Benchmarking Trees for American Options with Discrete Dividends

Summary

The document asks whether Monte Carlo simulation can benchmark tree methods for pricing American options with discrete dividends, and how such a simulation should be built. The response explains a key difficulty: Monte Carlo simulates paths forward, while American exercise valuation requires comparing immediate exercise value with continuation value at each step. The continuation value is not directly available from forward simulation, which makes a basic Monte Carlo approach unsuitable for this task.

The response notes that specialized American Monte Carlo methods address the problem but can be computationally demanding. It suggests testing a discrete-dividend model against real market data, on the grounds that market prices and market-maker scrutiny can expose flaws. No specific simulation algorithm, benchmark design, or empirical test is provided, so the document offers a caution and broad validation suggestion rather than a complete verification procedure.

Key ideas

• American option valuation requires comparing exercise value with continuation value at each time step.
• Basic forward Monte Carlo does not directly provide the continuation value needed for that comparison.
• Specialized Monte Carlo methods can handle American exercise but may be computationally demanding.
• The response recommends checking discrete-dividend models against real market data.
• The document gives no detailed algorithm or benchmark testing procedure.

Tags

# Monte Carlo American Options Discrete Dividends


# Monte Carlo American Options Discrete Dividends












Built some tree methods to price american options with discrete dividends. But I have no way to really verify my work. Questions below:

- Does it make sense to build a Monte Carlo pricer to use as a benchmark to measure the results of the trees against.

- What is the best way to build such a Monte Carlo pricer for american options with discrete dividends ?

Please help.

## Answer by Meph (score 1)

https://quant.stackexchange.com/a/59791

- No, it doesn't.

Monte Carlo is a forward-simulation method, whereas trees propagate backwards. This is a problem for valuing American options: at every timestep you have to take the $max()$ of the payoff and the current option price - but you don't know the option price.

- There are 'American MC' models to circumvent this but they are pretty heavy.

Practitioners of course hit this problem. What they do is test the discrete dividend model on real market data. The market is large enough, and market makers are now advanced enough, to find most holes in any new model you've built.

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