AbcdFunction Class Reference

Abcd functional form for instantaneous volatility More...

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

Inheritance diagram for AbcdFunction:

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: More...
Real	longTermVolatility () const
	volatility function value at time +inf: More...
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
Public Member Functions inherited from AbcdMathFunction
	AbcdMathFunction (Real a=0.002, Real b=0.001, Real c=0.16, Real d=0.0005)
	AbcdMathFunction (const std::vector< Real > &abcd)
Real	operator() (Time t) const
	function value at time t: More...
Time	maximumLocation () const
	time at which the function reaches maximum (if any)
Real	maximumValue () const
	maximum value of the function
Real	longTermValue () const
	function value at time +inf: More...
Real	derivative (Time t) const
Real	primitive (Time t) const
Real	definiteIntegral (Time t1, Time t2) const
Real	a () const
Real	b () const
Real	c () const
Real	d () const
const std::vector< Real > &	coefficients ()
const std::vector< Real > &	derivativeCoefficients ()
std::vector< Real >	definiteIntegralCoefficients (Time t, Time t2) const
std::vector< Real >	definiteDerivativeCoefficients (Time t, Time t2) const

Additional Inherited Members
Public Types inherited from AbcdMathFunction
typedef Time	argument_type
typedef Real	result_type
Static Public Member Functions inherited from AbcdMathFunction
static void	validate (Real a, Real b, Real c, Real d)
Protected Attributes inherited from AbcdMathFunction
Real	a_
Real	b_
Real	c_
Real	d_

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

shortTermVolatility()

Real shortTermVolatility

(

)

const

volatility function value at time 0:

\[ f(0) \]

longTermVolatility()

Real longTermVolatility

(

)

const

volatility function value at time +inf:

\[ f(\inf) \]

covariance() [1/2]

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

instantaneous covariance function at time t between T-fixing and S-fixing rates

\[ f(T-t)f(S-t) \]

covariance() [2/2]

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

\[ \int_{t1}^{t2} f(T-t)f(S-t)dt \]

volatility()

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

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

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

variance()

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

variance between tMin and tMax of T-fixing rate:

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

instantaneousVolatility()

Real instantaneousVolatility	(	Time	t,
		Time	T
	)		const

instantaneous volatility at time t of the T-fixing rate:

\[ f(T-t) \]

instantaneousVariance()

Real instantaneousVariance	(	Time	t,
		Time	T
	)		const

instantaneous variance at time t of T-fixing rate:

\[ f(T-t)f(T-t) \]

instantaneousCovariance()

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

instantaneous covariance at time t between T and S fixing rates:

\[ f(T-u)f(S-u) \]

primitive()

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

\[ \int f(T-t)f(S-t)dt \]