Credit risk pricing in a consumption-based equilibrium framework with incomplete accounting information

We present a consumption-based equilibrium framework for credit risk pricing based on the Epstein–Zin (EZ) preferences where the default time is modeled as the first hitting time of a default boundary and bond investors have imperfect/partial information about the firm value. The imperfect information is generated by the underlying observed state variables and a noisy observation process of the firm value. In addition, the consumption, the volatility, and the firm value process are modeled to follow affine diffusion processes. Using the EZ equilibrium solution as the pricing kernel, we provide an equivalent pricing measure to compute the prices of financial derivatives as discounted values of the future payoffs given the incomplete information. The price of a zero-coupon bond is represented in terms of the solutions of a stochastic partial differential equation (SPDE) and a deterministic PDE; the self-contained proofs are provided for both this representation and the well-posedness of the involved SPDE. Furthermore, this SPDE is numerically solved, which yields some insights into the relationship between the structure of the yield spreads and the model parameters.     

Epstein-Zin utility maximization on a random horizon

This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded ones. Focusing on the empirically relevant case where the risk aversion and the elasticity of intertemporal substitution are both larger than one, we characterize the optimal consumption and investment strategies using backward stochastic differential equations with superlinear growth on unbounded random horizons. This characterization, compared with the classical fixed-horizon result, involves an additional stochastic process that serves to capture the randomness of the horizon. As demonstrated in two concrete examples, changing from a fixed horizon to a random one drastically alters the optimal strategies.     

The roles of risk preferences,selection, and uncertain returns on land contracts

Using panel data on a statistically representative sample of Iowa farmland parcels from 1997 to 2017, we analyze the factors determining whether land is farmed by the owner or rented out under a cash rent or crop share contract. The landowner's decision to rent or operate the land depends on the distribution of expected net returns to the land, and so estimates of the factors affecting rental terms will be biased if the sample only includes rental contracts and excludes the owner-operator. Land with higher mean and/or lower variance of expected net returns is most likely to be rented out. Participants in the rental market will include the most risk-averse landowners and the least risk-averse tenants, while the least risk-averse landowners operate their own land. Our empirical results suggest that the rising use of cash rent contracts and declining incidence of owner-operation and crop-share rental contracts is consistent with falling coefficient of variation in expected net returns per acre.