A Semi-Analytical Pricing Formula for European Options Under the Rough heston-Cir model

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.

Heston‐GA Hybrid Option Pricing Model Based on ResNet50

“…Heston model has been widely used and studied because of the advantage of portraying a reasonable implied-volatility shape and the existence of the closed-form solution [5][6][7]. Up to now, the optimization of Heston model from the mathematical perspective mainly involves ve directions: considering the randomness of the constant terms [8][9][10][11][12], improving the geometric Brownian motion [13,14], adding a jump di usion process [15,16], changing the power of the variance [17,18], and considering the roughness of the volatility [19,20]. e mathematical enhancement endowed Heston models with more rigorous tting to real market dynamics, but two problems remain:…”