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More or less as the title states, for which options is the industry standard to price using Monte-Carlo simulation of the underlying, and for which of those options is this the only alternative?

I know rainbow options (best-of calls/puts, basket options etc.) and asian options are typical examples, do more exist?

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    $\begingroup$ Monte Carlo simulations always become handy for high dimensional problems (several state variables, etc.) This is when trees, finite differences and integral approximations become computationally costly. $\endgroup$ – Alex Jul 9 '20 at 20:29
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  1. Monte Carlo is more natural to perform a forward induction (think TARNs), whereas trees are more natural to do a backward induction/dynamic programming (think Bermudans).

Forward induction may be the way to go in case you have a trade that is path dependent (i.e. The price at a time depends on the past history of the process (in the sense that at a particular node/time, you need to look back in the tree to find the value at that point). Note that in Bermudans/ Americans this is NOT the case, although we also call them 'path dependent').

  1. Monte Carlo is better in high dimensions, whereas trees get computationally costly.
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