QuantLib_AbcdFunction man page

AbcdFunction — Abcd functional form for instantaneous volatility  

Synopsis

#include <ql/termstructures/volatility/abcd.hpp>

Inherits AbcdMathFunction.

Public Member Functions

AbcdFunction (Real a=-0.06, Real b=0.17, Real c=0.54, Real d=0.17)
Real maximumVolatility () const
maximum value of the volatility function
Real shortTermVolatility () const
volatility function value at time 0: [ f(0) ]
Real longTermVolatility () const
volatility function value at time +inf: [ f(inf) ]
Real covariance (Time t, Time T, Time S) const
Real covariance (Time t1, Time t2, Time T, Time S) const
Real volatility (Time tMin, Time tMax, Time T) const
Real variance (Time tMin, Time tMax, Time T) const
Real instantaneousVolatility (Time t, Time T) const
Real instantaneousVariance (Time t, Time T) const
Real instantaneousCovariance (Time u, Time T, Time S) const
Real primitive (Time t, Time T, Time S) const

Additional Inherited Members

Detailed Description

Abcd functional form for instantaneous volatility

[ f(T-t) = [ a + b(T-t) ] e^{-c(T-t)} + d ] following Rebonato's notation.

Member Function Documentation

Real covariance (Time t, Time T, Time S) const

instantaneous covariance function at time t between T-fixing and S-fixing rates [ f(T-t)f(S-t) ]

Real covariance (Time t1, Time t2, Time T, Time S) const

integral of the instantaneous covariance function between time t1 and t2 for T-fixing and S-fixing rates [ int_{t1}^{t2} f(T-t)f(S-t)dt ]

Real volatility (Time tMin, Time tMax, Time T) const

average volatility in [tMin,tMax] of T-fixing rate: [ sqrt{ ac{int_{tMin}^{tMax} f^2(T-u)du}{tMax-tMin} } ]

Real variance (Time tMin, Time tMax, Time T) const

variance between tMin and tMax of T-fixing rate: [ ac{int_{tMin}^{tMax} f^2(T-u)du}{tMax-tMin} ]

Real instantaneousVolatility (Time t, Time T) const

instantaneous volatility at time t of the T-fixing rate: [ f(T-t) ]

Real instantaneousVariance (Time t, Time T) const

instantaneous variance at time t of T-fixing rate: [ f(T-t)f(T-t) ]

Real instantaneousCovariance (Time u, Time T, Time S) const

instantaneous covariance at time t between T and S fixing rates: [ f(T-u)f(S-u) ]

Real primitive (Time t, Time T, Time S) const

indefinite integral of the instantaneous covariance function at time t between T-fixing and S-fixing rates [ int f(T-t)f(S-t)dt ]

Author

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Referenced By

The man pages AbcdFunction(3), covariance(3), instantaneousCovariance(3), instantaneousVariance(3), instantaneousVolatility(3), longTermVolatility(3), maximumVolatility(3), primitive(3), shortTermVolatility(3) and variance(3) are aliases of QuantLib_AbcdFunction(3).

Fri Sep 1 2017 Version 1.10.1 QuantLib