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On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model


Citation

Siow, Woon Jeng and Kilicman, Adem (2021) On multilevel and control variate Monte Carlo methods for option pricing under the rough Heston model. Mathematics, 9 (22). art. no. 2930. pp. 1-32. ISSN 2227-7390

Abstract

The rough Heston model is a form of a stochastic Volterra equation, which was proposed to model stock price volatility. It captures some important qualities that can be observed in the financial market—highly endogenous, statistical arbitrages prevention, liquidity asymmetry, and metaorders. Unlike stochastic differential equation, the stochastic Volterra equation is extremely computationally expensive to simulate. In other words, it is difficult to compute option prices under the rough Heston model by conventional Monte Carlo simulation. In this paper, we prove that Euler’s discretization method for the stochastic Volterra equation with non-Lipschitz diffusion coefficient E[|Vt−Vnt|p] is finitely bounded by an exponential function of t. Furthermore, the weak error |E[Vt−Vnt]| and convergence for the stochastic Volterra equation are proven at the rate of O(n−H). In addition, we propose a mixed Monte Carlo method, using the control variate and multilevel methods. The numerical experiments indicate that the proposed method is capable of achieving a substantial cost-adjusted variance reduction up to 17 times, and it is better than its predecessor individual methods in terms of cost-adjusted performance. Due to the cost-adjusted basis for our numerical experiment, the result also indicates a high possibility of potential use in practice.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
DOI Number: https://doi.org/10.3390/math9222930
Publisher: MDPI
Keywords: Rough Heston model; Weak convergence error rate; Monte Carlo method; Control variate method; Multilevel Monte Carlo method
Depositing User: Ms. Nur Faseha Mohd Kadim
Date Deposited: 15 Feb 2023 07:09
Last Modified: 29 Mar 2023 08:23
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3390/math9222930
URI: http://psasir.upm.edu.my/id/eprint/94432
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