1. Introduction I introduce the concept of Pearson-Wong diffusions and then show how this mathematical object can be put to use in macro-finance. Roughly speaking, Pearson-Wong diffusions link properties of stochastic processes to properties of … [Continue reading]

# The Predictability and Volatility of Returns in the Presence of Rare Disasters

1. Introduction I characterize the relationship between the variance premium at time $t$ and the excess returns over the next $h$ months in an economy with variable rare disasters as outlined in Gabaix (2011) using the parameter estimates given in … [Continue reading]

# Correct Prices Are Not Free

1. Introduction It takes hard work to maintain prices at their fundamental values. Accurate, responsive and informative prices do not occur by magic. Analysts have to diligently monitor firms prospects and security prices. Market makers have to … [Continue reading]

# Dyson Brownian Motion

1. Introduction I outline the construction of Dyson Brownian motion which governs the evolution of the eigen-values of an $(N \times N)$-dimensional stochastic process of Hermitian matrices. For instance, if $A(t)$ is such a process, … [Continue reading]

# Business Cycle Patterns

The chart below contains macroeconomic and financial data on the US economy from 1775 to 1943. The chart is from the St. Louis Federal Reserve Fraser Archives. I've run across this chart several times over the course of the past year and I find new … [Continue reading]