# simple example Libor Market Model (BGM)

Libor Market Model is a model where Libor forwards have log-normal distribution in their’s respective probability measures (called T-measure)

example of Libor Market Model with just 2 forwards:

$P_3(t)$ is a price at time t of zero-coupon bond paying at $T_3$

$T_1$, maturity $T_2$]

Libor Market Model

lets take a numeraire=bond $P_3(t)$

in LMM forward $P_3(t)$ measure de:
$W_1(t) and W_2(t)$ are usually correlated

$dW_1(t)dW_2(t)=\rho dt$

this drift(t) can be calculated (idea : Facebook

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