Journal of Finance and Economics
ISSN (Print): 2328-7284 ISSN (Online): 2328-7276 Website: http://www.sciepub.com/journal/jfe Editor-in-chief: Suman Banerjee
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Journal of Finance and Economics. 2019, 7(2), 75-80
DOI: 10.12691/jfe-7-2-5
Open AccessCase Study

Confidence Interval for Solutions of the Vasicek Model

Mohammad Ali Jafari1, Mehran Paziresh1, and Majid Feshari1

1Financial of Sciences, Kharazmi University, Tehran, Iran

Pub. Date: June 28, 2019

Cite this paper:
Mohammad Ali Jafari, Mehran Paziresh and Majid Feshari. Confidence Interval for Solutions of the Vasicek Model. Journal of Finance and Economics. 2019; 7(2):75-80. doi: 10.12691/jfe-7-2-5

Abstract

The forecast is very complex in financial markets. The reasons for this are fluctuation of financial data, Such as Stock index and rate interest data over time. The determining a model for forecasting fluctuations, can play a significant role in investor's decision making in financial markets. In the present paper, the Vasicek model the prediction of the rate interest on year later value, on using month data from the USA rate interest year 2017 and 2018, we will discuss, for this job, the first unknown parameters Vasicek model, as Average interest rate, Standard deviation of interest rate, and recursive mean of the model, using Euler maruyama maximum like lihood method, will be calibrate, and their values will be obtain by programming in the Maple software. And using a numerical method Euler Maruyama and computer simulation with the Maple software, for simulated data, gained averages and Standard deviations, confidence interval and their normal histogram will be the plot. Also, average of the solutions obtained from computer simulations is compared with real ones, and after analyzing and reviewing the results, performance of the Vasicek model will be measured, in interest rate value prediction. And in the end, this research is compared with internal article, and suggestions for future research will be raised.

Keywords:
the asset valuation models confidence interval Vasicek model stochastic differential equations calibration

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References:

[1]  Bjork, T. (2009). Arbitrage theory in continuous time. Oxford university pres.
 
[2]  Cyganowski, S., Kloeden, P., & Ombach, J. (2001). From elementary probability to stochastic differential equations with MAPLE. Springer Science & Business Media.
 
[3]  Gordon, M. J. (1962). The investment, financing, and valuation of the corporation. RD Irwin.
 
[4]  Hull, J. C., & Basu, S. (2016). Options, futures, and other derivatives. Pearson Education India.
 
[5]  Hull, J., Treepongkaruna, S., Colwell, D., Heaney, R., & Pitt, D. (2013). Fundamentals. Of futures and options markets. Pearson Higher Education AU
 
[6]  Klebaner, F. C. (2012). Introduction to stochastic calculus with applications. World Scientific Publishing Company.
 
[7]  ├śksendal, B. (2003). Stochastic differential equations. In Stochastic differential equations (pp. 65-84). Springer, Berlin, Heidelberg.
 
[8]  Owen, A. B. (2013). Monte Carlo theory, methods and examples. Monte Carlo Theory, Methods and Examples. Art Owen.
 
[9]  Rust, J. (1996). Numerical dynamic programming in economics. Handbook of computational economics, 1, 619-729.
 
[10]  Seydel, R., & Seydel, R. (2006). Tools for computational finance. (Vol. 3). Berlin: Springer.
 
[11]  Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of financial economics, 5(2), 177-188.