A recent literature shows how an increase in volatility reduces leverage. However, in order to explain pro-cyclical leverage it assumes that bad news increases volatility, that is, it assumes an inverse relationship between first and second moments of asset returns. This paper suggests a reason...

If the historical average annual real interest rate is m 0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year? Suppose the annual real interest rate r(t) reverts to m according to the Ornstein Uhlenbeck (OU) continuous time process...

We show that binomial economies with financial assets are an informative and tractable model to study endogenous leverage and collateral equilibrium: endogenous leverage can be highly volatile, but it is always easy to compute. The possibility of default can have a dramatic effect on...

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing," i.e., systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are...

Systemic risk must include the housing market, though economists have not generally focused on it. We begin construction of an agent-based model of the housing market with individual data from Washington, DC. Twenty years of success with agent-based models of mortgage prepayments give us hope...

A recent literature shows how an increase in volatility reduces leverage. However, in order to explain pro-cyclical leverage it assumes that bad news increases volatility, that is, it assumes an inverse relationship between first and second moments of asset returns. This paper suggests a reason...

For environmental problems such as global warming future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate, which reduces the present value of future costs. The result is highly sensitive to the choice of discount...

Our paper provides a complete characterization of leverage and default in binomial economies with financial assets serving as collateral. First, our Binomial No-Default Theorem states that any equilibrium is equivalent (in real allocations and prices) to another equilibrium in which there is no...

We review the theory of leverage developed in collateral equilibrium models with incomplete markets. We explain how leverage tends to boost asset prices, and create bubbles. We show how leverage can be endogenously determined in equilibrium, and how it depends on volatility. We describe the...

Much of the lending in modern economies is secured by some form of collateral: residential and commercial mortgages and corporate bonds are familiar examples. This paper builds an extension of general equilibrium theory that incorporates durable goods, collateralized securities and the...