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OK, so in this lecture, you're going to look at a simple example of how to simulate stock prices,

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assuming that the log returns come from a normal distribution.

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Now, this might seem at first to be a strange exercise, but it should get you thinking.

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We'll see how totally unpredictable randomness can lead to something that looks very much like a stock

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race time series.

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In fact, this exact method can be used for doing Montecarlo simulations and evaluating the Black-Scholes

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formula.

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Furthermore, it is also useful for when we want to analyze certain rules of thumb for Arima.

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This may not make too much sense right now, but you'll see how this kind of approach can help to validate

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some of the rules that we use for a rhema model selection.

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OK, so let's start by importing nonpaying matplotlib.

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The next step is to set a few constants will be using, such as the number of time steps, the initial

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price and the drift term.

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The next step is to run our simulation, so we'll start by taking the log of the price and setting it

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to last P last P is a variable will continue to update throughout the loop, since the current price

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will always depend on the last price.

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The next step is to create two arrays, to store log returns and our prices, and of course, these

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should both have length T.

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The next step is to enter a loop that goes 40 iterations inside the loop.

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We'll start by sampling a random log return from a zero mean normal distribution with standard deviation

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zero point zero one.

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The next step is to compute our new log price.

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This is equal to the old log price, plus the drifter, plus the random noise.

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The next step is to store the log return and the new price note that we don't actually make use of the

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log returns, but you may find them to be useful in later code for the price.

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Note that we have to take the exponential since we want to plot the price and not the log price.

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The final step in this loop is to assign P to last P so that last P has the correct value in the next

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iteration.

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OK, and so in the next block, we are going to plot our simulated time series.

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So as you can see, this certainly looks like a plausible stock price evolution in the coming lectures,

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you learn about the why behind what we just did.

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And hopefully this will give you some insight behind this exercise.