Simulation Methods Comparison and Parameter Estimation for a Fractional Stochastic Volatility Model with Application in Stock Price Analysis

Abstract

This paper studies continuous-time stock pricing models with stochastic volatility driven by fractional Brownian motion. We compare two ways for simulating the paths of stochastic volatility and stock price when the Hurst parameter of fractional Brown motion is between 0.5 and 1. The first approach, is to use truncated fractional Brownian motion to approximate the fractional Brownian motion and estimate the volatility by Monte Carlo integral and symbolic integral. In the second one, Euler method is employed in simulation, without truncating the fractional Brownian process. Simulating the fractional Brownian motion in the second approach, we use spectral representation. Simulation results show that the latter is more efficient than using the symbolic integral and Monte Carlo integral is the worst. The application of the stochastic model is illustrated through real financial data.