Forward rate
Quantitative Finance glossary · Quantitative Finance
Definition
Interest rate agreed today for borrowing/lending over a future period [T_1, T_2], implied by spot zero rates: F(0; T_1, T_2) = (1)/(T_2 - T_1)left((P(0,T_1))/(P(0,T_2)) - 1right) (simple-compounded). The instantaneous forward rate f(0,T) = -(partial ln P(0,T))/(partial T) is the state variable of the HJM framework. Under the expectations hypothesis, F(0;T_1,T_2) = mathbbE^mathbbQ^T_2[L(T_1;T_1,T_2)] — forwards are martingales under the relevant forward measure (free of risk premium only there).
Forward rate in plain English
A forward rate is an interest rate you lock in *today* for a loan that won't actually start until some future date — so there are no surprises when that day arrives. Here's the clever part: you don't need anyone to quote it, because it's already hidden inside today's rates for different lengths of time. If lending for two years pays a known rate and lending for one year pays another, basic 'no free money' logic pins down exactly what the rate must be for the second year alone — that implied second-year rate is the forward rate. Think of it like booking next summer's flight now at a fixed price: the airline sets that price from what it already knows about costs, and you've removed the guesswork.
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