mu = 0.12;                                        % Monitoring cost
sigma = sqrt(0.28);                               % Std dev lognormal
pibar = 0.9728;                                   % Survival probability
F = 0.03;                                         % Quarterly default rate

z = norminv(F);
omegabar = exp(z*sigma-0.5*sigma^2);              % find threshold omegabar

gamma = normcdf(z-sigma) + omegabar*(1-F);        % Phi(z) = F
g = normcdf(z-sigma);
gmmg = (1-mu)*normcdf(z-sigma) + omegabar*(1-F);

gammap = 1 - F;
gp = normpdf(z)/sigma;                            % gp = normpdf(z-sigma)/(sigma*omegabar)
lambda = gammap / (gammap-mu*gp);
upsilon = 1-gamma+lambda*gmmg;

gammapp = -normpdf(z)/(sigma*omegabar);
gpp = normpdf(z)/sigma*(-z)/(sigma*omegabar);
lambdap = mu*(gammap*gpp - gammapp*gp) / (gammap-mu*gp)^2;

s = lambda / upsilon;                             % equation A.1
k = 1 + (lambda*gmmg)/(1-gamma);                  % equation A.2      k = 1 /(1-gmmg*s)

omegabarps = -gmmg / ((gammap-mu*gp)*s);
omegabarpk = 1 / ((gammap-mu*gp)*s);
kp = (k*upsilon-lambdap*omegabarps)/(lambdap*omegabarpk);
nu = k/(kp*s);