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This book covers various applications of probability theory in the stock market. The first part of the book lays out the necessary background materials from probability theory along with a number of examples. The second part of the book lays out a theory of stocks, assuming that the price of a stock over time is a stochastic process. To analyze and forecast the price of a stock it is necessary to make certain simplifying assumptions about the underlying stochastic process. Depending on how and what assumptions are made we obtain different theories about the price movement of a stock: in the capital asset pricing model it is assumed that the random variables constituting the underlying stochastic process are mutually independent and identically distributed; the binomial stock pricing model is constructed from the simplifying assumption that the economy has two possible states, expansion and recession, and the stock price goes up or down according to which state the economy is in; the natural stochastic model under the efficient market hypothesis is that of a martingale, which is a special type of Markov process, and so forth.Highlights of the book include the following: (1) the dollar cost averaging strategy is analyzed using regression analysis; (2) the distribution of golden and death crosses is shown to follow an inverse sine distribution, which is an equalization probability distribution for simple random walks; (3) a possible autocorrelation phenomenon in the stock price movement is discussed—it is conceivable that a large amount of transactions occurring in a short period of time in exchange traded funds introduces an autocorrelation in the market indices; (4) the historical inflation data is studied in conjunction with the S&P 500 index—it is shown that the risk of deflation is now fairly high; (5) algorithmic stock trading strategies, using Markov chain models that are more general than martingales, are derived; (6) the Fibonacci retracement phenomenon is discussed using the mathematical theory of recurrent arithmetic functions; (7) an explicit martingale price model in terms of transition probabilities is derived without relying on the efficient market hypothesis.
eBook details
- Title: Probability and the Stock Market
- Author : Kichoon Yang
- Release Date : *
- Genre: Kindle Store,Kindle eBooks,Business & Money
- Pages : * pages
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