Suppose the forward rate as a function of time t evolves as where (t,T ) is a

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Suppose the forward rate as a function of time t evolves as 

dF(t, T) = u(t, T) dt + odZt,

where μ(t,T ) is a deterministic function of t and T . Show that the forward rate is normally distributed, where 

2+   F (t, T) = F (0, T) + (u, T) du to Zt.

Explain why F(t,T )−F(t,S) is purely deterministic. Deduce that the forward rates at different maturities are perfectly correlated.

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