can someone help me with this plz: here is a formula im given that calculates the ATM forward rate from 3 months to 12 months (the forward rate starting 3 months from now until the end of the year) Rate = [100 / (M - T)] * [(A / B) - 1] where A = 1 + RM / 100 B = 1 + (RT * T) / 100 where Rate = ATM Forward Rate M = term from now to maturity (1) RM = rate for the term M (ie the one year rate at issue date) T = term from issue date till 3 months RT = rate for the term T (the 3 month rate at issue date) is this formula correct? and if so, can someone plz explain how we come up with this formula? i dont understand intuitively how this formula is a measure of the forward rate 3 months from now. Thanks!
The ATM forward rate? What’s ATM doing here? Anyway, the forward rate is just the bootstrap value given in your notes.
ATM probably means the at-the-money value (zero PV pricing, no arbitrage, etc.) although its a rarely used terminology. here’s the intuition. forget your formulae, you can back into them. no arbitrage implies that starting with $1 you should break even between these two options: 1. investing for 1 yr at currently available 1 yr rate 2. investing for 3 mos at currently available 3 mos rate, followed by 9 mos at currently available 9 mos forward rate starting 3 mos from now (1+R12) = (1+R3).(1+3F9) where Ri = rates for i periods starting today, jFi = today’s forward rates for i periods starting after j periods solve for 3F9, you’re done. but i suspect you’re looking to derive the monster version of the simple formula. i was tempted, but no thanks.
thanks guys i was also confused with the ATM, but if its just the normal forward rate from 3 months to 12 months, then i understand.