Shifted LognormalSubtype of
Variation of the 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.