310.3. The upper panel below shows the default correlation, rho, under a single-factor credit model is 4.90% as a function of the individual default probabilities, denoted by pi. Under the simple credit model, all (both) credits have the same individual default probabilities; in this case, pi = 2.0%. The joint default probability is characterized by a bivariate standard normal distribution (joint CDF):

$$\rho = 4.90\% = \frac{\Phi\binom{k}{k} - \pi^2}{\pi(1 - \pi)}$$

Bivariate Standard Normal
$\pi(1) = 2.0\%$ and $\pi(2) = 2.0\%$

Asset Correlation	Joint Default Probability
-	0.040%
0.05	0.053%
0.10	0.069%
0.15	0.040%
0.20	0.110%
0.25	0.136%

In the lower panel, because they require a numerical solution, are listed the asset correlations implied by various joint default probabilities. For example, if two credits are uncorrelated, their joint PD = 2.0% * 2.0% = 0.040%; if their asset correlation is 0.05, the joint PD increases to 0.053%. Given a default correlation, rho, of 4.90%, what is the implied asset correlation?