Credit spreads

Central banks and market practitioners use interest rates prevailing in the government bond market to extract certain information, the most important of which is implied forward rates. These are an estimate of the market s expectations about the future directirMi of short-term interest rates. They are important because they signify the market s expectafirMis about the future path of interest rates however, they are also used in derivative pricing and to create synthetic bond prices from the extent of credit spreads of corporate bonds. 

The general rule of corporate bonds is that they are priced at a spread to the government yield curve. In absolute terms, the yield spread is the difference between the yield to maturity of a corporate bond and the benchmark, generally a yield to maturity of a govermnent bond with the same maturity. Corporate bonds include a yield spread on a risk-free rate in order to compensate two main factors, liquidity premium and credit spread. The yield of a corporate bond can be assumed as the sum of parts of the elements as shown in Figure 8.1, in which the yield spread relative to a default-free bond is given by the sum of default premium (credit spread) and liquidity premium. 

Credit spread Liquidity premium Maturity premium... 

Economic environment Where weak economic conditions and low expected growth increase the credit spread. Therefore, credit spread tends to increase during the economic recession and decrease during economic boom ... 

Financial market trend In which credit spread tends to be narrow in strong financial markets and vice versa ... 

As shown in previous sections, the credit spread on a corporate bond takes into account its expected default loss. Structural approaches are based on the option pricing theory of Black Scholes and the value of debt depends on the value of the underlying asset. The determination of yield spread is based on the firm value in which the default risk is found as an option to the shareholders. Other models proposed by Black and Cox (1976), Longstaff and Schwartz (1995) and others try to overcome the limitation of the Merton s model, like the default event at maturity only and the inclusion of a default threshold. This class of models is also known as first passage models . 

This equation can also be defined in terms of yield spread that reflects the yield premium required by a bondholder above the risk-free rate. The credit spread is given by Equation (8.17) ... 

FIGURE 8.6 The effect of leverage, variance and time to maturity on credit spread. (Reproduced from Merton (1974).)... 

The empirical evidence is that by including these assumptions, the Black Cox s model generates credit spread very similar to the ones observed in the market. 

Like Black and Cox s work, the authors find spreads similar to the market spreads. Moreover, they find a correlation between credit spread and interest rate. In fact, they illustrate that firms with similar default risk can have a different credit spread according to the industry. The evidence is that a different correlation between industry and economic environment affects the yield spread on corporate bonds. Then, the duration of a corporate bond changes following its credit risk. For high-yield bonds, the interest-rate sensitivity increases as the time to maturity decreases. 

The findings show that by increasing time to maturity, bonds with high ratings have an increasing/flat credit spread curve, while low rated bonds have a hump-shaped credit curve. Moreover, the credit spread becomes wider as the value of w increases. 

Leland and Toft (1996) updated Leland s results by investigating the effect of debt maturity on bond value, credit spreads and optimal amount of debt. In particular ... 

The credit spread is defined as the difference between the risky rate of a defaul-table bond and the risk-free rate of a default-free bond. In this case, with bonds priced at par, between coupon and risk-free rate, the pricing is performed like a valuation of a straight bond, including the default risk adjustment. The price is given by Equation (8.25) ... 

The research compares the model spread to the one observed in the market. In order to determine the term structure of credit spread. Eons uses historical probabilities by Moody s database, adopting a recovery rate of 48.38%. The empirical evidence is that bonds with high investment grade have an upward credit spread curve. Therefore, the spread between defaultable and default-free bonds increases as maturity increases. Conversely, speculative-grade bonds have a negative or flat credit yield curve (Figure 8.7). 

FIGURE 8.7 The term structure of credit spread for investment- and speculative-grade bonds. 

The recovery rate S is constant and exogenously determined The recovery rate depends on the seniority of debt to other liabilities, meaning that stochastic structure of credit spread is independent from the recovery rate ... 

Leland, H.E., Toft, K.B., 1996. Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads. J. Financ. 51 (3), 987-1019. 

Truck, S., Laub, M., Rachev, S.T., 2004 The terms structure of credit spreads and credit default swaps - an empirical investigation. Working Paper, September. 

Craisider a hypothetical situation. Assume that an option-free bond paying a semi-annual coupon 5.5% on par value, with a maturity of 5 years and discount rate of 8.04% (EUR 5-year swap rate of 1.04% plus credit spread of 700 basis points). Therefore, the valuation of a conventional bond is performed as follows (Figure 9.4). 

The reason to use implied volatility is that market anticipates mean reversion and uses the implied volatility to gauge the volatility of individual assets relative to the market. Implied volatility represents a market option about the underlying asset and therefore is forward looking. However, the estimate of implied volatility is conditioned by the choice of other inputs in particular, the credit spread applied in the option-free bond and the conversion premium of the tmderlying asset (Example 9.2). 

The risk-free rate affects both elements, option-free bond and embedded option. Conversely, the credit spread is applied to the risk-free rate in order to find the price of the option-free bond. If the credit spread is also included into the option pricing model, the option value rises. For instance, consider the scenario in which the risk-free rate is 1.04% and the option value is 0.46. If the risk-free rate is 7.04%, then the option value increases to 0.66. Figure 9.16 shows the effect of a different interest rate level. 

Following the risk neutral theory, the credit spread is not included into option valuation because it is independent from the default risk of the underlying asset. The inclusion of credit spread overvalues the option. 

Interest rates and credit spread A greater level of interest rates decreases the value of the option-free bond or bond floor. Because the credit spread is applied only into the bond floor valuation, a greater credit quality decreases the credit spread and interest rate, and increases the value of the option-free bond. Conversely, higher is the interest rates and credit spread, lower is the value of an option-free bond. 

In Chapter 8, we described several models to measure the term structure of credit spread and we introduced the model proposed by Longstaff and Schwartz (1995) for pricing fixed-rate debt. The authors propose also a model to valuing floating-rate notes. The equation derived for pricing floating-rate bonds is given by (10.2) ... 

Moreover, duration will be influenced by the floater s stmcture. In fact, the choice of the reference rate affects the duration depending on how much volatile the index is. The lower the frequency of couptm payments, the greater the price sensitivity between reset dates. Thus, while floating-rate notes have a lower price sensitivity to a change of the reference rate, fixed and floating-rate notes both have a price sensitivity to changes of credit spread reflecting the issuer s creditworthiness. A shift of the credit term structure will determine the decline of the bond s price. 

Consider the following example. We assume to have two hypothetical bonds, a treasury bond and a callable bond. Both bonds have the same maturity of 5 years and pay semiannual coupons, respectively, of 2.4% and 5.5%. We perform a valuation in which we assume a credit spread of 300 basis points and an OAS spread of 400 basis points above the yield curve. Table 11.1 illustrates the prices of a treasury bond, conventional bond and callable bond. In particular, considering only the credit spread we find the price of a conventional bond or option-free bond. Its price is 106.81. To pricing a callable bond, we add the OAS spread over the risk-free yield curve. The price of this last bond is 99.02. We can now see that the OAS spread underlines the embedded call option of the callable bond. It is equal to 106.81-99.02, or 7.79. In Section 11.2.3, we will explain the pricing of a callable bond with the OAS methodology adopting a binomial tree. 

Rate Flows Value Credit Spread Flows Value OAS spread Value... 

There are two main types of credit risk that a bond portfolio or position is exposed to. They are credit default risk and credit spread risk. Credit default risk is defined as the risk that the issuer will be unable to make timely payments of interest and principal. Typically, investors rely on the ratings agencies—Fitch Ratings, Moody s Investors Service, Inc., and Standard 8c Poor s Corporation—who publish their opinions in the form of ratings. 

DIHBir 6.2 The European Government Market Convergence Trade versus US Single-B Credit Spreads... 

Unless otherwise indicated, credit spread and bond volume data come from the Lehman Brothers Global Family of Indices... 

The terms spread or credit spread refer to the yield differential, usually expressed in basis points, between a corporate bond and an equivalent maturity government security or point on the government curve. It can also be expressed as a spread over the swap curve. In the former case, we refer to the fixed-rate spread. In the latter, we use the term spread over EURIBOR, or over the swap curve. 

---