of the cost of debt capital for enterprises functioning in emerging markets (EM). The methods of research: analysis and synthesis, system analysis, comparative analysis, empirical and statistical methods, factor analysis. Results. In this article key determinants of interest rates on debt capital for enterprises and their impact on the procedure of discount rate calculation are determined. The issue of the cost of debt calculation of enterprises in condition of absence of complete information concerning systematic and non-systematic crediting risks is studied. Differences between interest rate on the loan fixed in credit agreement and expected by creditors the cost of debt are identified. It is determined that the key factor impacting the deviation level of market value of debt capital from the nominal, and respectively, deviation of the cost of debt from the cost of capital is probability of default (PD). At the minimum values of PD, the contract interest rate corresponds to the rate of cost of debt and it is advisable to use it for discount rate calculation. Critical analysis of alternative methodological approaches of the cost of debt calculation is made. Ways of integrating of market information concerning credit default swaps into the process of expected cost of debt calculation are justified. Factors of shadowing of rates of the cost of debt and ways of reducing of shadow transactions’ level in the credit market are identified. Conclusions. At high PD values, expected by market premium for default risk may exceed the contract interest rate, which necessitates constant monitoring of credit risks and appropriate adaptation of interest rates. In the paper the algorithm of such adaptation are proposed. It is shown that in the case of non-use of interest rates adjustment taking into account changes in PD, CDS and LGD, premium for creditors’ systematic risk can differ significantly from market values of similar enterprises (peer-group), and estimated value of the cost of debt can acquire negative values. Contract (promised) interest rate should be set in such way that the premium for systematic risk of providing debt capital will be at the level of similar companies and does not change significantly as a result of probability of default changes. If in practice the opposite situation occurs, it is the evidence of contract interest rate shadowing, absence of effective system of assessment and management of credit risks. For solving the problem of interest rate transparency and filling of information gaps concerning PD borrowers in EM countries, should intensify CDS market. Keywords: debt capital, default probability, non-performing loans, credit default swap, credit spread, debt capital premium, shadow economy. JEL Classification E47 Formulas: 16; fig.: 0; tabl.: 3; bibl.: 15.
Read more26Accounting for Financial Instruments
No Abstract.
61A tree implementation of a credit spread model for credit derivatives
this paper we present a tree model for defaultable bond prices which can be used for the pricing of credit derivatives. The model is based upon the two-factor Hull-White (1994) model for default-free interest rates, where one of the factors is taken to be the credit spread of the defaultable bond prices. As opposed to the tree model of Jarrow and Turnbull (1992), the dynamics of default-free interest rates and credit spreads in this model can have any desired degree of correlation, and the model can be fitted to any given term structures of default-free and defaultable bond prices, and to the term structures of the respective volatilities. Furthermore the model can accommodate several alternative models of default recovery, including the fractional recovery model of Duffie and Singleton (1994) and recovery in terms of equivalent default-free bonds (see e.g. Lando (1998)). Although based on a Gaussian setup, the approach can easily be extended to non-Gaussian processes that avoid negative interest-rates or credit spreads
Read more13Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility
Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility
4Credit Spreads and Incomplete Information
Credit Spreads and Incomplete Information
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