Pricing European Options in Selected Stochastic Volatility Models

Abstract

In this paper four methods of calculating characteristic functions and their application to selected stochastic volatility models are considered. The methods applied are based on the assumption that the prices of European calls are evaluated numerically by means of the Gauss-Kronrod quadrature. Such approach is used to investigate computational efficiency of pricing European calls. Particular attention in this matter is paid to the speed of generating theoretical prices of the analyzed contracts.

Pricing European Options in the Heston and the Double Heston models

“…The results of the research carried out are shown in the graphs below -see Figures 3 and 4. The results obtained allow to state that the conclusions drawn previously [Orzechowski 2020] can be extended onto the double Heston model. It means that the computational efficiency of pricing European options depends on the way the characteristic functions and their inverse Fourier transforms are calculated.…”

“…The determination of the most efficient approach both in the Heston and the double Heston models, is based on the results generated with the use of codes developed in Mathematica 10.2. The methodology proposed in the research is compatible with the approach applied previously [Orzechowski 2020]. It means that the theoretical prices of European calls have been evaluated numerically by means of the Gauss-Kronrod quadrature.…”

“…There are many approaches to determining characteristic function of and calculating its inverse Fourier transform [Carr & Madan 1999, Attari 2004, Bates 2006and Orzechowski 2018. As some of the approaches has already been presented [Orzechowski 2020] in the later part of the article only formulas concerning the double Heston model are of interest. As before, for the purpose of the article, it is assumed that = 0.…”