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: \[ f(0) \] | |
| 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 |
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: \[ f(t) \] | |
| 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: \[ f(\inf) \] | |
| 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 | |
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_ |
Abcd functional form for instantaneous volatility
\[ f(T-t) = [ a + b(T-t) ] e^{-c(T-t)} + d \]
following Rebonato's notation.
instantaneous covariance function at time t between T-fixing and S-fixing rates
\[ f(T-t)f(S-t) \]
integral of the instantaneous covariance function between time t1 and t2 for T-fixing and S-fixing rates
\[ \int_{t1}^{t2} f(T-t)f(S-t)dt \]
average volatility in [tMin,tMax] of T-fixing rate:
\[ \sqrt{ \frac{\int_{tMin}^{tMax} f^2(T-u)du}{tMax-tMin} } \]
variance between tMin and tMax of T-fixing rate:
\[ \frac{\int_{tMin}^{tMax} f^2(T-u)du}{tMax-tMin} \]
instantaneous volatility at time t of the T-fixing rate:
\[ f(T-t) \]
instantaneous variance at time t of T-fixing rate:
\[ f(T-t)f(T-t) \]
instantaneous covariance at time t between T and S fixing rates:
\[ f(T-u)f(S-u) \]