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• PRERNA BAID

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Introduction A stock market is essentially a medium through which companies can raise additional finance by selling shares to the general public. The general public can either benefit from this venture by purchasing a stock at a lower price and then selling it at a higher price in the future and hence gaining a substantial profit or lose out if the value of the stock falls and they sell it at a lower price than the price they bought it in. Hence, investors often evaluate the possibility of future stock prices so that they are able to identify shares whose value would rise most and hence purchase those stocks rather than the ones whose market values are likely fall to in the stock market. A trend of the fall or rise of the stock prices of a company can be found and so financial analysts devise formulas in order to obtain the future value of a stock which is used to better inform potential investors about their stock options. The Black Scholes formula was developed in 1973 by Fischer Black, Myron Scholes and Robert Merton; it was used to calculate future European option prices using differentiation. It was realistically difficult to calculate the exact value of the future stock and hence it was merely an approximation or an estimate which helped investors to receive an idea about the future worth of a stock. Since then a lot of ideas have come up in order to estimate the future stock prices. However, the use of mathematics in predicting stock markets is often regarded as questionable due to the fluctuating nature of various economic variables like interest rates and exchange rates. Nevertheless, investors often want to reduce the risk in their decision making by logically evaluating their decisions rather than merely using intuition. Hence, mathematics plays a key role in the stock market. The variation in the stock prices can be mapped by a graph consisting of the stock prices of a firm against time in years. The stock prices of Walmart can be taken into consideration has currently it is expanding and has offered its shares on the stock exchange.

Here a best fit line can be drawn to somewhat assist in estimating the value of future stock prices by extrapolating the curve. Differential calculus is essentially calculating the slope of the graph at any given point. If the slope is negative, the value of the share tends to fall and hence the investment is not a good idea, however the higher the positive gradient of the best fit curve, the higher the prospects of being able to buy higher profits.

This best fit curve can then be compared with the shares of other companies and hence the most optimum investment can be procured by selecting the stock with the slope which is increasing the most along two points. However, this is not the most optimum method as the best time to purchase and sell the share in order to maximize profits cannot be selected. For this another method can be devised which is commonly known as the support and resistance method. This is done by making two lines called the support and resistance. The support line is formed by joining the lows and the resistance line is formed by joining the highs. If the support tends to have a higher slope than the resistance in the most immediate time then the stock should not be bought but when the difference between the slope resistance and support is the largest when the former is higher than that is a period when the stock should be bought.