If I have given vectors for return and volatility (i.e. I have two 1x10 vectors), and I assume at first that their correlation is 0 (meaning my covariance-variance matrix is just diagonal), how do I simulate daily stock prices for the 10 year period?


closed as off-topic by Joshua Ulrich, Clebson Derivan, olaker Feb 19 '14 at 20:06

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  • $\begingroup$ Use normrnd to simulate daily log returns, then convert to prices. Mvnrnd does the same simulation, but since you're dealing with a diagonal covariance matrix it just transforms it by the cholesky, which is the identity matrix. Note that this only means you simulate from a distribution with 0 correlations. It does not mean that the simulated correlation matrix will be an identity matrix. See this: mathworks.com/matlabcentral/fileexchange/… $\endgroup$ – John Feb 19 '14 at 21:53
  • $\begingroup$ there is the full commented code on this wii: en.literateprograms.org/Monte_Carlo_simulation_(Matlab) $\endgroup$ – lehalle Feb 19 '14 at 22:17

A very simple approach could be the following: draw a random number for each day for each stock. If you refer to "average/mean" by return and to "standard deviation/variance" by volatility, you could use these for the distribution parameters of the random numbers per stock. If you dislike that values can go below zero, apply Euler's exponential function on each random number. This link and its references explain a similar approach.