Dwight Grant

Theory of the Firm with Joint Price and Output Risk and a Forward Market

Expected utility maximizing farmers facing just price risk or both price risk and quantity risk behave similarly in the absence of a forward market. If forward contracting is possible, that is not true because variation in the commodity price affects a farmers wealth through the value of his futures position, the value of his output and through the covariance between price and output. This covariance affects a farmers optimal scale of production, his optimal forward position and the interrelationship between the scale of production and forward trading.

Cross-hedging foreign currency risk

Abstract This paper provides empirical evidence on the effectiveness of cross-hedging to reduce foreign exchange risk. Simple cross-hedges for currencies with and without futures contracts, multiple cross-hedges, portfolio hedges, and commodity cross-hedges are examined. Cross-hedges are found to be less effective than traditional similar-asset hedges. In some instances inter-temporal instability causes hedged positions to be riskier than unhedged ones although on the whole cross-hedging is shown to be a useful risk reduction technique.

Optimal hedging of uncertain and long-term foreign exchange exposure

Abstract This paper employs stochastic dynamic programming to analyze two hedging problems which arise frequently, especially in international finance. One is the hedging of an uncertain exposure when the arrival of new information is anticipated. It is shown that a risk-averse agent will hedge a fraction of his maximum potential exposure to reduce risk. The second problem concerns hedging an exposure which extends beyond the delivery date of the available forward contract. The solution yields a rule by which successive contracts can be linked to form an optimal hedging strategy. A short empirical study illustrates this rule.

Optimal Sequential Futures Trading

Hedgers adjust their futures market positions to reflect new information. Therefore, the anticipation of new information creates future decision points and thus a multiperiod decision problem. Previous studies (see [2], [4], [5], [7], and [8]) which solved the problem of choosing optimal futures market hedges have not addressed this issue. Rather, these studies have derived optimal hedges in one-period frameworks. In general, this solution is incorrect if, during the time the hedge is in effect, new information is anticipated.

Implementing No-Arbitrage Term Structure of Interest Rate Models in Discrete Time When Interest Rates Are Normally Distributed

The article develops a method for implementing nonarbitrage term structure of interest rate models for the single-factor model under the Heath-Jarrow-Morton (HJM) framework of the evolution of forward interest rates. The HJM framework is universal in the sense that it is based on the no-arbitrage condition, and it can accommodate nearly all existing models if interest rates - spot rate and forward rates - distributed normally. The implementation requires the calculation of drift adjustment terms (DATs) that are the functions of the volatilitys of forward rates. The method is equally effective with volatility functions that are integrable and those that are not. It is easy to understand, simple enough to implement for even difficult volatility functions, generalizable, and able to accommodate Monte Carlo simulations of interest rate modeling.

International diversification and hedging: A Japanese and U.S. perspective

Abstract The research examines international equity diversification from the perspectives of Japanese and U.S. American investors. It looks at the degree of risk reduction achieved through diversification as well as the impact of currency exposure on the riskiness of equity portfolios. The comparison of U.S. and Japanese perspectives indicates the importance of the numeraire in evaluating portfolio performance and currency risk management.

An Analytical Implementation of the Hull and White Model

One of the most parsimonious models of interest rate behavior is the “extended Vasicek” model of Hull and White. It has only one stochastic factor, but has the flexibility to match the initial term structure in the market, making it arbitrage-free. To build the market term structure into a trinomial valuation lattice, Hull and Whites implementation of the model involves a search process at each date plus forward induction. In this article, Grant and Vora show how this process may be streamlined considerably by using an analytic solution rather than a search at each date.

A market index futures contract and portfolio selection

Abstract This paper shows that if security returns are generated according to the market model and there is a futures market in the market index, then optimal portfolios can be selected in three steps: 1) select the optimal combination of firm unique characteristics; 2) select the optimal investment in the market; and 3) select the optimal investment in the risk-free asset. The futures market contract separates the choice of firm and market exposure and thus both simplifies the mathematics involved and increases the mean/variance efficiency of the optimal portfolio.

The Hull and White Model of the Short Rate: An Alternative Analytical Representation

Hull and White extend Ho and Lees no-arbitrage model of the short interest rate to include mean reversion. This addition eliminates the problem of negative interest rates and has found wide application. To implement their model, Hull and White employ a sequential search process to identify the mean interest rate in a trinomial lattice at each date. In this paper we extend Hull and Whites work by developing an analytical solution for the mean interest rate at each date. This solution applies equally well to trinomial lattices, interest rate trees, and Monte Carlo simulation. We illustrate the analytical result by applying it to an example originally used by Hull and White and then for valuing an option on a bond.

Analytical implementation of the Ho and Lee model for the short interest rate

Abstract Ho and Lee introduced the first no-arbitrage model of the evolution of the short interest rate. When expositing the Ho and Lee model, other authors used the method of numerical solutions and forward induction, an approach pioneered by Black, Derman, and Toy for their own model much later. This standard method of implementation is relatively complex and time consuming when applied to scenarios that enable the use of an interest-rate lattice. Under many assumptions, however, the Ho and Lee model will generate an interest-rate tree. Under these circumstances, implementation via numerical methods and forward induction appears to be impractical, if not impossible. In this paper, we show how to implement the model analytically. We demonstrate that it is relatively straightforward to identify at the initial date analytical expressions for all interest rates at all dates. Once these expressions are evaluated, the calculations to obtain interest rates are arithmetic operations. Our recommended method of implementation applies equally effortlessly to interest-rate trees and Monte Carlo simulation.