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The link in your comments mention section 11.6 of Numerical Methods in Economics by Kenneth Judd. I recommend giving that a read as well. It's only a few pages. Below some code that implements least squares Monte Carlo for the problem you gave: set.seed(42) fun <- function(x, y) x^2 + y^2 + x * y N <- 1e3L X <- runif(N) Y <- runif(N) Z <- fun(...

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I am not sure how to outline that process without going through some notation. The definition of the conditional expectation $f(a)=E[X|Z=a]$ is that the function $f$ is such that the squared norm $E[(X-f(Z))^2]$ is minimized. Least squares regression looks only for affine linear functions $f(a)=\beta\,a+\varepsilon$ (where $\beta,\varepsilon$ are the ...

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Let me explain in laymans terms how to go about doing this. Really I see no need to use a Brownian Bridge if you don't have path-dependent options; if it's just a single date expiry (with no averaging), just simulate to the expiration date for every simulation. Basically, you usually want to use RQMC instead of normal QMC (as mentioned in the first answer), ...

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As far as I know, there is not an analytical formula or approximation telling you what value of $\mu$ is a solution for the minimizing-equation $$\min _{\mu} E_{f}\left[G^{2}(X) \frac{f(X)}{g_{\mu}(X)}\right].$$ However, usually a good initial guess is to take $\mu$ such that the new distribution is centered around the strike of your option (or closer to the ...

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