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Estimating actual probability of defaul from structural models

In this paper, we study the probability of default, the credit default swap (CDS) implied probability of default, and the estimated actual probability of default from the structural models. We first show that the conditional risk-neutral probability of default is totally different from the CDS implied probability of default, and the CDS implied probability of default provides biased estimation of a corporation’s actual probability of default. Hence, the common belief that the CDS implied probability of default gives unbiased (or reliable) estimations of the firm’s probability of default is false. Furthermore, we use the credit spread risk premium as the difference of the physical measure and the risk-neutral measure of the credit spread to estimate the actual bond spread, and relate the credit spread risk premium in terms of the market price of risk and the credit spread volatility. Using the credit spread volatility and the risk-neutral credit spread and the market price of risk in hybrid HPD model, we obtain the estimated actual probability of default in a structural model. The estimated actual probability of default would be useful for credit rating agencies, investors, credit risk managers and regulators.