• "Separating the Components of Default Risk: A Derivative-Based Approach,"  Working Paper, New York University, October, 2006, pdf

In this paper, I propose a general pricing framework that allows the risk-neutral dynamics of loss given default (Q-LGD) and default probabilities (Q-PD) to be separately and sequentially discovered. The key is to exploit the differentials in Q-LGD 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 Q-PD 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 Q-LGD corresponding to that particular security. Using data on credit default swap premiums, I show that, cross-sectionally, Q-PD and Q-LGD are positively correlated. In particular, this positive correlation is strongly driven by firms' characteristics, including leverage, volatility, profitability and q-ratios. For example, 1 percent increase in leverage leads to .14 percent increase in Q-PD and .60 percent increase in Q-LGD. These findings raise serious doubts about the current practice, by both researchers and practitioners, of setting Q-LGD to a constant across firms.

• "Discrete-Time Dynamic Term Structure Models with Generalized Market Prices of Risk," Working Paper, Stanford University and New York University, March, 2006, (with Qiang Dai and Ken Singleton), under revision for resubmission to the Review of Financial Studies, pdf

This paper develops a rich class of discrete-time, nonlinear dynamic term structure models. Under the risk-neutral measure, the distribution of the state vector Xt resides within a family of discrete-time affine processes that nests the exact discrete- time counterparts of the entire class of continuous-time models in Duffie and Kan (1996) and Dai and Singleton (2000). Moreover, we allow the market price of risk, linking the risk-neutral and historical distributions of Xt, to depend generally on the state Xt. The conditional likelihood functions for coupon bond yields for the resulting nonlinear models under the historical measure are known exactly in closed form. As an illustration of our approach, we estimate a three factor model with a cubic term in the drift of the stochastic volatility factor and compare it to a model with a linear drift. Our results show that inclusion of a cubic term in the drift signifficantly improves the models statistical fit as well as its out-of-sample forecasting performance.

• "Risk-neutral Dynamics of Interest Rates," 2006, (with Ken Singleton) (pdf available soon)

A critical assumption underlying many term structure models in the literature is that the state variables are affine or exponentially affine under the risk-neutral measures. This assumption is mainly for convenience since it allows for analytical pricing of bond prices. This paper develops a simulation technique that can compute bond prices efficiently, allowing for general nonlinearity and inter-dependence of the state variables under the risk neutral measures. We show that this technique can be used to investigate whether US interest rates data exhibit any nonlinearity under the risk neutral measures while making no prior assumptions on the physical distribution of the state variables. A better understanding of the risk-neutral dynamics of interest rates will ultimately enhance our knowledge of the dynamics of premiums required by investors to bear interest rate risks.