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 - <p style="text-align: justify;">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.</p>