Q:discount rate used in FRA

  1. FRA formula: notional principal*(Rfloating –R forward) *(days/360)/[1+Rfloating*(days/360)] --when calculate the discounting rate, why not [1+Rfloating]^(days/360)? It is used to discount cash flow to PV and discount the Treasury security in Put-call parity. Is this because LIBOR is a add-on interest?

(1+a)^x = (1+ax) … this a reasonable approximation when a<0. This is also basis for derivation for sum of infinite geometric series. However both ways results should be very close

njblain Wrote: ------------------------------------------------------- > LIBOR uses a linear add-on calculation: 1 + (L x > D/360). This is simply how the rate is quoted. > If you use an EAR instead, the (1 + a)^(D/365) > calculation would get the right answer. There is > no inaccuracy in LIBOR - it is just a slightly > different scale. ----------------------------------------------------------- thanks! I understand your point. but what’s the meaning of " If you use an EAR instead, the (1 + a)^(D/365) calculation would get the right answer. " do you mean a is EAR, which is different from quoted Libor. tks!

njblain Wrote: ------------------------------------------------------- > Exactly right. > > Suppose you are given a 180-day HPR of 5%. This > means $100 becomes $105 after 180 days. After a > calendar year you will have (assuming the rate > continues) 1.05^(365/180) = $110.40. > > If you are given an EAR of 10.40%, the result is > identical. > > Suppose you are given a LIBOR rate of 10%. This > means that after a year $100 will become 100 x (1 > + (0.10 x 365 / 360)) = $110.14. -------------------------------------------------------- 1)LIBOR=10%, after one year $100 will be 100*[1+ (0.10 x 365 / 360)]=110.14 2)a 180-day HPR of 5% T-bill. its corresponding EAR=1.05^(365/180)=1.104 after one year $100 will be $100*1.104=110.4 3) there is a difference 110.4-110.14=0.26 4)use 110.14 as ending value in 2) calculation, the 180-day HPR is 4.88% in order to have same return after one year.