Year: 2023
Author: Hui Liang, Jingtang Ma, Zhengguang Shi
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 2 : pp. 206–238
Abstract
In this paper, a rough Heston model with variable volatility of volatility (vol-of-vol) is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques. Then the nonlinear fractional Riccati equation for the characteristic function of the asset log-price is derived. The existence, uniqueness and regularity of the solution to the nonlinear fractional Riccati equation are proved and the equation is solved by the Adams methods. Finally the Fourier-cosine methods are combined with the Adams methods to price the options.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2023-0009
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 2 : pp. 206–238
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Rough Heston model option pricing Hawkes process fractional differential equations Fourier-cosine methods.