Existence and Uniqueness Solution Under Non-Lipschiz Condition of the Mixed Fractional Heston's Model

Didier Alain Njamen Njomen, Eric Djeutcha, Louis-Aime Fono

Abstract

This paper focuses on a mixed fractional version of Heston model in which the volatility Brownian and price Brownian are replaced by mixed fractional Brownian motion with the Hurst parameter $H\in(\frac{3}{4},1)$ so that the model exhibits the long range dependence. The existence and uniqueness of solution of mixed fractional Heston model is established under various non-Lipschitz condition and a related Euler discretization method is discussed. An example on the American put option price using Least Squares Monte Carlo Algorithm to produce acceptable results under the mixed fractional Heston model is presented to illustrate the applicability of the theory. The numerical result obtained proves the performance
of our results.

Keywords

Brownian motion, fractional processes, mixed fractional Brownian, Heston mode, Monte Carlo Algorithm

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