High-Order Approximations to Call Option Prices in the Heston Model

20 Pages Posted: 19 Jan 2021

See all articles by Archil Gulisashvili

Archil Gulisashvili

Ohio University

Marc Lagunas

University of Oslo - Department of Mathematics

Raul Merino

University of Barcelona - Faculty of Mathematics

Josep Vives

University of Barcelona

Date Written: April 17, 2019

Abstract

In the present paper, a decomposition formula for the call price due to Alòs is transformed into a Taylor-type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of the call price found in a recent paper by Als, Gatheral and Rodoičić. We use the new decomposition to obtain various approximations to the call price in the Heston model with sharper estimates of the error term than in previously known approximations. One of the formulas obtained in the present paper has five significant terms and an error estimate of the form O(v³(|P| + v)), where v and P are the volatility-of-volatility and the correlation in the Heston model, respectively. Another approximation formula contains seven more terms and the error estimate is of the form O(v⁴(1 + |P|v)). For the uncorrelated Heston model (P = 0), we obtain a formula with four significant terms and an error estimate O(v⁶) Numerical experiments show that the new approximations to the call price perform especially well in the high-volatility mode.

Keywords: computational finance, Heston model, option pricing, price approximations, stochastic volatility models, vanilla options

Suggested Citation

Gulisashvili, Archil and Lagunas, Marc and Merino, Raul and Vives, Josep, High-Order Approximations to Call Option Prices in the Heston Model (April 17, 2019). Journal of Computational Finance, Vol. 24, No. 1, 2020, Available at SSRN: https://ssrn.com/abstract=3768521

Archil Gulisashvili

Ohio University ( email )

Athens, OH 45701-2979
United States
740-593-1281 (Phone)
740-593-9805 (Fax)

Marc Lagunas

University of Oslo - Department of Mathematics ( email )

Blindern, N-0162, Os
Norway

Raul Merino (Contact Author)

University of Barcelona - Faculty of Mathematics

Barcelona, 08007
Spain

Josep Vives

University of Barcelona ( email )

Gran Via de les Corts Catalanes, 585
Barcelona, 08007
Spain

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