Deriscope

The Excel Derivatives Periscope

Coverage

Model[Vanilla_Swaption]__Pricing_Method

Pricing Method refers to List of available pricing methods.
Available Pricing Method types:
<wb>Bachelier</wb>
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.
<wb>Black</wb>
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.
<wb>Black Displaced</wb>
Minimum required license: Basic
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.
<wb>G2</wb>
Minimum required license: Standard
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.
<wb>Gaussian1d</wb>
Minimum required license: Basic
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
VanillaOption Adjusted Spread may be also defined in situations where credit spreads are involved.
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.
<wb>JamshidianCIR</wb>
Minimum required license: Standard
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.
<wb>JamshidianExtendedCIR</wb>
Minimum required license: Standard
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.
<wb>JamshidianHullWhite</wb>
Minimum required license: Standard
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.
<wb>JamshidianVasicek</wb>
Minimum required license: Standard
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.
<wb>TreeBlackKarasinski</wb>
Minimum required license: Basic
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.
<wb>TreeCIR</wb>
Minimum required license: Basic
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.
<wb>TreeExtendedCIR</wb>
Minimum required license: Basic
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.
<wb>TreeHullWhite</wb>
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.
<wb>TreeVasicek</wb>
Minimum required license: Basic
Corresponds to the QuantLib TreeSwaption Engine powered with a
Vasicek Model one factor short rate model.
SDE: dr = a(b - r)dt + σdw
Tree implementation.