AbcdFunction Struct Reference

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

List of all 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.


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 maximumValue () const
 maximum value of the volatility function
Real shortTermValue () const
 volatility function value at time 0:

\[ f(0) \]


Real longTermValue () 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 primitive (Time t, Time T, Time S) const
Real volatility (Time T, Time tMax, Time tMin) const
Real variance (Time T, Time tMax, Time tMin) const

Public Attributes

Real a_
Real b_
Real c_
Real d_


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

volatility in [tMin,tMax] of T-fixing rate:

\[ \sqrt{ \int_{tMin}^{tMax} f^2(T-u)du }\]

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

variance in [tMin,tMax] of T-fixing rate:

\[ \int_{tMin}^{tMax} f^2(T-u)du \]