Consider a two factor lognormal Libor Market Model Ignore the drift, so that we can write dL i t dt i L i t (a i1 dW t 1 a i 2 dW t 2 ), where a 2 1i a 2 1i 1 and dW t 1 dW t 2 0 Now, let us suppose a i1 sin i Find corr (dL i ,dL j ) What advantage does this representation have if we wish to calibr...

Heres the derivation of corrdLi dLj and the advantage of this representation for correlation calibra ...

Consider a two-factor lognormal Libor Market Model. Ignore the drift, so that we can write dL i

Question:

Consider a two-factor lognormal Libor Market Model. Ignore the drift, so that we can write dLⁱ_t= . . . dt + σ_iLⁱ_t(a_i1dW_t1 + a_i₂dW_t²), where a²_1i + a²_1i = 1 and dW_t¹ dW_t² = 0. Now, let us suppose a_i1=sin θ_i. Find corr (dL_i,dL_j). What advantage does this representation have if we wish to calibrate correlations?