Columbia Business School Research

Selling information that is later used in decision making constitutes an increasingly important business in modem economies (Jensen 1991). Information is sold under a large variety of forms: industry reports, consulting services, database access, and/or professional opinions given by medical, engineering, accounting/ financial, and legal professionals, among others.

The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. This paper discusses some of the recent applications of the Monte Carlo method to security pricing problems, with emphasis on improvements in efficiency. We first review some variance reduction methods that have proved useful in finance. Then we describe the use of deterministic low-discrepancy sequences, also known as quasi-Monte Carlo methods, for the valuation of complex derivative securities.

We consider a general class of queueing systems with multiple job types and a flexible service facility. The arrival times and sizes of incoming jobs are random, and correlations among the sizes of arriving job types are allowed. By choosing among a finite set of configurations, the facility can dynamically control the rates at which it serves the various job types. We define system work at any given time as the minimum time required to process all jobs currently in the backlog.

In this article I begin by discussing the rationale for mandatory convertibles from the point of view of issuers as well as investors. In general, convertibles securities reduce the costs of "information asymmetry" that can make equity offerings especially expensive for some smaller, high-growth companies (or any firm with little additional debt capacity where management is convinced its shares are undervalued).

We develop a simulation algorithm for estimating the prices of American-style securities, i.e., securities with opportunities for early exercise. Our algorithm provides both point estimates and error bounds for the true security price. It generates two estimates, one biased high and one biased low, both asymptotically unbiased and converging to the true price. Combining the two estimators yields a confidence interval for the true price.

We propose and analyze a heuristic that uses region partitioning and an aggregation scheme for customer attributes (load size, time windows, etc.) to create a finite number of customer types. A math program is solved based on these aggregated customer types to generate a feasible solution to the original problem. The problem class we address is quite general and defined by a number of general consistency properties.

We give a unified probabilistic analysis for a general class of bin packing problems by directly analyzing corresponding mathematical programs. In this general class of packing problems, objects are described by a given number of attribute values. (Some attributes may be discrete; others may be continuous.) Bins are sets of objects, and the collection of feasible bins is merely required to satisfy some general consistency properties.

This study investigates the timing and method of adoption of Statement of Financial Accounting Standards(SFAS) No. 106: Employers' Accounting for Post-Retirement Benefits Other Than Pensions (FASB [1990]). Our study is motivated by the Financial Accounting Standard Board's (FASB) policy of extending the adoption period of new accounting standards beyond one fiscal year. Specifically, during 1991 and 1992, firms could adopt SFAS No. 106, disclose the expected impact of adoption, or delay adoption/disclosure until fiscal 1993.

In this paper we consider single machine scheduling problems with a common due-date for all jobs, arbitrary monotone earliness and tardiness costs and arbitrary breakdown and repair processes. We show that the problem is equivalent to a deterministic one without breakdowns and repairs and with an equivalent cost function of a job's completion time. A V-shaped schedule without idle times is shown to be optimal, if this equivalent cost function is quasi-convex.

We consider a single-item, periodic-review inventory model with uncertain demands in which each period's production volume is limited by a capacity level. The demand distributions, capacity levels, and cost parameters vary according to a periodic pattern. We prove that modified base-stock policies are optimal for the finite-horizon planning model and for both the infinite-horizon discounted and undiscounted cost criterion. We further show that the optimal base-stock levels can be calculated via a simple but efficient value-iteration method.

The paper demonstrates empirically that GAAP earnings have properties to serve as a substitute for dividends in equity valuation analysis. Dividends reduce subsequent GAAP earnings, and "intrinsic" equity prices calculated by forecasting earnings are thus reduced by current dividends. This is in accordance with the Miller and Modigliani principle—the displacement property—which states that the payment of dividends reduces prices, dollar for dollar.

We propose using a modification of the simple peak hour approximation (SPHA) for estimating peak congestion in multiserver queueing systems with exponential service times and time-varying periodic Poisson arrivals. This lagged pointwise stationary approximation (lagged PSA) is obtained by first estimating the time for the actual peak congestion by the time of peak congestion in an infinite server model and then substituting the arrival rate at this tiem int he corresponding stationary finite server model.

In this paper we provide valuation formulas for several types of American options on two or more assets. Our contribution is twofold. First, we characterize the optimal exercise regions and provide valuation formulas for a number of American option contracts on multiple underlying assets with convex payoff functions. Examples include options on the maximum of two assets, dual strike options, spread options, exchange options, options on the product and powers of the product, and options on the arithmetic average of two assets.

Decision-makers often do not or cannot predict at the time of choice how their tastes may change by the time the outcomes are experienced. This paper explores the implications of making decisions by maximizing experienced utility ex post rather than ex ante. Focusing on being satisfied with choice in retrospect results in quite different kinds of problems than a prospective orientation that projects one's current preferences into the future.

We provide a framework in which we link the valuation and asset allocation policies of defined benefits plans with the lifetime marginal productivity schedule of the worker and the pension plan formula. In turn, we examine the retirement policies that are implied by the primitives of the model and the value of pension obligations. Our model provides an explicit valuation formula for a stylized defined benefits plan. The optimal asset allocation policies consist of the replicating portfolio of the pension liabilities and the growth optimum portfolio independent of the pension liabilities.

We consider multimachine scheduling problems with earliness and tardiness costs. We first analyze problems in which the cost of a job is given by a general nondecreasing, convex function F, of the absolute deviation of its completion time from a (common) unrestrictive due-date, and the objective is to minimize the sum of the costs incurred for all N jobs. (A special case to which considerable attention is given to the completion time variance problem.)

We use firm-level panel data to explore the extent to which fixed investment responds to tax reforms in 14 OECD countries. Previous studies have often found that investment does not respond to changes in the marginal cost of investment. We identify some of the factors responsible for this finding, and employ an estimation procedure that sidesteps the most important of them. In so doing, we find evidence of statistically and economically significant investment responses to tax changes in 12 of the 14 countries.

This paper studies information system design in a model of double moral hazard in which there is both a decision problem and a control problem. If either problem is considered in isolation, an information system that provides more public information is preferred. However, an information system that provides less public information can, in fact, be desirable because of an interaction between the two problems. The benefit of choosing an information system that provides less information is that it serves as a substitute for commitment for the principal.

This article suggests that the introduction of bank branching restrictions and federal deposit insurance in the United States likely was motivated by political considerations. Specifically, we argue that these restrictions were instituted for the benefit of the small unit banks that were unable to compete effectively with large, multiunit banks. We analyze this "political hypothesis" in two steps.

This paper presents a stochastic multidimensional unfolding (MDU) procedure to spatially represent individual differences in phased or sequential decision processes. The specific application or scenario to be discussed involves the area of consumer psychology where consumers form judgments sequentially in their awareness, consideration, and choice set compositions in a phased or sequential manner as more information about the alternative brands in a designated product/service class are collected.

We use when-issued transactions data to assess the Treasury's current experiment with uniform auctions. When-issued volume is higher under uniform as compared to discriminatory auctions, suggesting a higher information release, which should reduce pre-auction uncertainty and the winner's curse. Under uniform auctions, when-issued volatility falls after the auction and again after the outcome announcement. The pattern is the opposite for discriminatory auctions. This is further evidence that uniform auctions increase pre-auction information and lower the short squeeze.

We consider the problem of precise estimation of service-level measures in multistage production-inventory systems when the system is managed for high levels of service. Precisely because the service level is high, stockouts, large backorders, and unfilled demands are rare and thus difficult to estimate by straightfoward simulation. We propose and analyze alternative estimators, based on changing the demand distribution to make these rare events less rare.

We study a new class of unconditional and conditional mean-variance spanning tests that exploits the duality between Hansen-Jagannathan bounds (1991) and mean-standard deviation frontiers. The tests are shown to be equivalent to standard spanning tests in population, but we document substantial differences in the small sample performance of alternative tests. Our empirical application examines the diversification benefits from emerging equity markets using an extensive new data set on U.S. and U.K.-traded closed-end funds. We find significant diversification benefits for the U.K.

This article successively introduces variable velocity, durability, and habit persistence in a standard two-country general equilibrium model and explores their effects on the variability of exchange rate changes, forward premiums, and the foreign exchange risk premium. A new feature of the model is that agents make decisions at a weekly frequency and face conditionally heteroskedastic shocks. Nevertheless, even the most complex model fails to deliver sufficiently variable risk premiums without causing forward premiums and exchange rates to be excessively variable.

The financial policy highly leveraged firms (HLFs) commonly follow implies uncertain leverage. Explicit allowance for this characteristic leads to two complementary pricing models. A recursive formula for the value of HLF follows from applying the adjusted present value (APV) approach to uncertain tax shields. This formula is used to evaluate the robustness of the simple APV rule and other valuation approaches used in practice.

When the surge of equity REIT initial public offerings (IPOs) came to market in 1993 and 1994, the quality as well as an obvious increase in the quantity of newly securitized real estate (approximately $15.1 billion in the first two years of this bull market), defined a new REIT marketplace. By the end of 1995, the implied market capitalization of equity REITs had reached $59 billion, fourfold its size in 1992, and these real estate companies controlled approximately $83 billion in real estate.

In this paper we discuss stochastic Economic Lot Scheduling Problems (ELSP), i.e., settings where several items need to be produced in a common facility with limited capacity, under significant uncertainty regarding demands, production times, setup times, or combinations thereof. We propose a class of production/inventory strategies for stochastic ELSPs and describe how a strategy which minimizes holding, backlogging, and setup costs within this class can be effectively determined and evaluated.

Case studies of a number of specific drugs have shown that these drugs reduced the demand for hospital care and, in some cases, led to decreases in mortality. For example, according to the Boston Consulting Group Inc., operations for peptic ulcers decreased from 97,000 in 1977, when H2 antagonists were introduced, to 19,000 in 1987; this is estimated to have saved $224 million in annual medical costs. The recent Scandinavian Simvastatin Survival Study indicated that giving the drug simvastatin to heart patients reduced their hospital admissions by a third during five years of treatment.