  The multidimensional COS method is a numerical tool to price financial
options, which depend on several underlyings. The method makes use of the
characteristic function $\varphi$ of the logarithmic returns of the underlyings
and it is advantageous if the Fourier-cosine coefficients $v_{\boldsymbol{k}}$
of the payoff function are given in closed-form. However, in important cases,
neither $\varphi$ nor $v_{\boldsymbol{k}}$ are given analytically but need to
be recovered numerically. We make the following main contributions: First, we
prove the convergence of the multidimensional COS method including numerical
uncertainty on $\varphi$ and $v_{\boldsymbol{k}}$. Second, we find explicit
formulas for two parameters required by the COS method in multivariate
dimensions: the truncation range and the number of terms. Third, we show
empirically and theoretically that the COS method is faster than a Monte Carlo
simulation in higher dimensions if a very high accuracy is required.

Computational Finance