Abcd functional form for instantaneous volatility More...
#include <ql/termstructures/volatility/abcd.hpp>
Inherits 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 |
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:
\[ f(T-u)f(S-u) \]
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 a | ( | ) | const |
Inspectors