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

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • 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.


  • Keywords


    Levy Process; Markov Chain Monte Carlo; Black- Scholes Model; Merton Model; Stochastic Differential Equations.

  • References


      [1] D.Applebaum, 2004, Levy Process and Stochastic Calculus, Cambridge University Press. http://dx.doi.org/10.1017/CBO9780511755323.

      [2] J.Bertion, 1998, Levy Process, Cambridge University Press.

      [3] P.Billingsley, 1995, Probability and Measures, 3rd ed, Wiley&Sons, New York.

      [4] R.Cont, P.Tankov, 2004, Fainancial Modeling With Jump Processes,Chapman&Hall/CRC Press.

      [5] J.S.Dagpunar, 2007, Simulation and Monte Carlo With Application in Finance and MCMC,Wiley&Sons. http://dx.doi.org/10.1002/9780470061336.

      [6] S.Dereich, F, Heidenreich, 2011, a Multilevel Monte Carlo Algorithm for Levy-Driven Stochastic Differential Equqtial Equations, Stochastics Processes and Their Applications, 121:1565-1587. http://dx.doi.org/10.1016/j.spa.2011.03.015.

      [7] M.B.Giles, Multi-level Monte Carlo Path Simulation, 2008, Operations Reserch, 56 (3):607-617. http://dx.doi.org/10.1287/opre.1070.0496.

      [8] M.B.Giles, B.J.Waterhouse, 2009, Multilevel Quasi-Monte Carlo Path Simulation,Radon Series Comp.Appl.Math8,1-18.

      [9] D.Henderson, P.Plaschko, 2006, Stochastic Differential Equations In Scientific Publishing,Singapore.

      [10] S.Heston, 1993, A Closed-fom Solutions Options with Stochastic Volatility with Applications to Bond and Currency Option, The Review of Finance Studies, 6(2):327-343. http://dx.doi.org/10.1093/rfs/6.2.327.


 

View

Download

Article ID: 4066
 
DOI: 10.14419/ijasp.v3i1.4066




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.