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# CVA calculation - Credit Risk - Chapter 14 Gregory

#### amegupte

##### New Member
Hi David,
This may seem a little silly, but i went through your video review of Gregory's Chapter 14 of the xVA challenge - CVA/DVA. The practice question at the end of the chapter involved using the risk free rate to calculate the discount factor. I did understand the entire calculation of the CVA however, I cant seem to recollect how did you derive the discount factor from the risk free rate. Could you please help?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @amegupte The discount factor is the present value of \$1.00 future dollar. If the rate is discrete, the df(T) = 1/(1+r/k)^(-k*T) = (1+r/k)^(-k*T) where k is the compound frequency; e.g., if T = 3 years, k = 1 period per year; annual compound frequency; r = 4.0%, then df(3.0) = (1+0.04/1)^-(3*1) = 0.888996359. But Gregory's are likely to be with continuous compound frequency such that df(T) = exp(-r*T); e.g., df(3.0) = exp(-0.04*3) = 0.886920437

Here is an actual GARP FRM question at https://www.bionicturtle.com/forum/threads/garp-2017-p2-76.10344/
... notice that the given assumption of "The current risk-free rate of interest is 2%" leads to df(1.0 year) = exp(-.02*1) = 0.9802; df(2.0 years) = exp(-0.02*2) = 0.9608; and df(3.0 years) = exp(-0.02*3) = 0.9418 ... or, actually, that's in my version (we had to give them several corrections to their initial version because it had three mistakes) .... alternatively, there is(was) a version where the compound frequency was annual such that df(1.0) = 1.02^(-1) = 0.9804; df(2.0) = 1.02^(-2) = 0.9612; and df(3.0) = 1.02^(-3) = 0.9423. Thanks,

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