CapeTools LMM Volatility/Correlation Models

CapeTools LMM Volatility/Correlation Models

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In total there are 23 functions present within the CapeTools LMM Volatility/Correlation Models category of functions.

General Description

Functions to create correlation and volatility models used by the Libor Market Model (LMM) LiborMarketModel() and LiborMarketModel() functions.

The correlation Model objects that can be created are :

LMMLinearExpCorrModel() (Exponential correlation model - rho{i,j}=e^{(-beta*abs(i-j))})

LMMFixedVolModel() (Extended exponential correlation model - rho{i,j}=rho+(1-rho)*e^{(-beta*abs(i-j))})

The volatility Model objects that can be created are :

LMMLinearExpVolModel() (Linear exponential volatility model - sigma(t)=((a*(T{i}-t)+d)*exp{-b(T{i}-t)}+c))

LMMLinearExpVolModel2() (Extended linear-exponential volatility model - sigma(t)=k_i*((a*(T{i}-t)+d)*exp{-b(T{i}-t)}+c))

LMMFixedVolModel() (Constant volatilities)

There are also two LMM process functions to be used for the LMM montecarlo framework.

Function list.

ABCDAdjFactors - Given a LMM ABCD volatility calculation object, returns an array of adjustment factors needed to match Black vols (the results from this function can be used to populate the 'weights' parameter within the LMMLinearExpVolModel2() function).
ABCDBlackErrors - Given a LMM ABCD volatility calculation object, returns an errors array between the black volatilities and the volatilities computed via the ABCDCalculator() object.
ABCDBlackErrors2 - Given a LMM ABCD volatility calculation object, returns an error indicator between the black volatility and the volatility computed via the ABCDCalculator() object.
ABCDCalculator - Creates a LMM ABCD calculator object ( f(T-t) = [ a + b(T-t) ] e^{-c(T-t)} + d ).
ABCDCapletCalib - Given a LMM ABCD volatility calculation object, calibrates the model for the a,b,c and d parameters.
ABCDLongTermVol - Given a LMM ABCD volatility calculation object, returns the instantaneous volatility when time to maturity = +infinity.
ABCDMaxLocation - Given a LMM ABCD volatility calculation object, returns the time to maturity at which the instantaneous volatility reaches maximum (if any).
ABCDMaxVolatility - Given a LMM ABCD volatility calculation object, returns the maximum of the instantaneous volatility.
ABCDModCov - Given a LMM ABCD volatility calculation object, returns the covariance (between two time points) between T and S fixing rates.
ABCDModInstCov - Given a LMM ABCD volatility calculation object, returns the instantaneous covariance at time u between T and S fixing rates ( f(T-u) * f(S-u) where f() is our internal instantaneous volatility function).
ABCDModInstVar - Given a LMM ABCD volatility calculation object, returns the instantaneous variance at time u of the T-fixing rate ( f(T-u) * f(T-u) where f() is our internal instantaneous volatility function).
ABCDModInstVol - Given a LMM ABCD volatility calculation object, returns the instantaneous volatility at time u of the T-fixing rate ( f(T-u) where f() is our internal instantaneous volatility function).
ABCDModVar - Given a LMM ABCD volatility calculation object, returns the variance (between two time points) of the T-fixing rate.
ABCDModVol - Given a LMM ABCD volatility calculation object, returns the volatility (between two time points) of the T-fixing rate.
ABCDShortTermVol - Given a LMM ABCD volatility calculation object, returns the instantaneous volatility when time to maturity = 0.0.
LMMFixedVolModel - Creates a volatility model of constant volatilities for the libor market model.
LMMLinearExpCorrModel - Creates an exponential correlation model for the libor market model.
LMMLinearExpCorrModel2 - Creates an extended exponential correlation model for the libor market model.
LMMLinearExpVolModel - Creates a linear-exponential volatility model for the libor market model.
LMMLinearExpVolModel2 - Creates a an extended linear-exponential volatility model for the libor market model.
LMMProcess - Creates a Libor Forward Model Process container object.
LMMProcess2 - Creates a Libor Forward Model Process container object.
LMMProcessDetails - Returns summary information regarding the rates underlying the LMMProcess.