Susumu Saito, Miyuki Hasegawa




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.


ISSN 2008-0050 (Print)

ISSN 1927-0097 (Online)




·         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


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