QUADRATIC TERM STRUCTURE MODELS FOR RISK-FREE AND DEFAULTABLE RATES

In this paper, quadratic term structure models (QTSMs) are analyzed and characterized in a general Markovian setting. The primary motivation for this work is to find a useful extension of the traditional QTSM, which is based on an Ornstein–Uhlenbeck (OU) state process, while maintaining the analytical tractability of the model. To accomplish this, the class of quadratic processes, consisting of those Markov state processes that yield QTSM, is introduced. The main result states that OU processes are the only conservative quadratic processes. In general, however, a quadratic potential can be added to allow QTSMs to model default risk. It is further shown that the exponent functions that are inherent in the definition of the quadratic property can be determined by a system of Riccati equations with a unique admissible parameter set. The implications of these results for modeling the term structure of risk-free and defaultable rates are discussed.     

EXPRESSING INVENTORY CONTROL POLICY IN THE TURNOVER CURVE

Estimation of the inventory level for an entire class of items is a valuable time saver when control of inventories at the aggregate level, rather than the item level, is of interest. Inventory approximation by location in supply chain network configuration and evaluation of inventory control policy shifts, are two examples of application. In this article, various popular inventory policies are related to a general function known as an inventory turnover curve that expresses inventory levels from the combined demand of multiple items. By knowing some basic item characteristics of representative items in a product class, the type of inventory policy being used, and the current aggregate inventory level, an inventory turnover curve can be constructed. This resulting turnover curve can be used to estimate inventory levels within 4.6%, on the average, of theoretically predicted ones.     

Operating efficiency of Canadian banks

This article assesses Canadian banks' ability to realize scale economies and cost complementarities in joint production. The Canadian banking system, with its 10 or so large banks and 50 smaller ones, offers a good database for a study of efficiency, especially since previous work suggests that the system's concentration has had little impact on system competitiveness. This article estimates a system of cost and cost share equations using Zellner's iterative seemingly unrelated regression technique, then evaluates scale economies and cost complementarities from the estimated cost functions' first and second partial derivatives. The article compares a model that classifies deposits as inputs with another that classifies them as outputs. The empirical findings indicate that deposits are better modelled as outputs than inputs; that Canadian banks organize to exhaust available sources of scale economies and economies in joint production; and that conclusions regarding scale economies and cost complementarities differ importantly according to whether deposits are modelled as inputs or as outputs.     

Snapshot samples

We consider a coverage model where an initial event that occurs at some point in time triggers an activity of random duration that leads to some subsequent event. A snapshot sample is constructed at a fixed point in chronological time either by sampling only subjects where the initial event has occurred but the subsequent event has yet to occur (active subjects), or by sampling only subjects where both the initial and subsequent events have occurred (inactive subjects). The biases inherent in snapshot sampling can be neatly characterized by the properties of two random variables: the history (defined as the time the initial event occurs as measured into the past from the chronological point of sampling), and the active time (defined as the length of time between the initial and subsequent events). Though snapshot samples are biased, recognizing the biases enables correct inferences to be drawn from snapshot-sampled data. Considering only the case where and are independent random variables, this paper presents the probability models associated with snapshot sampling, demonstrates the problems that can occur, offers procedures for overcoming these problems, and applies the methods to interesting data sets.     

From edgeworth to fisher to vickrey: A comment on Michael J. Boskin's Vickrey lecture

Irving Fisher has been overlooked as an influence on William Vickrey's work on taxation and as a link between Edgeworth and Vickrey. Vickrey was Fisher's last and greatest student.     

A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS

This paper gives a tree-based method for pricing American options in models where the stock price follows a general exponential Lévy process. A multinomial model for approximating the stock price process, which can be viewed as generalizing the binomial model of Cox, Ross, and Rubinstein (1979) for geometric Brownian motion, is developed. Under mild conditions, it is proved that the stock price process and the prices of American-type options on the stock, calculated from the multinomial model, converge to the corresponding prices under the continuous time Lévy process model. Explicit illustrations are given for the variance gamma model and the normal inverse Gaussian process when the option is an American put, but the procedure is applicable to a much wider class of derivatives including some path-dependent options. Our approach overcomes some practical difficulties that have previously been encountered when the Lévy process has infinite activity.