Stochastic differential equations and comparison of financial models with levy process using Markov chain Monte Carlo (MCMC) simulation

An available method of modeling and predicting the economic time series is the use of stochastic differential equations, which are often determined as jump-diffusion stochastic differential equations in financial markets and underlier economic dynamics. Besides the diffusion term that is a geometric Brownian model with Wiener random process, these equations contain a jump term that follows Poisson process and depends on the type of market. This study presented two different models based on a certain class of jump-diffusion stochastic differential equations with random fluctuations: Black- Scholes model and Merton model (1976), including jump-diffusion (JD) model, which were compared, and their parameters and hidden variables were evaluated using Markov chain Monte Carlo (MCMC) method.