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

Received date: December 23, 2014

Accepted date: January 20, 2015

Published date: January 25, 2015

DOI:

https://doi.org/10.14419/ijasp.v3i1.4066

Keywords:

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: December 23, 2014

Accepted date: January 20, 2015

Published date: January 25, 2015