CVA Calculation for Risky Bond (Solved Example) (FRM Part 2, Book 2, Credit Risk)

[@finRGB]

Learning Objective: Calculate CVA and CVA as a spread with no wrong-way risk, netting, or collateralization.

[@JIMMYMANIAR]

difficult concept explained with a simple example. Great stuff!

[@finRGB]

Glad that you found the video useful, Jimmy.

[@monikadixit9220]

simplistic way of explaining this topic.

[@sergeykaverin7460]

Please, explain the Probability_Default calculation. In general, Probability_Default = 1 - Survival_Probability. It means for 1-year period Survival_Probability = 1 - Probability_Default = 1 - 0.02 = 0,98 For the second period we have to use Probability_Default_2 = 1 - Survival_Probability_2 = 1 - Survival_Probability^2 = 1 - 0,98^2 = 0,0396. Means 3,96% And it makes sense: it is harder to survive for a long period. But in your video (timecode 5:54) - the longer we live - the default is more rare

[@finRGB]

Hello Sergey, the default probabilities that you have calculated (2%, 3.96% and by extension 5.88% for 3 years) are cumulative default probabilities: 2% for the period between today and end of first year, 3.96% for the period between today and end of the second year and so on. What the CVA formula needs as its input are marginal default probabilities (2%, 1.96%, 1.92%), where, 1.96% = 3.96% - 2%, 1.92% = 5.88% - 3.96%. Marginal default probability of 1.96% applies to the period between 1 year and 2 year and the probability of 1.92% applies between 2 year and 3 year.

[@moustafayounes1771]

How did you arrive to CVA 3,6554? I used the formula you have shown and took the sum of DF (2,77513) * EE (max =115,54) * PD ( 0,0588) = 18,86 divided by 3 years = 6,29 multiplied by LGD of 0,6= CVA 3,7714.

[@finRGB]

Respectively for the three years, the EE's are 115.5444, 111.8462, 108, the discount factors are 0.96153, 0.9246, 0.8890 and PDs are 0.02, 0.0196, 0.0192. This gives CVA to be 0.60 (115.5444 * 0.96153 * 0.02 + 111.8462 * 0.9246 * 0.0196 + 108 * 0.8890 * 0.0192) = 3.6554.

[@moustafayounes1771]

@@finRGB Thanks much appreciated!

[@VinodKumar-yp8gd]

​@@finRGBwhere did u used lgd in calculation

[@VinodKumar-yp8gd]

Hello why don't you discount first coupon 8%

[@j.o.ysticksrecordings9743]

​@@VinodKumar-yp8gdthere are total 3 payments and all 3 payments are considered and discounted to PV

[@ncx5083]

hey thanks for the great video.however am finding it but hard to understand the concept of Risky Value? why by taking out the CVA portion (which is the present value of expected future loss) from fair value of bond discounted at risk-free, why do we get a risky value? can you please help elaborate on this part?

[@finRGB]

Hello @ncx5083. Risk-free value of the bond (one obtained by discounting future cashflows at the risk free rate of interest) carries with it the assumption that the bond (or, its issuer) cannot default over the life of the bond (all cash flows are sort of guaranteed and hence, there are no losses owing to default). What CVA does is that it quantifies the expected loss owing to the default of the "counterparty" (in this case, the bond issuer). Adjusting the risk-free value by the CVA gives us the "risky value" of the bond (i.e. the value that duly takes into the account the possibility that the issuer can indeed default). Instead of arriving at the Risky Value directly, we are treating it to be a combination of two items (Risk Free and CVA), with each item (practically speaking) potentially being calculated by a separate team or function.

[@lucianturcu8276]

Do you know this type of problem is used also at the PRMIA CCRM exam?

[@rishabhshukla2908]

How do you arrived at 111.1004?Please if you can explain the concept without direct use of calculator..

[@finRGB]

Hello Rishabh, it's the total discounted value of the future cash flows 8, 8, 108 at 4% discount rate i.e. 8/1.04 + 8/1.04^2 + 108/1.04^3 = 111.1004

[@lucianturcu8276]

how was calculated credit spread? from Risky value?

[@finRGB]

If you use the TVM functionality of your financial calculator, set N = 3, PMT = 8, PV = -107.445 (Risky Value), FV = 100 and solve for I/Y. From this I/Y deduct the risk-free rate of 4% to get the credit spread of 1.2503%.

[@lucianturcu8276]

@@finRGB Thank you for the fast and clear answer!

[@Ju-eq8lc]

Hi, May i know if there is an Excel function for TVM to find the credit spread?

[@nashrahsafdar9233]

We calculate CVA for derivative transactions, why are we calculating it here for a Bond?

[@finRGB]

The intent of CVA is to capture default risk in present value terms - so you can very apply it to a simple (risky) bond. Also, given that exposure calculations are straightforward in this example, it helps illustrate the general concept and calculation of CVA.