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I know this is almost a month old, but... Unless it is a homework assignment, you could have a look at this paper by Del Moral and Shevchenko, which gives a different estimator than the one you're probably using. It gives both a crude Monte Carlo-estimator and a sequential Monte Carlo-estimator. You probably just want the crude Monte Carlo one. Eq. (27) ...


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To answer your question you need to look at what the distribution is of $S_T$. Since $dS = \sigma dW$ we have that $S_T$ is normal distribution with variance of $\sigma^2 (T)$. Now you get $E(-exp(-\gamma(x + qS_T))) = -exp(-\gamma x) E (exp(-\gamma q S_T))$. Given that $S_T$ is normal $-\gamma q S_T$ is normal as well. You just scale the variance with ...


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No fancy theory is needed to understand why a GBM is applied to model stock prices. To get an intuitive understand, simple Macro-economics should suffice to understand why it is being applied: it has a Brownian component it has (exponential) drift - this makes the model able to deal with stock prices growing in line with GDP (actually faster than gdp ...



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