Starting with the pioneering work of Benhabib and Farmer and Farmer and Guo, a large body of literature has developed in which Real Business Cycle (RBC) models, modified to include increasing returns to scale in production, can result in a continuum of equilibria indexed by agents’ expectations. Models with multiple equilibria successfully replicate essential macroeconomic features of the business cycle. In this regard, these models are similar to the neoclassical RBC model. Prior research has shown that the standard RBC model fails when confronted with the financial market data. In this paper, we examine the asset pricing implications of a model with indeterminacy. To our knowledge, this study is the first to undertake such an analysis.
While fluctuations in the standard RBC model are driven by technology shocks, in our model it is agents’ expectations that cause business cycles. Since financial markets are theorized to be driven, at least in part, by agents’ expectations, one might expect that this model would reflect well the behavior of such markets. If such an improvement is found, it would enhance support for the use of models with self-fulfilling expectations over traditional RBC models without indeterminacy.
The devastating effect of civil war on children in different regions of the world, and the inability of weak or unwilling governments to provide basic services for their citizens has led to the now general acceptance that when peace is brokered among warring parties, or the opportunity arises for innovative engagement in conflictaffected fragile states (CAFS), the reconstruction of education systems must be a top priority (Buckland, 2005).
From a political economy perspective, rapid educational reconstruction in the wake of severe and prolonged civil strife is widely considered fundamental for the reinvigoration of war-torn economies and the cultivation of peaceful civic relations (Buckland, 2005). Through the transmission of knowledge and skills, systems of education can facilitate the expansion of employment possibilities and economic productivity.
The bottom-up stress event model, proposed by Duffie and Singleton (1999), is a simple and intuitive model for portfolio credit risk. The model is seldom applied in practice since it is generally believed that the default times, as well as the loss distribution, of a portfolio under this modeling framework can only be generated by computationally expensive Monte Carlo simulation. In this note an alternative approach is taken, avoiding Monte Carlo simulations, making the model tractable and leading to efficient calibrations to data. The idea of the stress event model is easy to understand. Besides idiosyncratic default, each firm may default if there is a joint credit event (Duffie and Singleton 1999) or alternatively referred to as stress event (Schönbucher 2003).
This allows correlation through both changes in stress event intensity as well as through the occurrences of the stress events. The formal definition of the default time of a firm is given in Section 3. In Section 4, we develop a new approach to compute the loss distribution of a portfolio for the stress event model. We first identify independence conditions under which defaults of firms are independent. The loss distribution can then be decomposed into a series expansion for which each term admits a closed form expression. It turns out that only the first few terms of the series are needed to accurately approximate the loss distribution since stress events are infrequent. This leads to a very efficient method to compute the loss distribution of a portfolio.
