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P2.T6.413. Credit exposure profiles

Nicole Seaman

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AIM: Identify factors that affect the calculation of the credit exposure profile and summarize the impact of collateral on exposure. Identify typical credit exposure profiles for various derivative contracts and combination profiles.

Questions:

413.1. The following illustrates the credit exposure profile of an interest rate swap that matures in ten (10) years:


If we let (T) be ten year maturity and (t) be the specific horizon between today and maturity, each of the following is true about this exposure profile EXCEPT which is not?

a. Because the swap's maturity is ten years, the exposure peaks at about 1/3*10 or 3.33 years
b. If there exists a typical upward-sloping yield curve, then the receiver swap (i.e., counterparty who pays floating) has greater exposure than the payer swap (i.e., counterparty who pays fixed)
c. The profile is initially increasing due to the sqrt(t) which is called the diffusion effect
d. The profile is later decreasing due to [T-t] which is called the amortization effect


413.2. Consider the following exposure profile for a cross-currency swap:


Each of the following is TRUE about this profile, except which is the LEAST plausible?

a. The profile of the cross-currency swap can be determined as the combination of an interest rate swap, an FX forward trade, and a correlation assumption
b. The contribution of the FX forward trade, to the exposure profile, is greater than the contribution of the interest rate swap component
c. The fact that the PFE exposure does not tend back to zero at maturity (10 years) implies the initial value of the swap was significantly greater than zero
d. An increase in FX volatility assumption will increase the exposure


413.3. The following chart displays exposure profiles at the 95% and 98% confidence level for a credit defaults swap (CDS)


Each of the following is true (or at least plausible) about these CDS profiles EXCEPT for which is not?

a. These are profiles for long CDS protection where the expected recover rate is 30%
b. For a given confidence level, PFE must be less than ES (at the same confidence level) because ES corresponds to the expected exposure conditional on being above the relevant PFE value
c. At the 95% confidence level, increasing exposure in the early stages corresponds to scenarios in which the CDS premium (credit spread) will have widened
d. The abrupt jump displayed by the 98% PFE is due to a wrong-way risk correlation parameter: if this were switched to zero, the jump will disappear

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