**AN IMPROVEMENT IN THE
STOCHASTIC STOCK PRICE DIFFERENCES MODEL **

Susumu
Saito, Miyuki Hasegawa

**Abstract**

An
improvement of the equation in a stochastic model for stock price and foreign exchange
simulations was tried. In the improved equation, the random walk term in the
stochastic model is multiplied by the absolute value of the difference between
the current price and the price in the previous period divided by square root
of a time interval raised to the power of a certain value, plus a term which is
the price difference multiplied by a coefficient. As a result, a differences
distribution close to an actual distribution with a high peak and fat tails was
obtained, and a financial time series simulation model whose differences
distribution, option prices and final prices remain the same irrelevant of the
length of time interval was derived. The derived time series also show
movements close to actual movements in that they have continuous small or large
fluctuations and continuous price increase or decrease.

Lecture
Notes in Management Science (2011) Vol. 3: 167-178

3rd
International Conference on Applied Operational Research, Proceedings

©
Tadbir Operational Research Group Ltd. All rights reserved.

www.tadbir.ca

ISSN
2008-0050 (Print)

ISSN
1927-0097 (Online)

**ARTICLE OUTLINE**

·
**Introduction**

·
**Stochastic Model And
Its Final Improved Equation **

·
**Process To The Final
Equation **

·
**First Improvement **

·
**Third Improvement **

·
**The Results With The
Final Improved Equation **

·
**Time Series Results **

·
**Differences
Distribution **

·
**Discussion On The
Power Law Of Differences Distribution **

·
**Comparison Of Call
Option Prices For Different Numbers Of Iterations **

·
**Comparison Of The
Distributions Of Final Values From Simulations Using The Improved Equation **

·
**Conclusions And
Discussion **

·
**References**