Columbia Business School Research

An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex pricing problems have motivated the development of techniques that combine Monte Carlo simulation with dynamic programming. One class of methods approximates the option value at each time using a linear combination of basis functions, and combines Monte Carlo with backward induction to estimate optimal coefficients in each approximation.

Organizations worldwide use contact centers as an important channel of communication and transaction with their customers. This paper describes a contact center with two channels, one for real-time telephone service, and another for a postponed call-back service offered with a guarantee on the maximum delay until a reply is received. Customers are sensitive to both real-time and call-back delay and their behavior is captured through a probabilistic choice model. The dynamics of the system are modeled as an M/M/N multiclass system.

We consider a joint inventory-pricing problem in which buyers act strategically and bid for units of a firm's product over an infinite horizon. The number of bidders in each period as well as the individual bidders' valuations are random but stationary over time. There is a holding cost for inventory and a unit cost for ordering more stock from an outside supplier. Backordering is not allowed. The firm must decide how to conduct its auctions and how to replenish its stock over time to maximize its profits.

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence.

This paper surveys the literature on option pricing, from its origins to the present. An extensive review of valuation methods for European- and American-style claims is provided. Applications to complex securities and numerical methods are surveyed. Emphasis is placed on recent trends and developments in methodology and modeling.

This paper considers an overbooking problem with multiple reservation and inventory classes, in which the multiple inventory classes may be used as substitutes to satisfy the demand of a given reservation class (perhaps at a cost). The problem is to jointly determine overbooking levels for the reservation classes, taking into account the substitution options. Such problems arise in a variety of revenue management contexts, including multicabin aircraft, back-to-back scheduled flights on the same leg, hotels with multiple room types, and mixed-vehicle car rental fleets.

We present a simple model where a firm will commit to a strictly positive hurdle rate on investment proposals by managers even though the two parties are symmetrically informed about the investments' profitability. Facing a positive hurdle rate, a manager who derives partial benefits from the investment profits will have more incentive to collect information about the projects. The optimal hurdle rate trades off the benefit of more information with the cost of foregoing ex post positive Net Present Value (NPV) projects.

I propose an intertemporal precautionary saving model in which the agent's labor income is subject to (possibly correlated) shocks with different degrees of persistence and volatility. However, he only observes his total income, not individual components. I show that partial observability of individual components of income gives rise to additional precautionary saving due to estimation risk, the error associated with estimating individual components of income. This additional precautionary saving is higher, when estimation risk is greater.

Previous studies on international marketing have typically asked the question: "how is the demand characterized across countries?" Such analysis is then used to provide guidelines for firms to enter new markets and/or to allocate marketing resources across countries.

This article focuses on the role of threats in negotiations. Broadly speaking, a threat is a proposition that issues demands and warns of the costs of noncompliance. Even if neither party resorts to them, potential threats shadow most negotiations. Researchers have found that people actually evaluate their counterparts more favorably when they combine promises with threats rather than extend promises alone. Whereas promises encourage exploitation, the threat of punishment motivates cooperation.

Recommendations often play a positive role in the decision process by reducing the difficulty associated with choosing between options. However, in certain circumstances recommendations play a less positive and more undesirable role from the perspectives of both the recommending agent or agency and the person receiving the recommendation. Across a series of four studies, we explore consumer response when recommendations by experts and intelligent agents contradict the consumer's initial impressions of choice options.

Creative destruction presents a tough implementation challenge. It's expensive in terms of physical goods and executive and employee time. Creatively destroying requires stopping all or part of the existing system, destroying it, redesigning the new system, putting it in place, debugging it, and habituating employees to its entirely new features. That means retraining and re-establishing informal networks among longstanding employees, customers, and new employees. Finally, it means creating a new culture and aligning people, processes, networks, and structures with it.

Much of consumer research has focused on frequently purchased packaged goods, and so it might be understandable that the concept of risk has lingered in the shadows. Although risk is involved in the purchase of packaged goods, it is minor compared with that in the domains of much greater economic consequence: For most consumers in developed countries, decisions about where to live and how to invest for retirement are the two largest economic decisions they will make.

We analyze an airline yield management problem on a single flight leg in which the buyers' choice of fare classes is modeled explicitly. The choice model we use is very general and includes a wide range of discrete choice models of practical interest. The optimization problem is to find, at each point in time, the optimal subset of fare classes to offer. We characterize the optimal policy for this problem exactly and show it has a surprisingly simple form.

Any simulation procedure has difficulty achieving accuracy for rare events that lie in the tails of the probability distributions one is simulating from. But that is where the outcomes that produce defaults in a credit portfolio occur, making pricing and risk management for CDOs and similar instruments difficult and (computer) time-consuming. In this article, Glasserman introduces several approximation procedures for estimating the tails of the distribution of default risk exposure for a credit portfolio.

Tax evasion, by its very nature, is difficult to observe. We quantify the effects of tax rates on tax evasion by examining the relationship in China between the tariff schedule and the "evasion gap," which we define as the difference between Hong Kong's reported exports to China at the product level and China's reported imports from Hong Kong. Our results imply that a one-percentage-point increase in the tax rate is associated with a 3 percent increase in evasion.

One role of accounting is to discipline softer (more manipulable) sources of information. We use a principal-agent model of hidden actions and hidden information to study this role. In our model, there is both a verifiable signal (a publicly observed output) and an unverifiable signal (a productivity parameter privately observed by the agent). In a one-period setting, the optimal contract does not make use of the agent's report on the private signal. However, when the output is tracked over two periods, the agent's communication can be valuable.

This study examines whether the quality of online buying experience represents a competitive advantage for Internet firms focused on business to consumer e-commerce (“e-commerce” firms). Forrester Research, a consulting firm, estimates that revenues in the business to consumer segment will grow from $20 billion in 1999 to $184 billion by 2004. Such explosive growth is due, in part, to the superior shopping experiences that new e-commerce firms offer.

This paper analyzes the role of jumps in continuous-time short rate models. I first develop a test to detect jump-induced misspecification and, using Treasury bill rates, find evidence for the presence of jumps. Second, I specify and estimate a nonparametric jump-diffusion model. Results indicate that jumps play an important statistical role. Estimates of jump times and sizes indicate that unexpected news about the macroeconomy generates the jumps. Finally, I investigate the pricing implications of jumps.

Creative destruction tends to be a very disruptive and painful way of bringing about change — often so painful that it becomes virtually unsustainable. In many situations such highly destabilizing and painful changes can hurt more than they help. What is needed is a less disruptive approach to change — one that provides for a sustained series of successful changes, enabling firms to adapt to their ever-changing environments without being torn apart. An alternative to creative destruction called creative recombination is described.

We investigate whether the accruals anomaly is a manifestation of the glamour stock phenomenon documented in the finance literature. Value (glamour) stocks, characterized by low (high) past sales growth, high (low) book-to-market (B/M), high (low) earnings-to-price (E/P), and high (low) cash flow-to-price (C/P), are known to earn positive (negative) future abnormal returns. Note that "C" or cash flow is operationalized in the finance literature as earnings adjusted for depreciation.

Despite the obvious importance of understanding how business cycle fluctuations affect both individual companies and whole industries, not much marketing research focuses on the subject. Often, one only has aggregate information on the state of the national economy, even though cyclical contractions and expansions generally do not have an equal impact on every industry, nor on all firms in any given industry.

This paper presents a financial statement analysis that distinguishes leverage that arises in financing activities from leverage that arises in operations. The analysis yields two leveraging equations, one for borrowing to finance operations and one for borrowing in the course of operations. These leveraging equations describe how the two types of leverage affect book rates of return on equity.

We assemble bank-level and other data for Fed member banks to model determinants of bank failure. Fundamentals explain bank failure risk well. The first two Friedman-Schwartz crises are not associated with positive unexplained residual failure risk, or increased importance of bank illiquidity for forecasting failure. The third Friedman-Schwartz crisis is more ambiguous, but increased residual failure risk is small in the aggregate. The final crisis (early 1933) saw a large unexplained increase in bank failure risk.

Companies are collecting increasing amounts of information about their customers. This effort is based on the assumption that more information is better and that this information can be leveraged to predict customers' behavior in a variety of situations and product categories. For example, information about a customer's purchase behavior in one category can be helpful in predicting his potential behavior in a related category, which in turn could help a firm in its cross-selling efforts.

The authors propose that the revenue premium a brand generates compared with that of a private label product is a simple, objective, and managerially useful product-market measure of brand equity. The authors provide the conceptual basis for the measure, compute it for brands in several packaged goods categories, and test its validity. The empirical analysis shows that the measure is reliable and reflects real changes in brand health over time.