Mathematical Analysis of Financial Model on Market Price with Stochastic Volatility

The Heston model is one of the most popular stochastic volatility models for option pricing to measure the volatility of different parameters in the financial market. In this work, we study the statistical analysis of Heston Model by partial differential equations. The model proposed by Heston takes into account non-lognormal distribution of the assets returns, leverage effect and the important mean reverting property of volatility. We have assayed on the return distribution on the basis of different values of correlation parameter and volatility, then we measure the effects of parameters ρ (correlation coefficient) an σ (standard deviation) for different situation such as ρ > 0, σ > 0, ρ = 0, σ = 0, ρ σ < 0 etc. On return distribution of Heston Model which indicates market condition for buyers and sellers to buy and sell options. All solvers used in this analysis are implemented using MATLAB codes and the simulation results are presented graphically.