Implied forward rates

In short

• An interest rate forward names both the start date and the tenor: '2y3y' ($F_{2,3}$) is a three-year rate starting in two years; '3m6m' is a six-month rate starting in three months.
• No arbitrage: $(1+z_A)^A(1+IFR_{A,B-A})^{B-A} = (1+z_B)^B$.
• Equivalently, $1+IFR_{A,B-A} = (DF_A/DF_B)^{1/(B-A)}$.
• Rates must have the same periodicity before applying the formula; convert with $(1+APR_m/m)^m = (1+APR_n/n)^n$.
• Uses: breakeven test for 'invest short and roll vs invest long', building a forward curve, and setting the no-arbitrage fixed rate of an FRA and, later, swaps.