When Monte Carlo Is Preferred for Pricing Options

Summary

The document compares Monte Carlo simulation with tree methods for pricing options. It highlights two situations where simulation can be a natural choice: products with payoffs or values that depend on the path taken by the underlying, and problems with many risk dimensions. A forward simulation can track the evolution of a path-dependent trade, while a tree can become computationally expensive as dimensionality grows.

The discussion contrasts forward induction with the backward induction and dynamic programming commonly used for Bermudan options. It cautions that the label “path dependent” can include Bermudan and American exercise features, even though the answer distinguishes those from dependence on the process's past history at a given time. The examples mention target redemption notes, rainbow options, and Asian options, but the document does not establish that Monte Carlo is the industry standard or the only available method for any product.

Key ideas

• Monte Carlo simulation is suited to forward induction for some path-dependent trades.
• Tree methods naturally support backward induction and dynamic programming, as in Bermudan options.
• Monte Carlo can be more practical than trees when the problem has many dimensions.
• The document offers examples and general comparisons rather than definitive rules about industry practice.

Tags

# What options are typically priced in practice by Monte-Carlo simulation?


# What options are typically priced in practice by Monte-Carlo simulation?












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?

## Answer by Arshdeep (score 4)

https://quant.stackexchange.com/a/55554

- 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').

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

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.