The Heston Stochastic Volatility Model with Piecewise Constant Parameters - Efficient Calibration and Pricing of Window Barrier Options

18 Pages Posted: 24 Jul 2017 Last revised: 27 Jan 2019

See all articles by Daniel Guterding

Daniel Guterding

Technische Hochschule Mittelhessen

Wolfram Boenkost

Lucht Probst Associates GmbH

Date Written: January 26, 2019

Abstract

We present a simple and numerically efficient approach to the calibration of the Heston stochastic volatility model with piecewise constant parameters. Extending the original ansatz for the characteristic function, proposed in the seminal paper by Heston, to the case of piecewise constant parameters, we show that the resulting set of ordinary differential equations can still be integrated semi-analytically. Our numerical scheme is based on the calculation of the characteristic function using Gauss-Kronrod quadrature, additionally supplying a Black-Scholes control variate to stabilize the numerical integrals. We apply our method to the problem of calibration of the Heston model with piecewise constant parameters to the foreign exchange (FX) options market. Finally, we demonstrate cases in which window barrier option prices calculated using the Heston model with piecewise constant parameters are consistent with the market, while those calculated with a plain Heston model are not.

Keywords: Heston model, time-dependent parameters, characteristic function, window barrier options

JEL Classification: C63, G13

Suggested Citation

Guterding, Daniel and Boenkost, Wolfram, The Heston Stochastic Volatility Model with Piecewise Constant Parameters - Efficient Calibration and Pricing of Window Barrier Options (January 26, 2019). Available at SSRN: https://ssrn.com/abstract=3005953 or http://dx.doi.org/10.2139/ssrn.3005953

Daniel Guterding (Contact Author)

Technische Hochschule Mittelhessen ( email )

University of Applied Sciences
Wilhelm-Leuschner-Stra├če 13
Friedberg, 61169
Germany

Wolfram Boenkost

Lucht Probst Associates GmbH ( email )

Grosse Gallusstr. 9
Frankfurt, 60311
Germany

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