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Separating the Components of Default Risk: A Derivative-Based Approach (Job Market Paper)

by Anh Le of New York University

January 16, 2007

Abstract: In this paper, I propose a general pricing framework that allows the risk-neutral dynamics of loss given default (L Q ) and default probabilities (λ Q ) to be separately and sequentially discovered. The key is to exploit the differentials in L Q 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 λ Q 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 L Q corresponding to that particular security. Using data on credit default swap premiums, I show that, cross-sectionally, λ Q and L Q 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 .14% increase in λ Q and .60% increase in L Q . These findings raise serious doubts about the current practice, by both researchers and practitioners, of setting L Q to a constant across firms.

Previously titled: Credit Information from Equity Option Prices

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