This paper studies the economic foundations for maximum leverage ratio capital adequacy rules. The paper makes three contributions to the literature. First, we show how to determine the maximum leverage ratio such that the probability of insolvency is less than some predetermined quantity. Two,...

This paper studies capital adequacy rules based on Value-at-Risk (VaR), leverage ratios, and stress testing. VaR is the basis of Basel II, and all three approaches are proposed in Basel III. This paper makes three contributions to the literature. First, we prove that these three rules provide an...

The martingale theory of bubbles studies the existence and characterization of asset price bubbles in continuous time and continuous trading economies under both the no arbitrage (no free lunch vanishing risk) and no dominance hypotheses. We review this theory, with an emphasis on understanding...

This paper studies the optimal trading strategy of arbitrageurs in a dynamic economy where there are transaction costs and the arbitrageur's trades reduce (or eliminate) future arbitrage opportunities. In contrast to the standard textbook arbitrage trading strategy which has infinite present...

Jensen's alpha is well-known to be a measure of abnormal performance in the evaluation of securities and portfolios where abnormal performance is defined to be an expected return that exceeds the equilibrium risk adjusted rate. It is also well known that in estimating Jensen's alpha, a non-zero...

The martingale theory of price bubbles defines an asset bubble to exist when the asset's price process is a strict local martingale, that is, a local martingale that is not a martingale. Using this definition of a price bubble, for continuous semimartingales, we characterize the conditions under...

This paper develops a new model for studying foreign currency exchange rate bubbles. The model constructed is a modification of the Martingale-based bubble approach of Jarrow, Protter, and Shimbo [12], [13]. This model generates some new insights into our understanding of exchange rate bubbles...

This paper develops an arbitrage-free pricing theory for a term structure of fi xed income securities that incorporates liquidity risk. In our model, there is a quantity impact on the term structure of zero-coupon bond prices from the trading of any single zero-coupon bond. We derive a set of...

This paper documents the fact that in options markets, the (percentage) implied volatility bid-ask spread increases at an increasing rate as the option's maturity date approaches. To explain this stylized fact, this paper provides a market microstructure model for the bid-ask spread in options...

This paper studies bank runs in an extended Diamond and Dybvig model. The model is extended in two ways. One, agents have heterogeneous wealth and two, banks can invest in both liquid and illiquid assets. We argue that the underlying reason for bank runs is ambiguous property rights. Sequential...