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I am reading Longstaff and Schwartz Valuing Aerican Options by Simulation because monte carlo simulations, especially their use in option pricing, is interesting to me. However, I am having some difficulty getting through the numerical example - not from lack of understanding the big picture but recreating the example myself.

On page 116 the authors discuss stock price paths - they say they are generated under the risk neutral measure but I am missing some background here that will allow me create this example on my own for understanding (or a different example for me to work through). I feel that the authors left out some critical information here on exactly how this example was produced.

Can anyone explain to me how these stock prices are generated, or link me to resources so I can figure it out myself? It would go a long way towards me fully understanding this paper.

Thank you!

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  • $\begingroup$ Do you know how to simulate GBM (Geometric Brownian Motion) ? If so, do you know how to set $\mu$ and $\sigma$ for generating GBM under the risk neutral measure? $\endgroup$ – Alex C May 13 '16 at 22:53
  • $\begingroup$ I do know how to simulate GBM, however I have never set it up for generating GBM under the risk neutral measure. Can you point me to some posts/papers on this so I can learn? I assume then each of the steps is a simulation of a 3 period GBM. $\endgroup$ – user20664 May 13 '16 at 22:57
  • $\begingroup$ Alex C: forgot to tag you in the above comment $\endgroup$ – user20664 May 14 '16 at 1:08
  • $\begingroup$ "under the risk neutral measure" just means, for this purpose, that the drift rate of the GBM must be set equal to the risk free rate $r_f$, while the volatility must be set equal to the volatility of the stock. The reason for this choice is complicated to explain, but for simulation purposes that is all there is to it. So now you know what to do. $\endgroup$ – Alex C May 14 '16 at 2:37
  • $\begingroup$ @Alex C Oh wow that is simple. If you could put that into an answer maybe with a little more detail for passers-by I'll gladly mark this answered $\endgroup$ – user20664 May 14 '16 at 2:53

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