QuantLib_BatesProcess man page

BatesProcess — Square-root stochastic-volatility Bates process.

Synopsis

#include <ql/processes/batesprocess.hpp>

Inherits HestonProcess.

Public Member Functions

BatesProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > &dividendYield, const Handle< Quote > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Real lambda, Real nu, Real delta, HestonProcess::Discretization d=HestonProcess::FullTruncation)
Size factors () const
returns the number of independent factors of the process
Disposable< Array > drift (Time t, const Array &x) const
returns the drift part of the equation, i.e., $mu(t, mathrm{x}_t)$
Disposable< Array > evolve (Time t0, const Array &x0, Time dt, const Array &dw) const
Real lambda () const
Real nu () const
Real delta () const

Detailed Description

Square-root stochastic-volatility Bates process.

This class describes the square root stochastic volatility process incl jumps governed by [ begin{array}{rcl} dS(t, S) &=& (r-d-lambda m) S dt +sqrt{v} S dW_1 + (e^J - 1) S dN \ dv(t, S) &=& ppa ( heta - v) dt + sigma sqrt{v} dW_2 \ dW_1 dW_2 &=& rho dt \ omega(J) &=& ac{1}{sqrt{2pi \delta^2}} \xpleft[-ac{(J-0)^2}{2elta^2}right] \nd{array} ]

Examples: EquityOption.cpp.

Member Function Documentation

Disposable<Array> evolve (Time t0, const Array & x0, Time dt, const Array & dw) const [virtual]

returns the asset value after a time interval $Delta t$ according to the given discretization. By default, it returns [ E(mathrm{x}_0,t_0,Delta t) + S(mathrm{x}_0,t_0,Delta t) cdot Delta mathrm{w} ] where $E$ is the expectation and $S$ the standard deviation.

Reimplemented from StochasticProcess.

Author

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Referenced By

The man pages BatesProcess(3), drift(3), evolve(3) and factors(3) are aliases of QuantLib_BatesProcess(3).

Mon Apr 30 2018 Version 1.12.1 QuantLib