Default risk

Some EU Member States have also applied similar lifetime cancer risk estimates in judging tolerable risk levels. There is as yet no EU harmonized view on such default risk estimates at a policy level, although the starting point for the derivation of limit values for the general population in relation to the EU directives on ambient air and drinking water quality is the 10 lifetime risk for genotoxic carcinogens. 

Vol. 543 C. Benkert, Default Risk in Bond and Credit Derivatives Markets. IX, 135 pages. 2004. 

Vol. 582 J. Andritzky, Sovereign Default Risks Valuation Implications of Debt Crises and Bond Restructurings. 

Consumers expect to have multiple credit cards and to carry balances on more than one credit account. NO Lenders only extend a certain amount of credit per person to spread default risk across multiple borrowers. Assign everyone s single credit account at birth, funded jointly by multiple lenders. 

DEFAULT RISK AND DEFAULT SPREADS 8.2.1 The Theoretical Default Spread... 

We have stated that the yield premium required on a corporate bond accounts for the default risk exposure of such a bond. The level of yield spread is determined by the expected default loss of the bond and it is assumed that investors can assess the level of the default risk. This makes it possible to calculate the level of the theoretical default spread. 

This means that p f) is the expected value of the present value of the bond s cash flows, that is, the expected yield gained by buying the bond at the price p f) and holding it to maturity is r. If our required yield is r, for example this is the yield on the equivalent-maturity government bond, then we are able to determine the coupon rate C for which p r) is equal to 100. The default-risk spread that is required for a corporate bond means that C will be greater than r. Therefore, the theoretical default spread is C — r basis points. If there is a zero probability of default, then the default spread is 0 and C = r. 

Generally, the theoretical default spread is almost exactly proportional to the default probability, assuming a constant default probability. Generally, however, the default probability is not constant over time, nor do we expect it to be. In Figure 8.3, we show the theoretical default spread for triple-B-rated bonds of various maturities, where the default probability rises from 0.2% to 1 % over time. The longer dated bonds, therefore, have a higher aimual default risk and so their theoretical default spread is higher. Note that after around 20 years the expected default probability is constant at 1%, so the required yield premium is also fairly constant. 

Portfolio managers must also take account of a further relationship between default risk and interest-rate risk. That is, if two corporate bonds have the same duration but one bond has a higher default probability, it essentially has a shorter duration because there is a greater chance that it will experience premature cash flows, in the event of default. 

This means that an investor who holds bonds that carry an element of default risk should in theory take this default risk into consideration when calculating the duration of his or her portfolio. In practical terms this only has an effect with unrated or junk bonds, which have default probabilities much greater than 1%. Figure 8.5 shows how the theoretical duration of a bond decreases as its assumed default probability increases. 

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 . 

First, it considers both default risk and interest-rate risk ... 

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 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 equity value is the main variable for driving the default risk. 

Duffee, G.R., 1996b. Estimating the Price of Default Risk. Federal Reserve Board, Washington, DC. Duffee, G.R., 1998. The relation between treasury yields and corporate bond yield spreads. J. Financ. 53 (6), 2225-2241. 

Tudela, M., Young, G., 2003. A Merton-model approach to assessing the default risk of UK public companies. Bank of England Working Paper, No. 194, June. 

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. 

Kovalov, P., Linetsky, V., 2008. Valuing convertible bonds with stock price, volatility, interest rate, and default risk. Working Paper No. 2008-02, EDIC Center for Financial Research. 

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. 

Thus far our coverage of valuation has been on fixed-rate coupon bonds. In this section we look at how to value credit-risky floaters. We begin our valuation discussion with the simplest possible case—a default risk-free floater with no embedded options. Suppose the floater pays cash flows quarterly and the coupon formula is 3-month LIBOR flat (i.e., the quoted margin is zero). The coupon reset and payment dates are assumed to coincide. Under these idealized circumstances, the floater s price will always equal par on the coupon reset dates. This result holds because the floater s new coupon rate is always reset to reflect the current market rate (e.g., 3-month LIBOR). Accordingly, on each coupon reset date, any change in interest rates (via the reference rate) is also reflected in the size of the floater s coupon payment. 

The default risk component of a swap spread will be smaller than for a comparable bond credit spread. The reasons are straightforward. First, since only net interest payments are exchanged rather than both principal and coupon interest payments, the total cash flow at risk is lower. Second, the probability of default depends jointly on the probability of the counterparty defaulting and whether or not the swap has a positive value. See John C. Hull, Introduction to Futures and Options Markets, Third Edition (Upper Saddle River, NJ Prentice Hall, 1998). 

Although spreads may be viewed as a function of default risk and recovery risk, spread models do not attempt to break down the spread into its default risk and recovery risk components. 

The pricing of credit default swaps is determined in the credit default swap market by traders who determine the credit default swap spread through their assessment of the default risk of the reference obligations. This spread information can give valuable information about the key pricing components of the reference credit implied probability of default of the reference credit and recovery assumptions. These price... 

In the situation where the risk of a technical default risk is higher for credit default swaps than cash bonds. This results in protection sellers demanding a higher premium. For example, default swaps may be triggered by events that do not constitute a full default on the corresponding cash asset. 

Robert Jarrow and Stuart Turnbull, Pricing Derivatives on Financial Securities Subject to Default Risk, Journal of Finance 50, no. 1 (1995), pp. 53-86. Kamakura Risk Information Services Credit Risk Overview Kamakura s Press Release, Kamakura Launches Basel II Default Probability Service and Announces First Client, October 31, 2002. 

As credit becomes the new buzzword in Europe, portfolio managers have to pay attention to the spread or risk premium that they receive as compensation for taking on increased default risk. 

A much easier method of generating leverage in a credit portfolio is through credit default swaps (CDS). They let investors take on or lay off default risk in an unfunded manner. Selling default protection enables one to receive the premium associated with the additional credit risk without the need to buy a bond of that entity, and in the process creates enormous leverage, especially for higher rated credits. The increased liquidity and the compression of bid/offer spreads have added to the attractiveness of this market. 

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