- QuantLib
- AbcdFunction
 
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: 
 | |
| 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: 
 | |
| Real | longTermVolatility () const | 
| volatility function value at time +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
![\[ f(T-t) = [ a + b(T-t) ] e^{-c(T-t)} + d \]](form_373.png) 
following Rebonato's notation.
| Real covariance | ( | Time | t, | 
| Time | T, | ||
| Time | S | ||
| ) | const | 
instantaneous covariance function at time t between T-fixing and S-fixing rates
![\[ f(T-t)f(S-t) \]](form_377.png) 
integral of the instantaneous covariance function between time t1 and t2 for T-fixing and S-fixing rates
![\[ \int_{t1}^{t2} f(T-t)f(S-t)dt \]](form_378.png) 
| Real volatility | ( | Time | tMin, | 
| Time | tMax, | ||
| Time | T | ||
| ) | const | 
average volatility in [tMin,tMax] of T-fixing rate:
![\[ \sqrt{ \frac{\int_{tMin}^{tMax} f^2(T-u)du}{tMax-tMin} } \]](form_379.png) 
variance between tMin and tMax of T-fixing rate:
![\[ \frac{\int_{tMin}^{tMax} f^2(T-u)du}{tMax-tMin} \]](form_380.png) 
| Real instantaneousVolatility | ( | Time | t, | 
| Time | T | ||
| ) | const | 
instantaneous volatility at time t of the T-fixing rate:
![\[ f(T-t) \]](form_381.png) 
| Real instantaneousVariance | ( | Time | t, | 
| Time | T | ||
| ) | const | 
instantaneous variance at time t of T-fixing rate:
![\[ f(T-t)f(T-t) \]](form_382.png) 
| Real instantaneousCovariance | ( | Time | u, | 
| Time | T, | ||
| Time | S | ||
| ) | const | 
instantaneous covariance at time t between T and S fixing rates:
![\[ f(T-u)f(S-u) \]](form_383.png) 
indefinite integral of the instantaneous covariance function at time t between T-fixing and S-fixing rates
![\[ \int f(T-t)f(S-t)dt \]](form_384.png)