Execution protocols for complex options orders allow market participants to execute multi-leg trades such as verticals, calendars, straddles, strangles, and others as a single trade at a net price. The costs to execute complex orders are significantly lower than the costs of simple orders. Part...

Complex options strategies figure prominently in discussions of the options market, but little is known about their frequency or why they are traded. We present a novel approach to group the legs of complex trades reported by OPRA into complex packages, and thus identify the strategies. We find...

This paper is a self-contained introduction to the concept and methodology of "value at risk," which is a new tool for measuring an entity's exposure to market risk. We explain the concept of value at risk, and then describe in detail the three methods for computing it: historical simulation;...

We use a martingale approach to study optimal intertemporal consumption and portfolio policies in a general discrete-time, discrete-state-space securities market with dynamically incomplete markets and short-sale constraints. We characterize the set of feasible consumption bundles as the...

The dynamics of the unobservable "short" or "instantaneous" rate of interest are frequently estimated using a proxy variable. We show the biases resulting from this practice (the "proxy" problem) are related to the derivatives of the proxy with respect to the short rate and the (inverse)...

The options-based approach to studying irreversible investment under uncertainty emphasizes that the opportunity cost of investment includes the value of the option to wait that is extinguished when an investment is undertaken. Thus, the investment decision is affected by the determinants of the...

This paper is a self-contained introduction to the concept and methodology of "value at risk," which is a new tool for measuring an entity's exposure to market risk. We explain the concept of value at risk, and then describe in detail the three methods for computing it: historical simulation;...

We study a source of bias in value-at-risk estimates that has not previously been recognized. Because value-at-risk estimates are based on past data, a trader will often have a good understanding of the errors in the value-at-risk estimate, and it will be possible for her to choose portfolios...