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Volume 39, Issue 2
Rough Heston Models with Variable Vol-of-Vol and Option Pricing

Hui Liang, Jingtang Ma & Zhengguang Shi

DOI: 10.4208/aam.OA-2023-0009

Ann. Appl. Math., 39 (2023), pp. 206-238.

Published online: 2023-06

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  • 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.

  • Keywords

Rough Heston model, option pricing, Hawkes process, fractional differential equations, Fourier-cosine methods.

  • AMS Subject Headings

60G22, 60G55, 65R20, 91G20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-39-206, author = {Liang , HuiMa , Jingtang and Shi , Zhengguang}, title = {Rough Heston Models with Variable Vol-of-Vol and Option Pricing}, journal = {Annals of Applied Mathematics}, year = {2023}, volume = {39}, number = {2}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2023-0009}, url = {http://global-sci.org/intro/article_detail/aam/21834.html} }
TY - JOUR T1 - Rough Heston Models with Variable Vol-of-Vol and Option Pricing AU - Liang , Hui AU - Ma , Jingtang AU - Shi , Zhengguang JO - Annals of Applied Mathematics VL - 2 SP - 206 EP - 238 PY - 2023 DA - 2023/06 SN - 39 DO - http://doi.org/10.4208/aam.OA-2023-0009 UR - https://global-sci.org/intro/article_detail/aam/21834.html KW - Rough Heston model, option pricing, Hawkes process, fractional differential equations, Fourier-cosine methods. AB -

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.

Hui Liang, Jingtang Ma & Zhengguang Shi. (2023). Rough Heston Models with Variable Vol-of-Vol and Option Pricing. Annals of Applied Mathematics. 39 (2). 206-238. doi:10.4208/aam.OA-2023-0009
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