Apparently, they like to ask this a lot, so let’s be prepared and figure out the details carefully. For simplicity, let’s use a 2-year semiannual 6% fixed-payer swap at as an example: 1) a fixed-pay semiannual swap - pay 6% fixed and receive LIBOR - 2-year tenor - settlement/payment dates: month 6, 12, 18, 24 2) long position on a series of 3 forward rate agreements (FRAs) - pay 6% fixed and receive LIBOR - the series contains three 6-month FRAs: 6 x 12, 12 x 18, 18 x 24 - settlement/determination dates: month 6, 12, 18 - payment dates: month 12, 18, 24 3) a series of 3 long call and 3 short put interest rate options - 6% strike rates (for both calls and puts) - 3 “pairs” of calls and puts - expiration dates (for each “pair”): month 6, 12, 18 - payment dates: month 12, 18, 24 Are the three of them equivalent? Do the settlement/payment dates match? Am I mistaken anywhere?? Thanks!
How about some rates? Let us use 6-month LIBOR= 5%, 12-month LIBOR=5.2%, 18-month LIBOR=5.5%, 24-month LIBOR=6%
I see you already gave the fixed rates…no need for those LIBOR rates. The swap and the 3 FRA’s are equivalent (almost, note below) because: 1. After 6 months from today, the swap buyer pays 6% (annual), and receive 6-month LIBOR announced on day 180. Same thing at the remaining 3 periods. 2. The first FRA, pays 6% after 12 months, not after 6 months as the swap. S, I think you will also need to throw in 6-month LIBOR at t0, to make the two equivalent. 3. The call-put pairs result in a fixed 6% interest rate, so yes they are the same as the 3 FRA’s (noting the problem with the first 6-month period. 4. The call-put pairs cost money upfront, while the other two don’t. I don’t know if you agree, but that’s my thinking on this.
Thanks, Dreary. So the first 6x12 FRA pays in month 12? I thought only options pay in arrears, FRAs pay the “interest savings” upfront? In that case, should we include an extra 0x6 FRA to make an equivalent payment in month 6? Thanks again!
I think so. 6x12 FRA means for the first 6 months, you get nothing. On day 180, you lock in a 6-month return of whatever 6-month LBOR is. on day 360, you get interest for the last 6 months, but for the first 6 months you’re on your own. The swap with 6% fixed pay is same as a semi-annual bond, paying 6% coupon. If you buy a bond for $100, and receive $3 every 6-months, plus principle on day 720, your return is same as the swap you described above, which is 6%.
So the swap is actually equivalent to 4 FRAs instead of 3? Is that the case with the options too?