P1.T3.409.3 correction needed?

[GVD]

Hi David,

I was doing exercises 409.3 and found a different value: 2.4703 million. I had obtained my result by considering floating rate as as a floating bond. I think you have to discount at 6 months 1/(1+2%/2)^1 and at 1 year as (1+2%/2)^2 ...and not as (1+2%/2)^0.5 and (1+2%/2)^2 as here you might be mixing annual and semi-annual discounting. Our results are the same for the semi-annual discounting.
Thanks!

 

[David Harper CFA FRM]

Hi @GVD

Yes, great catch, I agree. I was mistakenly discounting annually; as you say, it should be semi-annually discounting, in which I get $2,470,395 (we both get 2.471 per "The present value of the forgone payments = $500,000 + $1,000,000/(1+2.0%/2)^(0.5*2) + $1,000,000/(1+2.0%/2)^(1.0*2) = $2,470,395"

I have corrected the answer to the following (copied below), see source at
https://forum.bionicturtle.com/threads/p1-t3-409-interest-rate-and-currency-swaps.8017/

409.3. C. $2.471 million
At the end of the fourth year (the current moment of the question), in the exchange Cantrans Bank is owed $100 MM * (4.0% - 3.0%)/2 = $500,000.
Default also implies two that Cantrans will not receive two anticipated (expected) payments:

• At 4.5 years: $100 MM * (4.0% - 2.0%)/2 = $1.0 million, and
• At 5.0 years: $100 MM * (4.0% - 2.0%)/2 = $1.0 million

The present value of the forgone payments = $500,000 + $1,000,000/(1+2.0%/2)^(0.5*2) + $1,000,000/(1+2.0%/2)^(1.0*2) = $2,470,395

In regard to credit exposure (which is actually a Part 2, T6 Credit Risk topic), please note that current credit exposure = max(value, 0). In this case of this interest rate swap:

• Immediately prior to default, Cantrans has a positive (mark-to-market) present value position of +$2.471 million such that Cantrans has the credit exposure of $2.471 million.
• However, the counterparty has a credit exposure of zero (0) = max(-$2.471 million, 0)

Thank you!