We derive an option-pricing formula from recursive preference and estimate rare disaster probability. The new options-pricing formula applies to far-out-of-the money put options on the stock market when disaster risk dominates, the size distribution of disasters follows a power law, and the...

The potential for rare macroeconomic disasters may explain an array of asset-pricing puzzles. Our empirical studies of these extreme events rely on long-term data now covering 28 countries for consumption and 40 for GDP. A baseline model calibrated with observed peak-to-trough disaster sizes...

From 1836 to 2011, the average real rate of price change for gold in the United States is 1.1% per year and the standard deviation is 13.1%, implying a one-standard-deviation confidence band for the mean of (0.1%, 2.1%). The covariances of gold's real rate of price change with consumption and...

We build on the Maddison GDP data to assemble international time series from before 1914 on real per capita personal consumer expenditure, C. We also improve the GDP data in many cases. The C variable comes closer than GDP to the consumption concept that enters into usual asset-pricing...

Satisfactory calculations of the welfare cost of aggregate consumption uncertainty require a framework that replicates major features of asset prices and returns, such as the high equity premium and low risk-free rate. A Lucas-tree model with rare but large disasters is such a framework. In a...

Long-term data for 30 countries up to 2006 reveal 232 stock-market crashes (multi-year real returns of -25% or less) and 100 depressions (multi-year macroeconomic declines of 10% or more), with 71 of the cases matched by timing. The United States has two of the matched events--the Great...

The potential for rare macroeconomic disasters may explain an array of asset-pricing puzzles. Our empirical studies of these extreme events rely on long-term data now covering 28 countries for consumption and 40 for GDP. A baseline model calibrated with observed peak-to-trough disaster sizes...

Rare events (RE) and long-run risks (LRR) are complementary approaches for characterizing macroeconomic variables and understanding asset pricing. We estimate a model with RE and LRR using long-term consumption data for 42 economies, identify these two types of risks simultaneously from the...

Barro et al. (2022) investigate the quantity of safe assets held in the cross-section of developed countries and find that the average safe-asset ratio (ratio of safe assets to total assets) was 37% in 2015 and has remained relatively stable over time. They also document a crowding-out...