Credit curves

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. 

I a Yield Curve I a Credit Curve I a Dividends 29 Volatilitv I... 

This last equation shows the direct relationship between the probability of default and the market credit default swap quotes. Therefore, using equation (21.14) and the term structure of credit, we may be able to boot-strap the market implied probability of default from the credit curves, which are in effect the range of credit default swap quotes by maturity. Equation (21.14) is only approximate because in practice we would need to ensure that the timing of projected cash flows are accurately reflected in the pricing model. For example, the actual payment on the contingent leg may depend on the settlement date for the swap. 

The credit curves (or default swap curves) reflect the term structure of spreads by maturity (or tenor) in the credit default swap markets. The shape of the credit curves are influenced by the demand and supply for credit protection in the credit default swaps market and reflect the credit quality of the reference entities (both specific and systematic risk). The changing levels of credit curves provide traders and arbitragers with the opportunity to measure relative value and establish credit positions. 

The probability of survival for a credit may be viewed as a decreasing function against time. The survival probabilities for each traded reference credit can be derived from it s credit curve. The survival probability is a decreasing function because it reflects the fact that the probability of survival for a credit reduces over time. For example, the probability of survival to year 3 is higher than the probability of survival to year 5. 

Under nonvolatile market conditions, the shape of the survival probability and the resulting credit curve will take a different form to the shape implied in volatile market conditions the graphs may change to reflect the higher perceived likelihood of default. For example, the shape of the survival probability may take the form as shown in Exhibit 21.19. 

The corresponding credit curves, which are consistent with these survival probabilities, take the form shown in Exhibit 21.20. This shows that the credit curve inversion is consistent with the changes in the survival probability functions. 

For example, the change in profit and loss as a result of bumping the credit curve by 1 bp, assuming we have a short credit (i.e., bought credit protection) that is... 

PVCL = present value of the contingent leg payments discounted at the original credit curve... 

Therefore, to hedge against profit and loss (P8cL) movements for small changes in the credit curve, we would use the following hedge ratio. 

PVCL 2 = present value of the hedging contingent leg payments discounted based on the bumped credit curve (i.e., original credit curve plus 1 bp)... 

To better understand the future relative performance, we should carry out extensive stress tests on user-defined assumptions. A portfolio can be stress-tested by analyzing the performance under different scenarios comprising various interest rate and credit curve assumptions. 

In the corporate market some issuers have well-populated credit curves, which enables relative value comparisons for a particular name. Traditionally, European financial institutions have been (and still are) the leading borrowers in the bond market. However, the number of nonfinancial issuers with well-formed credit curves continues to grow. Exhibit 26.17 lists the top five non-financial borrowers, ranked by the number of... 

Fig. 25. Partial pressure of Te2 along the three-phase curves for various solid solutions. Same credit source as for Fig. 24.

The kinetic curve would then be the result of two curves, one representing the 1st order decay attributed to isospecific polymerization centers, and the other representing a stationary state attributed to the less stereospecific centers. This expression can be credited with taking into consideration a stationary state and, furthermore, it is in agreement with the inverse correlation between productivity and isotacticity of the polymer found experimentally. In fact, assuming Is to be the isotacticity of propylene produced by the isospecific centers, unstable with time, and IA the isotacticity of polypropylene produced by the less specific centers, stable with time, the total isotactic index IIt is given by the expression ... 

The first measurement of (what is now called) a t(A] curve comes from Pockels ). She did many experiments on her kitchen table and realized the relevance of sweeping the surface before measuring. Langmuir gave generous credit to her work, although he largely independently developed the film balance that nowa-... 

Very creditable attempts have also been made to evaluate reactivity in other chemically initiated systems, e.g. Bu"OTiCl3/a-methylstyrene. Here the mechanism of initiation is complex and the concentration of active centres must be evaluated from precise kinetic curves. In spite of this difficulty Sigwalt s group in particular continues to produce some excellent work. 

Tills, the area under the curve is the sum of the product of each expenditure or credit times the difference between the mean time for receipt of revenue F... 

Figure 2. The evolution of the intergalactic ion CIV (C abundance as a function of redshift, in units of its contribution to the closing density. The constancy of the curve indicates that vigorous star formation was already underway when the universe was only 7% (where redshift is 6) of its present age. Credit Robert A. Simcoe (18).

We assume we have constructed a market curve of Libor discount factors where Df(t) is the price today of 1 to be paid at time t. From the perspective of the asset swap seller, it sells the bond for par plus accrued interest. The net up-front payment has a value 100 F where P is the market price of the bond. If we assume both parties to the swap are interbank credit quality, we can price the cash flows off the Libor curve. 

---