Maximum Likelihood Default Model
Overview
Maximum Likelihood
Default Correlations
the probability of the ith asset defaulting given a realization of the latent factor {% Z %} is given by
{% p_i(Z) = Prob(A_i \leq \Phi^{-1}(p_i)|Z) %}
{% p_i(Z) = Prob(w_iZ + \sqrt{1-w_i^2} \epsilon_i \leq \Phi^{-1}(p_i)|Z) %}
{% = \Phi[\frac{\Phi^{-1}(p_i) - w_iZ}{\sqrt{1-w_i^2}}] %}
Computations
