Hi @Carlos Madrid Apologies for the typo on page 19, indeed there is incorrectly shown an extra square root (this has been tagged for a fix and revision). In regard to CR-13 (aka, R45 Gregory), actually Deepa is currently working on the updated (2018) version including Gregory's XVA Chapter 9 (actually, it's an update to each of Chapter 4, 5, 6. 7. 9, 12, 14 and 17) so it's not currently available but will be fairly soon. Thank you!
Hi David and Nicole,
here one more typo in the same reading De Laurentis, Chapter 3 "Ratings Assignment Methodologies" on page 21: View attachment 1378View attachment 1379
The cumulated normal disribution operator N is missing.
On page 4 you have the excerpt below saying Debt holders receive Max(F-Vt,0), but for example if the firm value is 80 and the face value of debt is 100, don't the debt holders get 80 back rather than (100-80)=20?
HI @Karim_B Yes, absolutely you are correct, we mangled this (although I can see why, the source Stulz is confusing as usual). We will replace with this (cc: @Nicole Seaman ):
"If the debt is risky, there is no guarantee the principal amount will be repaid in full. Specifically, if the value of the firm falls below the principal amount, if V(T) < F, then the firm is insolvent and the debt holders can only recover the firm's value. Therefore, the payoff to debt holders is Min[V(T), F]; i.e., their payoff must be at least equal to the firm's value but cannot be greater than the principal amount. Further, Min[V(T), F] = F - Max[F - V(T), 0], which illustrates that the debt holders' payoff is economically equivalent to the debt principal minus the payoff of a put option on the firm's assets, V(T), with an exercise price equal to K. Consider the same example where F = $100. If V(T) = $120, then debt holders receive Min(100, 120) = 100 - Max(100 - 120, 0) = $100. But if V(T) = $80, then debt holders receive Min(100, 80) = 100 - Max(100 - 80, 0) = $80."
@silver7 I apologize but the Study Note appears to have a typo (it has been a struggle to cope with all of the different CVA assignments). cc @Nicole Seaman. The Study note page 13 should read "... so the probability that the counterparty has survived must enter into the calculation as S(n)."
Question 708.3 is correct: S(I) is the survival probability of the institution and S(n) is the survival probability of the counterparty. The first term is unilateral CVA such that we've basically got LGD*EE*PD each for the counterparty; i.e., LGD(counterparty)*EE(counterparty)*PD(counterparty). In BCVA the institution's own credit risk is added such that the two terms are (without respect to the +/-):
@rnavarro yes understood, but (per the link I shared to you) does it still also contain numerator ... µT + 1/2 σ(a)^2; i.e., missing the final "T"?
I don't know how many of the many errors we've contributed have been corrected
Hi @David Harper CFA FRM , In the study notes of this topic, in page 4, it says that "If the debt is risky, that is, when the value of the firm falls below the principal amount to be paid back (V(t) < F) then the debt holders receive the maximum of F − V(t) or zero." However, I believe that when the value V falls below F, debt holders won't receive the maximum of F - V(t) and 0; debt holders will receive less than the loan amount F BY AN AMOUNT equal to F - V(t). But it is not that debt holders receive f-v. As a result, if the value of the firm is greater than f, then max is = to 0 and debt holders receive the whole loan amount back. If f is greater than v, then they receive less than the loan amount f by an amount f-v. Please let me know what you think. Thanks.
Hi @JulioFRM Yes, I absolutely agree, it is our mistake in the text. Thank you, and apologies for any confusion. It can be difficult to follow Stulz's confusing language, but it should read:
"If the debt is risky, the debt holders are not guaranteed full repayment of the principal amount, F. Specifically, if the value of the firm falls below the debt's principal amount, then the debt holders can only be repaid the (reduced) value of the firm; i.e., if V(t) < F then debt repayment equals V(t). This can be restated in option terms: if the value of the firm falls below the principal amount to be repaid, then the debt holders receive the face value minus the difference, F - V(t). That is, if V(t) < F then debt repayment F - [F-V(t)] = V(t). In this way, we can express the repayment in option terms that accommodates any future V(t):
D(T) = F - Max[F - V(t). 0] = F - [Put option on firm's assets, V(t), with exercise price of debt principal, F]"
@Nicole Seaman after i replied, I noticed this had already been captured. (and it's already in wrike). Moved to this thread.
The first one is correct. And same is used to answer correctly in GARP's Mocks.
In denominator, both calculations are the standard deviations of default probabilities of each variable.
In numerator the calculation is a covariance of PDs of both variables.
Can you post the specific reading that you are referring to and if possible the page that this is located on? This thread is for all readings in Topic 6, so it is helpful to know which reading you are referring to so I don't have to search through everything. I want to make sure this is fixed in the document.