## Shifted Lognormal

Subtype of Vol TypeVariation of the Black whereby the logmormal distribution of

**is shifted by a certain amount**

*F(T)***to the right.**

*θ*When interest rates are negative, a positive

**is used so that the lognormal distribution is shifted to the left towards the negative rates regime.**

*θ*The shifted lognormal terminal distribution arises from the dynamics

**, which treats**

*d(F+θ) = σ(F+θ)dw***as being always positive.**

*d(F+θ)*It follows that a positive

**results to an**

*θ***at time**

*F***of which the lognormal distribution is shifted to the left by an amount equal to**

*T***.**

*θ*Note this volatility convention reduses to the

**convention when**

*Black***.**

*θ = 0*