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QuantLib_AbcdFunction

NAME

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 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

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

Real variance (Time tMin, Time tMax, Time T) constvariance 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) constinstantaneous volatility at time t of the T-fixing rate: [ f(T-t) ]

Real instantaneousVariance (Time t, Time T) constinstantaneous variance at time t of T-fixing rate: [ f(T-t)f(T-t) ]

Real instantaneousCovariance (Time u, Time T, Time S) constinstantaneous covariance at time t between T and S fixing rates: [ f(T-u)f(S-u) ]

Real primitive (Time t, Time T, Time S) constindefinite 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 () constInspectors

Author

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