Vol_Spec__Vol_Type__Shifted_Lognormal

Variation of the Vol Spec::Vol Type::Black whereby the logmormal distribution of *F(T)* is shifted by a certain amount *θ* to the right.

When interest rates are negative, a positive *θ* is used so that the lognormal distribution is shifted to the left towards the negative rates regime.

The shifted lognormal terminal distribution arises from the dynamics *d(F+θ) = σ(F+θ)dw*, which treats *d(F+θ)* as being always positive.

It follows that a positive *θ* results to an *F* at time *T* of which the lognormal distribution is shifted to the left by an amount equal to *θ*.

Note this volatility convention reduses to the *Black* convention when *θ = 0*.