AbcdFunction (3) Linux Manual Page

QuantLib::AbcdFunction – Abcd functional form for instantaneous volatility

Synopsis

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

Inherits std::unary_function<Real, Real>.

Public Member Functions

AbcdFunction (Real a=-0.06, Real b=0.17, Real c=0.54, Real d=0.17)

Real operator() (Time u) const
volatility function value at time u: [ f(u) ]
Real maximumLocation () const
time at which the volatility function reaches maximum (if any)
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 T, Time tMax, Time tMin) const

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

Real a () const

Real b () const

Real c () const

Real d () const

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 T, Time tMax, Time tMin) const

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

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

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

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 ]

Real a () const

Inspectors

Author

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