In this paper, I propose a general pricing framework that allows the risk neutral dynamics of loss given default (Lℚ) and default probabilities (λℚ) to be separately and sequentially discovered. The key is to exploit the differentials in Lℚ exhibited by different securities on the same underlying firm. By using equity and option data, I show that one can efficiently extract pure measures of λℚ that are not contaminated by recovery information. Equipped with this knowledge of pure default dynamics, prices of any defaultable security on the same firm with non-zero recovery can be inverted to compute the associated Lℚ corresponding to that particular security. Using data on credit default swap premiums, I show that, cross-sectionally, λℚ and Lℚ are positively correlated. In particular, this positive correlation is strongly driven by firms' characteristics, including leverage, volatility, profitability and q-ratio. For example, 1% increase in leverage leads to 0.14% increase in λℚ and 0.60% increase in Lℚ.
Separating the Components of Default Risk: A Derivative-Based Approach
