Dynamic Relational Contracts under Complete Information

This paper considers a long-term relationship between two agents who both undertake a costly action or investment that together produces a joint benefit. Agents have an opportunity to expropriate some of the joint benefit for their own use. Two cases are considered: (i) where agents are risk neutral and are subject to limited liability constraints and (ii) where agents are risk averse, have quasi-linear preferences in consumption and actions but where limited liability constraints do not bind. The question asked is how to structure the investments and division of the surplus over time so as to avoid expropriation. In the risk-neutral case, there may be an initial phase in which one agent overinvests and the other underinvests. However, both actions and surplus converge monotonically to a stationary state in which there is no overinvestment and surplus is at its maximum subject to the constraints. In the risk-averse case, there is no overinvestment. For this case, we establish that dynamics may or may not be monotonic depending on whether or not it is possible to sustain a first-best allocation. If the first-best allocation is not sustainable, then there is a trade-off between risk sharing and surplus maximization. In general, surplus will not be at its constrained maximum even in the long run.

Modeling Dependence Structure and Forecasting Market Risk with Dynamic Asymmetric Copula

We investigate the dynamic and asymmetric dependence structure between equity portfolios from the US and UK. We demonstrate the statistical significance of dynamic asymmetric copula models in modelling and forecasting market risk. First, we construct “high-minus-low" equity portfolios sorted on beta, coskewness, and cokurtosis. We find substantial evidence of dynamic and asymmetric dependence between characteristic-sorted portfolios. Second, we consider a dynamic asymmetric copula model by combining the generalized hyperbolic skewed t copula with the generalized autoregressive score (GAS) model to capture both the multivariate non-normality and the dynamic and asymmetric dependence between equity portfolios. We demonstrate its usefulness by evaluating the forecasting performance of Value-at-Risk and Expected Shortfall for the high-minus-low portfolios. From back-testing, e find consistent and robust evidence that our dynamic asymmetric copula model provides the most accurate forecasts, indicating the importance of incorporating the dynamic and asymmetric dependence structure in risk management.