## Convergence and biases of Monte Carlo estimates of American option prices using a parametric exercise rule.(English)Zbl 1178.91195

Summary: This paper presents an algorithm for pricing American options using Monte Carlo simulation. The method is based on using a parametric representation of the early exercise decision. It is shown that, as long as this parametric representation subsumes all relevant stopping-times, error bounds can be constructed using two different estimates, one which is biased low and one which is biased high. Both are consistent and asymptotically unbiased estimators of the true option value. Results for high-dimensional American options confirm the viability of the numerical procedure. The convergence results of the paper shed light into the biases present in other algorithms proposed in the literature.

### MSC:

 91G20 Derivative securities (option pricing, hedging, etc.) 91G60 Numerical methods (including Monte Carlo methods) 65C05 Monte Carlo methods
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### References:

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