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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.

In this paper, we first apply cosine radial basis function neural networks to solve the fractional differential equations with initial value problems or boundary value problems. In the examples, we successfully obtained the numerical solutions for the fractional Riccati equations and fractional Langevin equations. The computer graphics and numerical solutions show that this method is very effective.

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A SEMI-ANALYTICAL PRICING FORMULA FOR EUROPEAN OPTIONS UNDER THE ROUGH HESTON-CIR MODEL

Cosine Radial Basis Function Neural Networks for Solving Fractional Differential Equations

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2 results

A SEMI-ANALYTICAL PRICING FORMULA FOR EUROPEAN OPTIONS UNDER THE ROUGH HESTON-CIR MODEL

Cosine Radial Basis Function Neural Networks for Solving Fractional Differential Equations