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CVA calculation - Credit Risk - Chapter 14 Gregory

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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
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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