24 Jul DO THEY APPEAR TO RESEMBLE A NORMAL DISTRIBUTION?
A popular model for stock prices is the following. If P0 is the current stock price then the price Show more A popular model for stock prices is the following. If P0 is the current stock price then the price k periods from nowk (where a period could be a day week or any other component of time and k is any positive integer) is given by P_k= P_0 e^(((?-0.5?^2 )k+?Z?k ) ). Here e is the exponential function (EXP in Excel) is the mean percentage growth rate per period of the stock ? is the standard deviation of the growth rate per period and Z is a normally distributed random variable with mean 0 and standard deviation 1. Both and ? are typically expressed in decimal form such as = 0.01for a 1% mean growth rate. Suppose a period is defined as a month the current price of the stock (as of the end of December 2010) is $75 = 0.006 and ? = 0.028. Use simulation to obtain 500 possible stock price changes from the end of December 2010 to the end of December 2013. Each simulated change will be the price at the end of 2013 minus the price at the end of 2010. (Note that you can simulate a given change in one line and then copy it down.) Create a histogram of these changes to see whether the stock price change is at least approximately normally distributed. Also use the simulated data to estimate the mean price change and the standard deviation of the change. Use simulation to generate the ending stock prices for each month in 2011. ( Use k =1 again to get Januarys price from Decembers use k = 1 again to get Februarys price from Januarys and so on) Then use a data table to replicate the ending December 2011 stock price 500 times. Create a histogram of these 500 values. Do they appear to resemble a normal distribution? Show less
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