A $10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8%. The fixed rate on the swap is 5%, current 90-day LIBOR is 5% and 270-day LIBOR is 5.4%. To calculate the value to fix-paying-investor we need the discount rate. in the answer, it calculate discount rate like: (1 + 0.05 × (90/360)) why not (1+0.05)^(90/360)? why use simple interest rates? Is that assumed that for all swap related calculation is based on simple interest calculation?
On what occasion do we use Simple Interest rates? Is there a standard of some sort?
The annualized rate is 5% not 105% It sounds like ou’re just taking the 90 day libor and de-annualizing it and it happens to be used in the discounting.
Yes I am de-annualizing it on a compounded base. The answer given is using Simple de-annualization. 90day’s interest is 90/360 of annual interest. My question is, since a lot of fixed income calculation assume compounded interest rate, why do we use simple interest rate all of a sudden? or it that I am just haven’t done enough question yet?
Swaps, Swaptions, & FRAs use this convention. The reason for it is that the LIBOR term structure is quoted in annualized terms. For example: 180-Day Rate: 6.0% (Actual 180 day rate = 6.0%*(180/360) = 3.0% 360- Day Rate: 7.0% (Actual 360 day rate = 7.0%*(360/360) = 7.0% You just have to undo the convention for annualizing the rates.
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