P2.T6.417. Credit value adjustment (CVA)

[Nicole Seaman]

AIMs: Explain the motivation for and the challenges of pricing counterparty risk. Describe credit value adjustment (CVA). Calculate CVA and the CVA spread with no wrong-way risk, netting, or collateralization.

Questions:

417.1. The following graphs two (of the four) components which directly inform the credit value adjustment (CVA) of a five-year interest rate swap:

The calculations do assume a constant hazard rate (default intensity). Consider the following descriptions of the two components plotted above, which inform the swap's CVA calculation:

I. The solid blue line is potential future exposure (PFE)
II. The dotted red line is the marginal (aka, unconditional) default probability

Which of the above statements is (are) likely true?

a. Neither
b. I. only
c. II. only
d. Both


417.2. CityBank is going to enter into a swap contract with FinCorp. From CityBank's perspective, the EPE (expected positive exposure) of the trade is 6.00% and the expected negative exposure (ENE) is 4.20%. CityBank's credit spread is 110 basis points per annum, while FinCorp's credit spread is 250 bps. From CityBank's perspective, the maximum PFE is 18.0%. Which is nearest to estimate of the BCVA (bilateral credit value adjustment)?

a. 5.49 bps
b. 10.38 bps
c. 23.00 bps
d. 42.58 bps


417.3. CityBank enters a long position in an over-the-counter (OTC), out-of-the-money (OTM) put option with a five year term. The strike price of the put is $50.00 while the current asset price is $70.00 with asset volatility of 30.0%. The risk-free rate is 4.0% with continuous compounding. N(d1) = 0.870 and N(d2) = 0.680. CityBank assumes the present-valued expected exposure (EE) to the counterparty equals the option's present value. The probability of default by the counterparty is 8.0% with loss given default (LGD) of 75.0%. Which is nearest to the credit risk-adjusted value of the long option position, where credit risk-adjusted refers to incorporating an approximate credit valuation adjustment (CVA)?

a. $3.76
b. $4.25
c. $6.99
d. $8.51

Answers here:

• In forum

 

[Abhinav Agrawal]

Are these answers correct?
1. d Both
2. 6%*250bps-4.2%*100bps = 10.8 bps doesn't match any of the options
3. Again cannot get to any of the answers. I calculate value of put = X*E ^(-r*t)*N(-d2) - S*N(-d1)= 19.96
Spread = PD * LGD = 0.75*0.08 = 6 bps. How do I get the dollar value of CVA?

 

[Nicole Seaman]

Hello @Abhinav Agrawal,

The answers to the daily practice questions are in a separate section of the forum that is accessible to paid members. If you would like to gain full access to the forum, along with our materials, you can purchase a package HERE. Thank you for using Bionic Turtle!

Nicole

 

[David Harper CFA FRM]

hi @Abhinav Agrawal

Sorry, I had a couple typos that I forget to revert to this copy (Question) only (they were already corrected in the source Q&A):

1. Not both, just one is correct. Hint: does CVA use PFE?
   
2. [typo fixed above] CityBank's credit spread should be 110, then your calc will work!
3. It should be N(d2) = 0.680, such that put option price should be exactly $4.00. Then your spread is multiplied by the $4.00 notion, per Gregory's 12.4 approximation, so we can use $4.00 risk free - (4*pd*lgd)

+1 star for contribution (typos here)

 

[zanderover]

"II. The dotted red line is the marginal (aka, unconditional) default probability"

Is this correct?
Shouldn't it read "marginal (aka, conditional)" instead of unconditional?. In this case i would suspect the red dotted line to be a straight line. If unconditional, it would indeed slope downwards.

Or am i missing something here?

 

[David Harper CFA FRM]

Hi @zanderover

I appreciate the question (I think it's easy to confuse this), but I think it's okay; i.e., the dotted red line slopes down to reflect what Gregory calls a marginal probability and what I would prefer to call an unconditional probability. For example, let's say the default intensity (aka, hazard rate) is 10%. In my opinion then,

• The hazard rate (λ) represents a (continuous) conditional PD and would be graphed by a horizontal line, Y = 10%
• (for context only) The cumulative PD would be increasing with decay; e.g., 5-year cumulative PD = 1 - exp(-10%*5) = 39.35%
• The unconditional PD would be decreases, per the graph above; e.g., 5-year unconditional PD = exp(-10%*5)*(1-10%) = 6.07%; 6-year unconditional PD = exp(-10%*6)*(1-10%) = 5.49%. It can also be calculated as an approximation: 6-year unconditional PD = (6-year cumulative PD) - (5-year cumulative), still necessarily decreasing for a given constant conditional PD (default intensity)

So, for this reason, I do intend "unconditional" ... and Gregory calls this "marginal." Let me know if you still disagree? Thanks!