from scipy.stats import norm, multivariate_normal

def default_correlation(asset_corr, pd):
    # Inverse der kumulativen Normalverteilung für PD
    z = norm.ppf(pd)
    # Berechnung der gemeinsamen Ausfallwahrscheinlichkeit
    mean = [0, 0]
    cov_matrix = [[1, asset_corr], [asset_corr, 1]]
    p_joint = multivariate_normal.cdf([z, z], mean=mean, cov=cov_matrix)
    p_joint=float(p_joint)
    # Berechnung der Default-Korrelation
    default_corr = round((p_joint - pd * pd) / (pd * (1 - pd)),4)
    return default_corr


print(default_correlation(0.3, 0.01))