A fractional version of the Cox–Ingersoll–Ross interest rate model and pricing double barrier option with Hurst index

AbstractIn this work, we study the existence and uniqueness of the solution to a fractional version of the Cox–Ingersoll–Ross (fCIR) stochastic differential equation. The strong convergence of this equation is analyzed and according to it’s framework, we obtain the price of the double barrier option under transaction cost. Finally, we verify the effect of the parameters of the model on the value of the option.