Topic and Objectives
The notion of an economy as a network of more or less tightly linked units has recently become popular in the finance and economics literature, especially in the aftermath of the financial and economic crisis. In this project we analyze the implications of different network structures for equilibrium asset prices and returns. One special aspect we focus on is the fact that links in a network can have a direction and that it can make a difference if a link is from node i to node j or the other way around. A simple example for such a directed link is a customer-supplier relationship between two firms. Shocks to the profitability of a large customer will certainly have a negative impact on the small supplier and, among other things, increase its default risk, while a shock to the small supplier is much less likely to have significant consequences for the large customer. Another important aspect of this kind of shock propagation is that it has a time dimension and does not happen in one single instant. In the above example the riskiness of the supplier increases, implying a higher likelihood of negative shocks in the future, and this in turn might negatively affect other firms linked to the supplier. These two features cannot be captured by a pure diffusion/correlation framework (due to its inherent symmetry) or by contemporaneous jumps. We therefore propose a model featuring multiple economic units ('firms') whose dividends are linked via self-exciting and mutually exciting jump processes. With such processes, a downward jump in the cash flow of one firm then increases the probability of subsequent negative shocks to its own cash flow as well as to those of other firms. The direction and magnitude of this shock propagation characterizes the network structure of our economy, which thus manifests itself only indirectly via the dynamics of jump risks as state variables, but not directly in the level of cash flows. Aggregate consumption, a key quantity in any equilibrium model, is driven by the sum of all the individual jumps, but a given jump always affects the cash flows of only one firm at a time.
- The directedness and timing of shocks have first-order implications for key asset pricing quantities like valuation ratios, expected returns, and return volatilities. Taking these features into account can lead to a substantially different interpretation of empirical findings, e.g., concerning a flight-to-quality effect.
- Our model featuring mutually and self-exciting jumps together with recursive utility is flexible, but still tractable, and provides a theoretical explanation for empirical results with respect to network centrality. It allows a precise analysis of the equilibrium impact of directed shock propagation in a multi-asset economy, which is an important step beyond the existing literature.