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

Xin-Jiang He, Sha Lin

Abstract


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

Keywords


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



DOI: https://doi.org/10.21914/anziamj.v61i0.14608



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.