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Fractional Riccati equation and its applications to rough Heston model using numerical methods


Siow, Woon Jeng and Kilicman, Adem (2020) Fractional Riccati equation and its applications to rough Heston model using numerical methods. Symmetry, 12 (6). art. no. 959. pp. 1-20. ISSN 2073-8994


Rough volatility models are recently popularized by the need of a consistent model for the observed empirical volatility in the financial market. In this case, it has been shown that the empirical volatility in the financial market is extremely consistent with the rough volatility. Currently, fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form and therefore, we must rely on numerical methods to obtain a solution. In this paper, we will be giving a short introduction to option pricing theory (Black–Scholes model, classical Heston model and its characteristic function), an overview of the current advancements on the rough Heston model and numerical methods (fractional Adams–Bashforth–Moulton method and multipoint Padé approximation method) for solving the fractional Riccati equation. In addition, we will investigate on the performance of multipoint Padé approximation method for the small u values in Dαh(u−i/2,x) as it plays a huge role in the computation for the option prices. We further confirm that the solution generated by multipoint Padé (3,3) method for the fractional Riccati equation is incredibly consistent with the solution generated by fractional Adams–Bashforth–Moulton method.

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Official URL or Download Paper: https://www.mdpi.com/2073-8994/12/6/959

Additional Metadata

Item Type: Article
Divisions: Institute for Mathematical Research
DOI Number: https://doi.org/10.3390/sym12060959
Publisher: Multidisciplinary Digital Publishing Institute
Keywords: Fractional Riccati equation; Rough volatility models; Classical Heston model; Rough Heston model; Characteristic function; Fractional Adams–Bashforth–Moulton method; Multipoint Padé approximation method
Depositing User: Ms. Nuraida Ibrahim
Date Deposited: 21 Sep 2021 23:14
Last Modified: 21 Sep 2021 23:14
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3390/sym12060959
URI: http://psasir.upm.edu.my/id/eprint/89064
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