Abcd Class 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 notation.


Public Member Functions

 Abcd (Real a=-0.06, Real b=0.17, Real c=0.54, Real d=0.17, bool aIsFixed=false, bool bIsFixed=false, bool cIsFixed=false, bool dIsFixed=false)
Real operator() (Time u) const
 instantaneous volatility at time to maturity u:

\[ f(u) \]


Real a () const
Real b () const
Real c () const
Real d () 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 volatility (Time tMin, Time tMax, Time T) const
Real variance (Time tMin, Time tMax, Time T) const
Real covariance (Time tMin, Time tMax, Time T, Time S) const
Real shortTermVolatility () const
 instantaneous volatility when time to maturity = 0.0
Real longTermVolatility () const
 instantaneous volatility when time to maturity = +inf
Real maximumLocation () const
 time to maturity at which the instantaneous volatility reaches maximum (if any)
Real maximumVolatility () const
 maximum of the instantaneous volatility
std::vector< Real > k (const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t) const
 adjustment factors needed to match Black vols
Real error (const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t) const
 volatility error
Real maxError (const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t) const
 volatility max error
EndCriteria::Type calibration (const std::vector< Real > &blackVols, const std::vector< Real >::const_iterator &t, const boost::shared_ptr< EndCriteria > &endCriteria=boost::shared_ptr< EndCriteria >(), const boost::shared_ptr< OptimizationMethod > &method=boost::shared_ptr< OptimizationMethod >())
 calibration

Friends

class AbcdCostFunction


Member Function Documentation

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

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

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

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

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

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

Real covariance ( Time  tMin,
Time  tMax,
Time  T,
Time  S 
) const

covariance in [tMin,tMax] between T and S fixing rates:

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