# QuantLib_AnalyticH1HWEngine man page

AnalyticH1HWEngine — Analytic Heston-Hull-White engine based on the H1-HW approximation.

## Synopsis

`#include <ql/pricingengines/vanilla/analytich1hwengine.hpp>`

Inherits **AnalyticHestonHullWhiteEngine**.

### Public Member Functions

AnalyticH1HWEngine(const boost::shared_ptr<HestonModel> &model, const boost::shared_ptr<HullWhite> &hullWhiteModel,RealrhoXV,SizeintegrationOrder=144)AnalyticH1HWEngine(const boost::shared_ptr<HestonModel> &model, const boost::shared_ptr<HullWhite> &hullWhiteModel,RealrhoSr,RealrelTolerance,SizemaxEvaluations)

### Protected Member Functions

std::complex<Real>addOnTerm(Realphi,Timet,Sizej) const

### Additional Inherited Members

## Detailed Description

Analytic Heston-Hull-White engine based on the H1-HW approximation.

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_{S,v} dt, rho_{S,r} >= 0 \ dW_1 dW_3 &=& rho_{S.r} dt \ dW_2 dW_3 &=& 0 dt \ \nd{array} ].PP References:

Lech A. Grzelak, Cornelis W. Oosterlee, On The Heston Model with Stochastic, http://papers.ssrn.com/sol3/papers.cfm?…

Lech A. Grzelak, Equity and Foreign Exchange Hybrid Models for Pricing Long-Maturity Financial Derivatives, http://repository.tudelft.nl/assets/uui…

**Tests**

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

## Author

Generated automatically by Doxygen for QuantLib from the source code.

## Referenced By

addOnTerm(3) and AnalyticH1HWEngine(3) are aliases of QuantLib_AnalyticH1HWEngine(3).