A test problem

A test problem has been proposed to compare the performance of the different methods. It corresponds to the computation of a $d$ dimensional at-the-money American min-put option in the Black-Scholes model.

The assets are uncorrelated, have the same volatility and the same initial value :

$$S_{t}^{i}=100\exp ((r-\sigma ^{2}/2)t-\sigma W_{t}^{i})\;\;\;\mbox{ for each } \;i=1,...,d$$

where $W=(W^{1},...,W^{d})$ is a standard Brownian motion. The payoff function is

$$g(x)=[100-\min \{x^{1},...,x^{d}\}]^{+}.$$

Numerical tests will be performed for different dimensions with $\sigma =20\%$ and $r=5\%$ . Results will be collected and compared by J. Cvitanic.

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