You wish to predict the future stock price of Stark Industries (STRK) to develop a trading strategy. One way to model stock prices (in a "normal" market) is to use Brownian Motion. In this model, each day's price is estimated using the previous day's price plus a random amount. For this problem, we will be adding a random number coming from a normal distribution. For the distribution, the standard deviation will be 0.5% of the previous day's price and the mean will be +0.1% of the previous day's price. The mean will be positive if the price one day before is higher than the price two days before, and negative otherwise. For example, to estimate the price for day three, add a random number to the price on day two. The mean and standard deviation of this random number is calculated using the stock price on day two and the trend in price from day one to day two. Simulate the stock price of STRK over one year (250 trading days). Repeat this for many (100,000+) repeated simulations. Produce a A. convergence plot demonstrating that you ran enough simulations B. "spaghetti plot" that shows the daily price for each simulation. Your x-axis should be the trading day (1:250) and the y-axis is the stock price ($). Plot all simulations on this plot, no need for a legend. C. properly-binned, relative-frequency histogram of the stock price only at the end of one year over your repeated simulations Calculate and explain, according to the model, D. Is the stock price after one year normally distributed? E. The probability that the stock price will be above 550 after one year F. The probability that the stock price will be below 450 after one year G. If you bought the stock on day one for $500, would you have made a profit after one year? Problem Parameters: • The stock price on day one is $500 • For day two only, use a mean of zero for the random number • There are 250 trading days in the year Hints/Clarifications: • First, get your program to work for a single trading year before repeating it for multiple simulations • Reset all your quantities at the beginning of each simulation