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

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 : basel iii basics black scholes c++ calculator counterparty credit risk credit risk credit risk modelling cva derivative accounting foreign exchange risk fx fx forward hedge accounting ias 39 ifrs interest rate hedging interest rate swap interest rate swap valuation libor LMM ois option otc derivatives pca python quantitative risk analysis quantlib simple example swap