It has been reported in several industry publications (e.g., CreditFlux, Reuters, Derivatives Week Online) that the CDS market is likely to switch to a fixed coupon basis with upfront points. This change will lead to some fundamental changes in the risk profiles of these contracts, and in particular will affect how they can be used in hedging spread and default risk. This Learning Curve article will explore some of the most basic changes that participants in the credit markets will need to keep in mind.
The Reduced Form Model
Nearly all participants in the CDS market employ a reduced form hazard rate representation of the default risk for reference entities, and calibrate it via market‐observable quotes for contracts using an assumption of recovery rates in the event of default. The analysis presented here will follow this convention as well.
The basic strategy is to find a hazard rate that equates the fee and protection legs of the contract in terms of value. For an all‐running spread contract, the equivalence is
In the above, s is the spread, D() represents discount factors, h represents a (fixed) hazard rate, and R the assumed recovery rate. In the left‐hand term, the first summand is the coupon should no default occur in a time period, and the second is the amount of accrued coupon payable on default. Every term involves the hazard rate h and as such is risky. For a contract with an upfront component, the expression is.
The UF is the upfront points, and is not subject to default risk, while s’ is the fixed coupon. This is the primary difference that affects the hedging characteristics as outline in what follows. Note that “equivalent” contracts – an all running contract compared to a fixed coupon contract with points upfront – will yield the same hazard rate in calibration. This is due to the risk‐neutral approach being employed.
Figure 1 shows the points upfront that will produce an equivalent contract for various levels of par spreads. Equivalents for both 40% and 25% assumed recovery are shown; the fixed coupon for the points upfront contracts is 500 basis points. The effect of varying assumptions about recovery is clear, and of increasing importance as par spreads widen.
There is some debate about whether quoting conventions will change when the contract format changes. For example, the CDX.NA.IG index contract is quoted in spread terms but is traded with a fixed coupon and essentially points upfront to account for the difference between the spread quote and the coupon. Systems and habits in the single name market seem geared toward a similar solution. In that sense, examining the sensitivity to the par spread of the upfront points contract makes sense, and represents a risk measure most participants will find natural given the market’s history. Since the upfront portion of the contract is risk free, the sensitivity of these contracts to spread moves is always smaller in magnitude than the equivalent all running contract. Figure 2 shows this relationship. Note there is a systematic difference at both recovery levels; this will indicate higher hedge ratios for the points upfront contracts, with higher spreads leading to larger differences.
All running contracts are going to exhibit much greater sensitivity to defaults in comparison to point upfront contracts, which leads to much, much higher hedge ratios for the upfront contracts. A jump‐todefault sensitivity for a par spread contract is essentially equal to the protection payment associated with default. The upfront points contract has a mark‐to‐market value that is essentially equal to the points paid upfront. In a jump‐to‐default scenario, that mark‐to‐market value disappears. A par spread contract has no mark‐to‐market value, by definition. Figure 3 shows the sensitivities of the upfront contracts. It is important to note that the par spread contracts would have ‐60% or ‐75% sensitivities (depending on the recovery assumption) at all spread levels. This leads to hedge ratios for the upfront contracts coming in at up to five times larger levels at 4500 basis point par spread levels.
Understanding the implications of a switch to upfront contracts is going to be important in adjusting hedging strategies going forward. This is particularly true for strategies involving these contracts as hedges for default risk.
This week’s Learning Curve was written by Mark Ferguson, Research Director, Anuj Gupta, Quantitative Analyst, and Rohan Douglas, CEO, all of Quantifi, Inc. Mr. Douglas is also an adjunct professor at the Polytechnic Institute of NYU in New York