Credit Exposure Profiles

[WhizzKidd]

Hi @David Harper CFA FRM

I am trying to understand the credit exposure profiles in Ch13.

For an IRS (Pay Fix, Recieve Float):
The scenario in the notes where i_fix>i_flt initially, then reverses afterward, as the yield curve slopes upwards. Why initially when I am paying net on the swap the credit exposure is positive and not below 0 instead? Because credit risk is when money is owed to me and the counterparty may default, which makes sense when I am receiving net on the swap (when i_flt>i_fix), but not in the former case. Or another way, if MTM=PV(received cashflows)-PV(Paid cashflows), if i_fix(paid) < i_float, then PV (paid)>PV (received), which implies a (-MTM), which is when there is no credit risk. Am I understanding this right?


For a CDS (Long CDS):
It says the exposure profile is positive since the credit spread may widen. Again we are paying the spread, and the exposure on a CDS is when we don't receive the payout at default. Is it because the MTM of the CDS is becoming greater since we locked in an initial spread lower than what the market is telling us it is now (as it widens)? So the MTM becomes more positive over time, hence greater credit risk?

I think I am a bit confused on why the profile is >0 when I am paying on the instrument.

 

[David Harper CFA FRM]

Hi @WhizzKidd I think you mean Gregory Chapter 8? (Oh, I notice it is also CR-13 in the FRM syllabus). Both of your examples (IRS and CDS) have in common that we presume their initial value is zero to both counterparties (why would either buyer/seller enter into the derivative contract if it had negative PV?). So, if you enter a contract with zero PV and, in the early years, you are paying cash to your counterparty, you must have a (weighted average) expectation of receiving payments in the later years, and this is pretty much the definition of credit exposure!

So in regard to the the IRS, please see my recent thread at https://forum.bionicturtle.com/threads/pfe-of-cds-and-cross-currency-swap.9334/#post-49148 where @bpdulog asked: The study notes say that "The overall high interest rates paid are expected to be offset by the gain on the notional exchange at the maturity of the contract, and this expected gain on exchange of notional leads to a significant exposure for the payer of the high interest rate." I don't understand why they are expecting a gain in this transaction? Aren't they just receiving back the initial currency exchange and doesn't the gain depend on what the FX rates are at the end of the transaction? and i replied

Hi @bpdulog Yes, it is true that "Aren't they [i.e., the counterparty in a cross currency swap who is paying the higher interest rate] just receiving back the initial currency exchange and doesn't the gain depend on what the FX rates are at the end of the transaction?" but there is always the premise that at initiation the swap is a fair deal with initial market value of zero to both counterparties. If you are the counterparty paying the higher coupon, then the only way the swap is fair to you is if you expect the notional exchange to "make you whole." (or put another way, if the initial value is zero but you are negative cash flow in the early periods, then you must be positive in later periods). So the coupons and notional amounts are assumed to be sized to reflect the current forward rate (as a predictor of the notional value exchanged at the end of the swap). I hope that clarifies!

Re: the CDS: the broad pattern is similar for the protection buyer. If you are the protection buyer, then you pay current premiums in exchange for a contingent payoff in the case of a credit event. I just borrowed (Gregory's) Figure 8.20 from the same thread (copied below). Notice the exposure profile at PFE 95% is essentially similar to an interest rate swap (i.e., "diffusion" as it increases then "amortization" as it approaches maturity). The key here (IMO) is to recognize that the mark to market value of the CDS increases as the reference credit deterioriates; so it's basically true what you suggest ("Is it because the MTM of the CDS is becoming greater ..."! Keep in mind this profile is not even plotting expected exposure (a conditional average that must be positive because it excludes the negatives), it is plotting potential future exposure (i.e., the tail of the distribution, a feature that increases even if the distribution becomes more disperse). This plot is technically a product of the spread volatility and duration, but conceptually it's increasing (initially, amortizing) because "in the tail" of spread volatility indicates the MtM value of this CDS can increase due to widening spreads on the reference (credit deterioration); which would be a MtM gain to us as the long CDS position, but the potential of unrealized gain constitutes credit exposure for us (!).

Although the 95% PFE curve is a function of spread and duration, I think it's okay to think of this also as weighted average in the following way (because to me its more intuitive): I think Gregory's example has something like a 2.0% default probability. If you are the long the CDS, and there is a 98% probability that you will not need to receive the payout from the protection seller, would you say your credit exposure is zero? No, because there is a 2.0% probability you will need to collect. So the current price reflects a weighted average, and if the probability of default goes up, then your weighed average goes up. To me that's an easier way to think about the 95% curve. I hope that's helpful!