A chaotic approach to interest rate modelling

This paper presents a new approach to interest rate dynamics. We consider the general family of arbitrage-free positive interest rate models, valid on all time horizons, in the case of a discount bond system driven by a Brownian motion of one or more dimensions. We show that the space of such models admits a canonical mapping to the space of square-integrable Wiener functionals. This is achieved by means of a conditional variance representation for the state price density. The Wiener chaos expansion technique is then used to formulate a systematic analysis of the structure and classification of interest rate models. We show that the specification of a first-chaos model is equivalent to the specification of an admissible initial yield curve. A comprehensive development of the second-chaos interest rate theory is presented in the case of a single Brownian factor, and we show that there is a natural methodology for calibrating the model to at-the-money-forward caplet prices. The factorisable second-chaos models are particularly tractable, and lead to closed-form expressions for options on bonds and for swaptions. In conclusion we outline a general international model for interest rates and foreign exchange, for which each currency admits an associated family of discount bonds, and show that the entire system can be generated by a vector of Wiener functionals.Received: March 2004, Mathematics Subject Classification (2000): 91B28, 91B30, 91B50, 60H07JEL Classification: E43We are grateful to J. Boland, D. Brody, P. Carr, M. Davis, F. Delbaen, D. Filipovi, R. Jarrow, M. Grasselli, P. Hunt, T. Hurd, D. Madan, P. Malliavin, H. Rasmussen and M. Zervos for stimulating discussions. We thank D. Brody, M. Grasselli, T. Hurd and M. Zervos, in particular, for suggesting a number of improvements in the arguments presented here. We are grateful for helpful comments by participants at the Frontiéres en Finance seminar, Paris, May 2002, the Mathematics in Finance conference, Kruger Park, RSA, August 2002, the Imperial College finance seminar, February 2003, the 13th annual Derivative Securities Conference, New York, April 2003, the Analysis of Random Markets Workshop, Banach Center, Warsaw, October 2003 and the Quantitative Methods in Finance Conference, Sydney, December 2003, where this work was presented. LPH acknowledges the hospitality of the Institute for Advanced Study, Princeton, where part of this work was carried out. AR acknowledges financial support from the Department of Mathematics, Kings College London.     

Three questions you need to ask about your brand

Traditionally, the people responsible for positioning brands have concentrated on the differences that set each brand apart from the competition. But emphasizing differences isn't enough to sustain a brand against competitors. Managers should also consider the frame of reference within which the brand works and the features the brand shares with other products. Asking three questions about your brand can help: HAVE WE ESTABLISHED A FRAME?: A frame of reference--for Coke, it might be as narrow as other colas or as broad as all thirst-quenching drinks--signals to consumers the goal they can expect to achieve by using a brand. Brand managers need to pay close attention to this issue, in some cases expanding their focus in order to preempt the competition. ARE WE LEVERAGING OUR POINTS OF PARITY?: Certain points of parity must be met if consumers are to perceive your product as a legitimate player within its frame of reference. For instance, consumers might not consider a bank truly a bank unless it offers checking and savings plans. ARE THE POINTS OF DIFFERENCE COMPELLING?: A distinguishing characteristic that consumers find both relevant and believable can become a strong, favorable, unique brand association, capable of distinguishing the brand from others in the same frame of reference. Frames of reference, points of parity, and points of difference are moving targets. Maytag isn't the only dependable brand of appliance, Tide isn't the only detergent with whitening power, and BMWs aren't the only cars on the road with superior handling. The key questions you need to ask about your brand may not change, but their context certainly will. The saviest brand positioners are also the most vigilant.     

Setting Public Service Outcome Targets: Lessons from Local Public Service Agreements

Public agencies in the UK and elsewhere are increasingly required to set outcome targets as a strategy for improving their services. A crucial element of this 'results orientation' is a clear definition of the desired outcomes and a specification of appropriate performance indicators. A recent example of this policy in the UK—Local Public Service Agreements (LPSAs)—is examined in this article. The authors' analysis of the first generation of LPSAs shows that just under half of the indicators used were measures of outcome. The authors explain the 'wicked' issues in outcome measurement that emerged from the research.     

Some problems in modelling the optimal division of a ‘cake’ between an unknown number of participants

The trade-off between the survival time of a fixed population and its consumption rates, when resources are exhaustible, has been studied by Koopmans. A link is established between this model and the traditional neoclassical literature on optimum population. The model is embedded in a larger model in which limited control over population growth rates is feasible, but in which the initial population size acts as a constraint on development. The optimal depletion rate of the exhaustible resource and optimal survival times are then explored. This facilitates a sensitivity analysis of the optimal policy and a discussion of the robustness of the results of Koopmans.     

Market Structure and the Demand for Free Trade

We examine a heterogenous goods duopoly model, wherein governments simultaneously and noncooperatively choose whether or not to provide subsidies for their firms and then firms noncooperatively choose output levels, either sequentially or simultaneously. We find that government trade policy and market structure are interdependent. First, the trade regime alters traditional firm preferences over sequential versus simultaneous play. Second, different market structures influence governments' preferences about free trade versus subsidies. Further, if one of the firms is a potential leader, allowing for endogenous market structure generates equilibrium outcomes that sometimes reinforce, and sometimes counter, traditional results in the strategic trade literature .     

Teaching business ethics: Bringing reality to the classroom

This paper presents an alternative method for discussing ethical issues. The method supports the use of the real world situations and emphasizes the interaction of all constituencies. The method incorporates the use of newspaper reports of real-life occurrences. It also stresses the use of local stories when possible.Dietrich L. Schaupp is a Professor of Management at West Virginia University. Dr. Schaupp has previously published in theJournal of Business Ethics. His current research interests focus on quality and ethics.Michael S. Lane is an Associate Professor of Management at West Virginia University. Dr. Lane has previously published in theJournal of Business Ethics. His current research interests focus on business ethics and strategic goals.     

Institutional Trading and Soft Dollars

Proprietary data allow us to distinguish between institutional investors' orders directed to soft-dollar brokers and those directed to other types of brokers. We find that soft-dollar brokers execute smaller orders in larger market value stocks. Allowing for differences in order characteristics, we estimate the incremental implicit cost of soft-dollar execution at 29 (24) basis points for buyer- (seller-) initiated orders. For large orders, incremental implicit costs are 41 (30) basis points for buys (sells). However, we document substantial variability in these estimates, and research services provided by soft-dollar brokers may at least partially offset these costs.