An efficient Monte Carlo simulation for new uncertain Heston–CIR hybrid model

Abstract

In this paper, we consider two new stock models in which their differential equations are modeled by Liu process in uncertain environment. Firstly, we study the uncertain Schobel–Zhu–Hull–White hybrid model and obtain its closed European call option pricing using Liu calculus. Also, we solve this model by Monte Carlo simulation to ensure the performance of Monte Carlo method. Our main purpose is to present a new model, uncertain Heston–CIR hybrid model, in which its uncertain differential equations cannot be solved and so we can calculate the option value via Monte Carlo simulation. Finally, some examples are stated for illustrating these models to obtain successful results and show the efficiency of Monte Carlo method.