A Long Run Risks Model With Rare Disaster

Equity premium puzzle is one of the most important puzzles in finance and economics. For this reason, over the last20years, attempts to resolve the equity premium puzzle have become a major research impetus in finance and economics. It becomes most financial economists’pursue to find an asset pricing model that can resolve the puzzle. And at the same time the potential implications of the model are not contradicted with the reality.The long run risks model and rare disaster model are two outstanding models to resolve the equity premium puzzle among the abundant attempts. Banal, Kiku and Yaron (2010) present the idea that combine the long run risks with rare disaster risk to resolve the equity premium puzzle. The main of this paper is to develop and improve Banal, Kiku and Yaron (2010)’s model. We improve their model in two aspects:1. Different from their assumption that the size of the disaster is drawn from exponential distribution, we assume it follows power-law distribution which is fitted from22countries’consumption data over100years or so.2. Different from their assumption that the jumps in expected growth rate and the jumps in consumption volatility are independent, we assume that jumps in consumption volatility are the square of the jumps in expected growth, which is more intuitive. Based on above two new assumptions, we develop this paper’s model-long run risks model with rare disaster.Firstly, we solve the long run risks model with rare disaster and get the analytical expression of the equity premium. According to the analytical expression, the equity premium consists of short run risk premium, long run risk premium, volatility risk premium and disaster risk premium. And disaster contributes the equity premium through its mean, variance, skewness and kurtosis. Secondly, we calibrate the model and compare it with the most advanced long run risks model. We find that model of this paper can resolve the equity premium perfectly, which is superior to the long run risks model. Finally, we provide an empirical evaluation of the model. Model is consistent with the reality no matter on price-dividend ratio to predict long-run consumption growth, dividend growth and excess return or price-dividend ratio to predict future realized volatility of consumption and excess stock returns.