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3.2.3 Different Quotations and Different Currencies

Let us consider the situation where we bought protection against the default of a certain borrower by entering into a CDS where we pay a premium C1. Some time later, the credit of the same borrower deteriorates and we sell, for the same maturity and amount, protection receiving a higher coupon C2. As far as our income is concerned we have a risky annuity

(3.18)

that is, an income that is heavily subjected to credit risk. During the financial crisis of 2007 to 2009 a new type of CDS quotation became common, one that would make any gain or loss immediate and eliminate a situation such as the one above.

In the new CDS contract, the premium paid by the protection buyer would be split into two parts, a coupon similar to the old one but taking only a small set of specific values (25, 100, 500, and 1,000 bps) and an upfront premium. Let us consider the situation above in the new framework. We buy protection against the default of a certain borrower by paying an up-front premium U1 and a running coupon C100 of, say, 100 bps, so that the present value of the protection leg is

(3.19)

A quote screen for Germany CDS rate. Source: Thomson Reuters Eikon.

FIGURE 3.3 A quote screen for Germany CDS rate. Source: Thomson Reuters Eikon.

which is negative since we are paying for the protection. When the credit of the borrower deteriorates, we sell protection by receiving an up-front premium U2 (with U2 > U1) and a running coupon which remains equal to 100 bps, that is, C100, so that the present value of the protection leg is

(3.20)

The difference between the two is U2 – U1, a gain that we realize immediately.

The new quotation is fairly recent and the trading community is still used to the old one. From Figure 3.3 we can see how the CDS is quoted in this transition period. In the top left corner we have circled the old quote. In the center of the page (also circled) we have the four quotes for the up-front we need to pay in case the running coupon is one of the four possible types (25, 100, 500, 1,000 bps). In the case of a borrower with as good a credit as Germany, we see that the up-front payment for the 100, 500, and 1,000 bps running coupons is negative. This might seem bizarre but it simply states that

the present value of those coupons is already higher than the present value of the recovery leg and so, for the contract to be worth zero at inception, the up-front needs to be negative. We notice that next to the up-front there is the equivalent conventional spread, that is, that spreadfor which the following is true

(3.21)

where x = 25, 100, 500, 1,000 and Cx is the running coupon paid in conjunction with the up-front Ux. We also note, surprisingly, that the conventional spreads are different from one another whereas we would expect them to be the same. The reason is that there are different levels of demand for the four types of up-front. For example, it would be strange to enter into a CDS contract on Germany agreeing to pay such a high running coupon as 1,000 bps and therefore the demand for that contract (and probably the 500 bps as well) is likely to be small. Not surprisingly the two equivalent spreads closest to the one in the top left corner are the ones corresponding to the 25 and 100 bps running coupons.

As far as the calibration of the hazard rates hk,k+1 is concerned, the process is identical, except that now we need to apply our solver algorithm to

(3.22)

Those who have read the screen shown in Figure 3.3 carefully might have noticed that the quote displayed is for the CDS level in USD. What does the specification of the currency entail? This is a very complex field and we are simply going to describe what is available in the market.

There are four types of CDS traded in the market with varying levels of liquidity:

┠CDS spread paid in USD to protect USD-denominated debt

┠CDS spread paid in foreign currency to protect USD-denominated debt

┠CDS spread paid in USD to protect foreign currency-denominated debt

┠CDS spread paid in foreign currency to protect foreign currency denominated debt

The first type is the one we have dealt with even though it was not explicitly stated. An entity issues debt in USD and we pay a premium in USD to buy protection against its default.

The fourth type tends to be the least common and this has to do with the willingness of investors to purchase debt in foreign currency. In general investors are wary of buying debt in local currency[1] since a government could in principle fend off default by printing money to pay off the debt: due to the subsequent inflation, investors would be holding something almost worthless. This is particularly true for small emerging markets (larger ones such as India can rely on local investors who are more willing to take the risk than foreign ones) and less so for large, developed countries (e.g., Japan, Canada, etc.).

As far as Euro zone members are concerned, the Euro should be considered, when it comes to debt, a foreign currency since individual members have no money-printing ability. As a consequence, the CDS spread in local currency to protect debt in local currency (e.g., spread in South African Rand to protect South African Rand-denominated debt) is usually very low. Since the government has the option to print money, the default on local debt is unlikely.

The second and third type are the most interesting ones and are sometimes referred to as quanto CDS. The third is becoming common in the context of sovereign European debt. The connection between FX and credit is very interesting. Ehlers and Schobucher [35] look at it in great detail (their main focus is entities issuing debt not in their home currencies). The reason is that there is a strong correlation between credit and FX in case of default. When a country defaults (and one could argue the same for some very large and important corporates), the currency tends to depreciate very rapidly, that is, the value of X/USD, the number of X we receive for one U.S. Dollar, increases considerably. To model this can be very challenging in the sense that not only do we need a model where the correlation between FX and credit is not zero, but a diffusion model for FX (the standard approach) might not be enough and we need to turn to a jump-diffusion model. This is because we need to deal with a situation where the motion of the underlying is fairly volatile on average but with sudden, rare and large jumps. While interesting to mention, these types of CDS would rarely be traded by a treasury desk or a development institution.

  • [1] The alternative use of local and foreign here is probably confusing, but we have already mentioned when discussing FX forwards that this is the way traders tend to think. Although USD is a currency foreign to many countries, it is so commonly used that it holds a special status. Currencies that are non-USD are referred to as foreign, and currencies that not only are non-USD but tend to be weaker currencies are referred to as local. A trading desk in say, South Africa, would have traders trading USD instruments and traders trading local instruments by which we intend South African Rand (ZAR) or other African currencies denominated instruments.
 
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