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

  • Authors

    • Kianoush Fathi Vajargah Department of Statistics,Islamic Azad University,Tehran,North Branch,IRAN
    2015-01-25
    https://doi.org/10.14419/ijasp.v3i1.4066
  • Levy Process, Markov Chain Monte Carlo, Black- Scholes Model, Merton Model, Stochastic Differential Equations.

  • Abstract

    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.

  • References

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  • Received date: 2014-12-23

    Accepted date: 2015-01-20

    Published date: 2015-01-25