A semi-analytical pricing formula for European options under the rough Heston-CIR model


  • Xin-Jiang He University of Wollongong
  • Sha Lin Zhejiang Gongshang University




rough Heston-CIR model, semi-analytical, fractional Riccati equation, European options.


We combine the rough Heston model and the CIR (Cox–Ingersoll–Ross) interest rate together to form a rough Heston-CIR model, so that both the rough behaviour of the volatility and the stochastic nature of the interest rate can be captured. Despite the convoluted structure and non-Markovian property of this model, it still admits a semi-analytical pricing formula for European options, the implementation of which involves solving a fractional Riccati equation. The rough Heston-CIR model is more general, taking both the rough Heston model and the Heston-CIR model as special cases. The influence of rough volatility and stochastic interest rate is shown to be significant through numerical experiments. doi:10.1017/S1446181120000024

Author Biographies

Xin-Jiang He, University of Wollongong

School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia.

Sha Lin, Zhejiang Gongshang University

School of Finance, Zhejiang Gongshang University, Hangzhou, Zhejiang Province, China.





Articles for Printed Issues