The term under the square root is the determinant of the (positive definite?) covariance matrix. If we take rho13 = rho23 = 0, rho12 >= 1 we get NaN. But what is there is noise in the data?
The term exp(-w/b) should never underlfow?
BTW what's PSD?
The square root term crashes if the determinant is less that zero. Both the 1/denominator and exp term blow up if the determinant is zero although the analytic version of the equation does not because the exp term goes to zero much faster than the 1/sqrt term goes to infinity.
In theory, if the rho values come from a covariance matrix computed from real-valued data, PSD is guaranteed. In practice, round-off errors in the statistical sums could lead to violations of PSD and a negative determinant. Note that if the original data contains complex values, PSD is not guaranteed and the sqrt() term may crash (or need to be computed as a complex value).
If the rho values come from some other estimation process (e.g., each rho being estimated from market data, disjoint historical data sets, or the intuitions of the user ), then all bets are off.