Andrew J. Morton

Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation

This paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates. The methodology, based on the equivalent martingale measure technique, takes as given an initial forward rate curve and a family of potential stochastic processes for its subsequent movements. A no-arbitrage condition restricts this family of processes, yielding valuation formula for interest rate sensitive contingent claims that do not explicitly depend on the market prices of risk. Examples are provided to illustrate the key results. Copyright 1992 by The Econometric Society.

Equivalent martingale measures and no-arbitrage in stochastic securities market models

We characterize those vector-valued stochastic processes (with a finite index set and defined on an arbitrarystochasic base) which can become a martingale under an equivalent change of measure.This question is important in a widely studied problem which arises in the theory of finite period securities markets with one riskless bond and a finite number of risky stocks. In this setting, our characterization gives a criterion for recognizing when a securities market model allows for no arbitrage opportunities (free lunches). Intuitively, this can be interpreted as saying if one cannot win betting on a process, then it must be a martingale under an equivalent measure, and provides a converse to the classical notion that one cannot win betting on a martingale.

Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation

This paper studies the binomial approximation to the continuous trading term structure model of Heath, Jarrow, and Morton (1987). The discrete time approximation makes the original methodology accessible to a wider audience, and provides a computational procedure necessary for calculating the contingent claim values derived in the continuous time paper. This paper also extends and generalizes Ho and Lees (1986) model to include multiple random shocks to the forward rate process and to include an analysis of continuous time limits. The generalization provides insights into the limitations of the existing empirical implementation of Ho and Lees model.

Implied volatility functions in arbitrage-free term structure models

Abstract We test six term structure models in the Heath, Jarrow, and Morton (1992) class using Eurodollar futures and options data from 1987∗1992. We study the time series of implied interest rate volatilities from these models. Using one-day lagged implied volatilities, our one-and two-parameter models simultaneously price an average of 18.5 options each day with an average absolute error of one-and-a-half to two basis points. Although the models fit well, we document systematic strike- price and time-to-maturity biases for all models. We also implement simple trading strategies to test whether the models identify genuine biases.

Computational experience with a dual affine variant of Karmarkar's method for linear programming

The purpose of this paper is to describe computational experience with a dual affine variant of Karmarkars method for solving linear programming problems. This approach was implemented by the authors over a twelve week period during the summer of 1986. Computational tests were made comparing this implementation with MINOS 5.0, a state-of-the-art implementation of the simplex method. Our implementation compares favorably on publicly-available linear programming test problems with an average speedup of about three over MINOS 5.0.

A modified Lin-Kernighan traveling-salesman heuristic

The classic Lin-Kernighan traveling-salesman heuristic is modified so that the scope of its depth search is widened. The modification yields a simple yet effective heuristic that can be easily coded and adapted for general OR applications.

Distances between traveling salesman tours

Two metrics, based respectively on k-OPT and 2-OPT, for measuring the distance between traveling salesman tours are considered and their relationship worked out.