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Glasserman's book is the book I would recommend on Monte Carlo methods as well.

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there is a C++ implemented version in the gold part of the Kooderive open source project.

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This is the book from a masters degree. http://perso.telecom-paristech.fr/~bianchi/athens/Proba_Num_11-12.pdf

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I think you are confused with what's exactly log-normally distributed. The distribution of option prices can't be normal or log-normal because the prices can't be negative. In general, we don't model option prices, we model the underlying stochastic processes (i.e: geometric brownian motion, mean-reverting etc). We then use the distribution of those ...

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In general, an option payoff cannot be normal, as the payoff is generally positive, while a normal variable can be negative. For a standard call option, the distribution function can be computed from the distribution of the underlying stock. Specifically, consider the vanilla European option payoff $X=(S_T-K)^+$. Then, for $x < 0$, \begin{align*} P(X \le ...

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Let's take a call option on a stock with exercise price K. What is the risk-neutral probability of a payoff x? Probability (x=0) = p(stock <=K). Also we have prob(payoff = x>0) = probability (stock=x+K). Hence the required density function f has two parts, (a) an accumulation point at zero representing the probability of being out of the money and ...

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Of course LSMC can be used in any case where you would benefit from early exercise (and the contract's not too convoluted I guess). So yes, if the Bermudan/American call is on a dividend-paying stock, then L-S could/would be used same way as for a put. But what happens if you try to price a Bermudan call without dividends with L-S? You should in theory get ...

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