Black Displaced
Subtype of Pricing MethodAssumes that the underlying forward rate F follows the displaced Black process so that it is lognormally distributed with a horizontal shift at any future time.
Concretely F is diffused as d(F+θ) = σ(F+θ)dw in its martingale measure, which treats 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 model reduses to the Black model when θ = 0.
The QuantLib engine used is the BlackCapFloor with a non-trivial displacement amount in the interest rate case and the YoYInflationUnitDisplacedBlackCapFloor in the inflation case.