# 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, **Real** rhoXV, **Size** integrationOrder=144)**AnalyticH1HWEngine** (const boost::shared_ptr< **HestonModel** > &model, const boost::shared_ptr< **HullWhite** > &hullWhiteModel, **Real** rhoSr, **Real** relTolerance, **Size** maxEvaluations)

### Protected Member Functions

std::complex< **Real** > **addOnTerm** (**Real** phi, **Time** t, **Size** j) 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?abstract_id=1382902

Lech A. Grzelak, Equity and Foreign Exchange Hybrid Models for Pricing Long-Maturity Financial Derivatives, http://repository.tudelft.nl/assets/uuid:a8e1a007-bd89-481a-aee3-0e22f15ade6b/PhDThesis_main.pdf

**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

The man pages addOnTerm(3) and AnalyticH1HWEngine(3) are aliases of QuantLib_AnalyticH1HWEngine(3).