The Weak Convergence Rate of Two Semi-Exact Discretization Schemes for the Heston Model

Annalena Mickel and Andreas Neuenkirch
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Annalena Mickel: DFG Research Training Group 1953, University of Mannheim, B6, 26, D-68131 Mannheim, Germany
Andreas Neuenkirch: Mathematical Institute, University of Mannheim, B6, 26, D-68131 Mannheim, Germany

Risks, 2021, vol. 9, issue 1, 1-38

Abstract: Inspired by the article Weak Convergence Rate of a Time-Discrete Scheme for the Heston Stochastic Volatility Model, Chao Zheng, SIAM Journal on Numerical Analysis 2017, 55:3, 1243–1263 , we studied the weak error of discretization schemes for the Heston model, which are based on exact simulation of the underlying volatility process. Both for an Euler- and a trapezoidal-type scheme for the log-asset price, we established weak order one for smooth payoffs without any assumptions on the Feller index of the volatility process. In our analysis, we also observed the usual trade off between the smoothness assumption on the payoff and the restriction on the Feller index. Moreover, we provided error expansions, which could be used to construct second order schemes via extrapolation. In this paper, we illustrate our theoretical findings by several numerical examples.

Keywords: Heston model; discretization schemes for SDEs; exact simulation of the CIR process; Kolmogorov PDE; Malliavin calculus (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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