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Simulate a time series of stock price using Monte-Carlo simulations

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Alessandro
Alessandro on 8 Mar 2016
Edited: Rick Rosson on 8 Mar 2016
Hy everyone, I need to compute a time series of stock price assuming that they are driven by a random walk. What would be the best way to approach the problem, i.e. the right function to do so? I should replicate it 10.000 times (N=10.000).
thanks for the help.

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Alessandro
Alessandro on 8 Mar 2016
the random walk has a standard normal distribution ~N(0,1) and I should use T random walks (from t=1,...T). Any other information? Thank you
Rick Rosson
Rick Rosson on 8 Mar 2016
A few additional points:
  • Remember to put something in your code to prevent the stock price from falling below 0.
  • Also, in the real-world, stock prices tend to drift higher over time, so the assumption of a zero mean is not realistic. The mean should be a positive number, although possibly quite small in relative terms. Furthermore, the size of the mean is usually proportional to the current price of the stock, as is the standard deviation.
  • It might be interesting to consider the relative sizes of the mean versus the standard deviation of the net change per period.

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Accepted Answer

Rick Rosson
Rick Rosson on 8 Mar 2016
Edited: Rick Rosson on 8 Mar 2016
Here is some code to get you started:
N = 10000;
P = nan(N,1);
P(1) = ...
for k = 2:N
P(k) = P(k-1) + ...
end
figure;
plot(P);

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