# QuantLib_AnalyticHestonHullWhiteEngine man page

AnalyticHestonHullWhiteEngine — Analytic Heston engine incl. stochastic interest rates.

## Synopsis

`#include <ql/pricingengines/vanilla/analytichestonhullwhiteengine.hpp>`

Inherits AnalyticHestonEngine.

Inherited by AnalyticH1HWEngine.

### Public Member Functions

AnalyticHestonHullWhiteEngine (const boost::shared_ptr< HestonModel > &hestonModel, const boost::shared_ptr< HullWhite > &hullWhiteModel, Size integrationOrder=144)
AnalyticHestonHullWhiteEngine (const boost::shared_ptr< HestonModel > &model, const boost::shared_ptr< HullWhite > &hullWhiteModel, Real relTolerance, Size maxEvaluations)
void update ()
void calculate () const

### Protected Member Functions

std::complex< Real > addOnTerm (Real phi, Time t, Size j) const

### Protected Attributes

const boost::shared_ptr< HullWhite > hullWhiteModel_

## Detailed Description

Analytic Heston engine incl. stochastic interest rates.

This class is pricing a european option under the following process

[ begin{array}{rcl} dS(t, S) &=& (r-d) S dt +sqrt{v} S dW_1 \ dv(t, S) &=& ppa ( heta - v) dt + sigma sqrt{v} dW_2 \ dr(t) &=& ( heta(t) - a r) dt + \ta dW_3 \ dW_1 dW_2 &=& rho dt \ dW_1 dW_3 &=& 0 \ dW_2 dW_3 &=& 0 \ \nd{array} ].PP References:

Karel in't Hout, Joris Bierkens, Antoine von der Ploeg, Joe in't Panhuis, A Semi closed-from analytic pricing formula for call options in a hybrid Heston-Hull-White Model.

A. Sepp, Pricing European-Style Options under Jump Diffusion Processes with Stochastic Volatility: Applications of Fourier Transform (http://math.ut.ee/~spartak/papers/stochjumpvols.pdf)

Tests

the correctness of the returned value is tested by reproducing results available in web/literature, testing against QuantLib's analytic Heston and Black-Scholes-Merton Hull-White engine

## Member Function Documentation

### void update () [virtual]

This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes.

Implements Observer.

## Author

Generated automatically by Doxygen for QuantLib from the source code.

## Referenced By

The man pages AnalyticHestonHullWhiteEngine(3) and hullWhiteModel_(3) are aliases of QuantLib_AnalyticHestonHullWhiteEngine(3).

Mon Apr 30 2018 Version 1.12.1 QuantLib