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
Date Written: January 26, 2019
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: Suggested Citation