A Mathematical Analysis of Stock Price Oscillations within Financial Markets

The application of econophysics in modeling investment assets' market behavior is considerably increasing and is highly becoming an area of interest for market actors including quants and econophysicists. This study investigated stock price oscillatory behavior in stock markets. We applied mathematical methods to derive the stock market price oscillatory model from the physics field. We considered two distinct price level cases that is, high and low price cases and presented/ derived a corresponding model for each case. We managed also to derive an explicit time function which measures and calculate the time taken by stock prices to oscillate between two values. Also, from the low-price oscillation model we managed to investigate stock price motion at different times with all other external forces held constant. Results obtained showed that, although stock price movement (volatility) is time dependent, it is propelled and fueled by market forces such as stock volume, market size and classical forces of demand and supply. Above all we evaluated our model using means difference test of hypothesis using actual and estimated stock price data. We failed to reject our null hypothesis and concluded that, there is no statistical significant difference in the means which highly support the precision of our model. Despite all this, we sensed a gap that other researchers can work on such as the application of simple harmonic oscillations in stock markets and interestingly we recommended the use of the current advanced software such as R studio for precise and accurate results and viable conclusions