Deriscope

## The Excel Derivatives Periscope

##### Products

Model[Vanilla_Swaption]__Pricing_Method

Pricing Method refers to List of available pricing methods.
Available Pricing Method types:
Bachelier
Assumes that the underlying forward swap rate F follows the Bachelier process so that it is normally distributed at any future time.
Concretely F is diffused as dF = σdw in its martingale measure.
Note this choice expects volatility input with Vol Spec::Vol Type = Normal
The QuantLib engine used is the BachelierSwaptionEngine.
Black
Assumes that the underlying forward swap rate F follows the Black process so that it is lognormally distributed at any future time.
Concretely F is diffused as dF = σFdw in its martingale measure, where σ may be time dependent.
Note this choice expects volatility input with Vol Spec::Vol Type = Black
The QuantLib engine used is the BlackSwaptionEngine.
Black Displaced
Assumes that the underlying forward swap 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 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.
This model reduses to the Black model when θ = 0.
Note this choice expects volatility input with Vol Spec::Vol Type = Shifted Lognormal
The QuantLib engine used is the BlackSwaptionEngine with a non-trivial displacement amount.
G2
Corresponds to the QuantLib G2Swaption Engine powered with a
G2 Model two-factor short rate model.
SDE: r = φ(t) + x(t) + y(t)
where dx = -axdt + σdw1
and dy = -bydt + ηdw2
Semi-analytic implementation.
Gaussian1d
Corresponds to the QuantLib Gaussian1dSwaption Engine powered with a one-dimensional gaussian short rate model.
Here the user must also supply an object of type
Gaussian 1d Model containing the volatility and mean reversion parameters that specify the exact dynamics of the short rate diffusion.
Optionally the Gaussian 1d Model may be calibarated so that its parameters are compatible with a given set of market volatilities.
The calibration is achieved through the
local function GSR Model::Calibrate.

An
An example would be a bermudan callable fixed bond, of which the call right may be priced if viewed as a swaption to enter into a one leg swap with notional reimbursement at maturity and an exercise-linked rebate paying the notional.
JamshidianCIR
Corresponds to the QuantLib JamshidianSwaption Engine powered with a
CIR Model one factor short rate model.
SDE: dr = k(θ - r)dt + sqrt(r)σdw
Semi-analytic implementation.
QuantLib warning: This class was not tested enough to guarantee its functionality.
JamshidianExtendedCIR
Corresponds to the QuantLib JamshidianSwaption Engine powered with a
Extended CIR Model one factor short rate model.
Formula: r(t) = μ(t) + r΄(t)
where is as in the CIR model and μ(t) is the deterministic time-dependent parameter used for term-structure fitting.
Semi-analytic implementation.
QuantLib warning: This class was not tested enough to guarantee its functionality.
JamshidianHullWhite
Corresponds to the QuantLib JamshidianSwaption Engine powered with a
Hull White Model one factor short rate model.
SDE: dr = (θ - αr)dt + σdw
Semi-analytic implementation.
JamshidianVasicek
Corresponds to the QuantLib JamshidianSwaption Engine powered with a
Vasicek Model one factor short rate model.
SDE: dr = a(b - r)dt + σdw
Semi-analytic implementation.
MarketModel
Makes use of the
QL Market Model type.
The disclaimer described in
QL MM Data applies also here.
The pricing is carried out by mapping the given
Vanilla Swaption object into an equivalent object of type QL Multi Step Swaption
Note a market object of type
Market Model Curve is also required that supplies the assumed evolution of the relevant forward rates and a model object of type Market Model that supplies the simulation specifications.
TreeBlackKarasinski
Corresponds to the QuantLib TreeSwaption Engine powered with a
Black Karasinski Model one factor short rate model.
SDE: dln(r) = (θ - α ln(r))dt + σdw
Tree implementation.
TreeCIR
Corresponds to the QuantLib TreeSwaption Engine powered with a
CIR Model one factor short rate model.
SDE: dr = k(θ - r)dt + sqrt(r)σdw
Tree implementation.
QuantLib warning: This class was not tested enough to guarantee its functionality.
TreeExtendedCIR
Corresponds to the QuantLib TreeSwaption Engine powered with a
Extended CIR Model one factor short rate model.
Formula: r(t) = μ(t) + r΄(t)
where is as in the CIR model and μ(t) is the deterministic time-dependent parameter used for term-structure fitting.
Tree implementation.
QuantLib warning: This class was not tested enough to guarantee its functionality.
TreeHullWhite
Corresponds to the QuantLib TreeSwaption Engine powered with a
Hull White Model one factor short rate model.
SDE: dr = (θ - αr)dt + σdw
Tree implementation.
TreeVasicek