Value at risk (VaR) of interest rate swap

[[email protected]]

http://forum.bionicturtle.com/threads/question-9-value-at-risk-var-of-interest-rate-swap.1113/

Hi David,
I am looking at the question in the above link. In this question, I understand that right after the reset the value of the floating leg is the notional. Then should not its duration be 0 since it's like we get all cash right away? If its duration is 1, then its value is not just the notional, because now it has the market risk.

Thanks.

 

[David Harper CFA FRM]

ldcn, you would be correct if the coupon waited one year to determine the prevailing rate. But, in this case, as a typical swap, when the floater resets, the prevailing LIBOR is determined at the reset (say, LIBOR = 4% at reset which is time 0) but paid one year later. So, you have duration ~1 as this one coupon is itself like a 1-year zero coupon bond. At that moment, the bond prices at par and the 4% coupon will be paid in one year (e.g., $4 on 100 MM notional). The nonzero duration arises b/c your next coupon, in one year, is fixed. So if we go forward six months, and rates increase to 5%, you are still getting the $4 coupon six month later (not $5). So, you do have market risk until the coupon. In this way, when the coupon sets at the begging of the period but pays at end of period, Mac duration is nearest to "time to next coupon" ... although in practice is it sometimes rounded down to zero. Thanks, David

 

[[email protected]]

Got it. Very helpful explanation. Thank you.
So the duration of floating leg should be 0 right before the reset/interest payment, right?

 

[David Harper CFA FRM]

yes, exactly ... just like a zero coupon, duration tends to zero as reset approaches, then jumps to "time to coupon" on the reset. thanks, David