Neil D. Pearson

Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case

Abstract We employ a martingale approach to study a dynamic consumption-portfolio problem in continuous time with incomplete markets and short-sale constraints. We introduce a notion of minimax local martingale and transform the dynamic problem into a static problem of maximizing expected utility over the consumption bundles that satisfy a single budget constraint formed using that measure. We establish the existence of and characterize the minimax local measure, provide sufficient conditions for the dynamic consumption-portfolio problem to have a solution, and relate the optimal policies to the solution of quasi-linear partial differential equation.

Is the Short Rate Drift Actually Nonlinear

Ait-Sahalia (1996) and Stanton (1997) use nonparametric estimators applied to short-term interest rate data to conclude that the drift function contains important nonlinearities. We study the finite-sample properties of their estimators by applying them to simulated sample paths of a square-root diffusion. Although the drift function is linear, both estimators suggest nonlinearities of the type and magnitude reported in Ait-Sahalia (1996) and Stanton (1997). Combined with the results of a weighted least squares estimator, this evidence implies that nonlinearity of the short rate drift is not a robust stylized fact. Copyright The American Finance Association 2000.

Open-end mutual funds and capital-gains taxes

Despite the fact that taxable investors would prefer to defer the realization of capital gains indefinitely, most open-end mutual funds regularly realize and distribute a large portion of their gains. We present a model in which unrealized gains in the funds portfolio increase expected future taxable distributions, and thus increase the present value of a new investors tax liability. In equilibrium, managers interested in attracting new investors pass through taxable capital gains to reduce the overhang of unrealized gains. This model contains a number of empirical predictions that are consistent with data on actual fund overhangs.

Recent Advances in Estimating Term-Structure Models

In the past 10 years, increasingly sophisticated statistical techniques have been applied to the estimation of increasingly complex models of the term structure of interest rates. In reviewing this literature, we highlight the facts that have been established and the key unresolved issues. The data indicate that within a wide range of interest rates, mean reversion in rates is, at best, weak. Whether mean reversion is stronger for very high or very low levels of rates is an unresolved issue. The absolute volatility of rates increases as the level of rates increases, but the strength of this effect and the role and nature of either stochastic-volatility or regime-switching components in rates are still unclear. Unfortunately, these unresolved issues have important implications for fixed-income option pricing and risk measurement, including value-at-risk calculations. Models of the term structure of interest rates are widely used in pricing interest rate derivatives and instruments with embedded options, such as callable bonds and mortgage-backed securities. Many such models are based on the simplifying assumption that changes in interest rates of all maturities are driven by changes in a single underlying random factor, often taken to be the “short” or “instantaneous” rate of interest. Both the decision to use a one-factor model and the choices made within that framework are crucial. The evolution of interest rates over time, and thus the prices of options and other derivatives, is determined entirely by these choices. Models of interest rate volatility (sometimes implicit) also play key roles in risk measurement—for example, in value-at-risk calculations. Unfortunately, theory provides little guidance about the modeling choices. As a result, the last decade has seen the development of a large and growing academic literature devoted to estimating how expected changes and volatilities of interest rates are related to their levels and, sometimes, other variables. This literature is scattered in different places and often emphasizes the statistical and econometric techniques used rather than the implications of the analysis for interest rate models. Therefore, it is not easily accessible to many practitioners. This article is the first step in remedying this problem. We summarize in one place the substantive implications of the recent academic literature for dynamic models of the evolution of interest rates. Much of the recent academic literature we review focuses on one-factor models, but researchers have known for at least 10 years that at least three factors are needed to fully capture the variability of interest rates. Why then consider one-factor models? The answer is that research has shown that roughly 90 percent of the variation in U.S. Treasury rates can be explained by the first factor, which can be interpreted as corresponding to changes in the general level of interest rates. Thus, any relationship between the level of interest rates and their expected changes and volatilities will be dominated by the influence of this first factor. In one-factor models, this factor is typically identified with the instantaneous or short rate of interest. The recent academic literature studying the behavior of the yields on short-term bonds or deposits can be interpreted as a detailed explanation of the first factor by using the yield on a particular instrument (e.g., one-month LIBOR) as a proxy for the short rate. According to the recent literature, what model features appear to be essential in describing the fundamental properties of interest rates? First, the new literature does not provide conclusive evidence based solely on the data about whether interest rate levels tend to return to a constant long-run level and, if they do, whether this tendency is stronger for extreme levels of interest rates. Second, with respect to interest rate volatility, the “absolute” volatility of the short rate, defined as the standard deviation of rate changes scaled by the square root of the time between changes, clearly increases as the level of interest rates increases. Inferences about the relationship between the level and volatility of the short rate are sensitive, however, to the treatment of the years between 1979 and 1982, the years of the U.S. Federal Reserves so-called experiment in targeting monetary aggregates rather than targeting interest rate levels. In particular, the data from this period suggest a strong relationship between volatility and the level of interest rates; when this period is excluded or treated as a distinct regime with a lower probability of occurring, the data suggest a much weaker relationship between interest rate level and volatility. Finally, modeling the volatility of interest rates requires more than a simple “level effect”; that is, some sort of stochastic-volatility effect seems to be in play. But the additional volatility component can be described adequately (in a statistical sense) in a variety of competing ways.

An Efficient Approach for Pricing Spread Options

Spread options are options whose payoff is based on the difference in the prices of two underlying assets. The price of a spread option is the (discounted) double integral of the option payoffs over the risk-neutral joint distribution of the terminal prices of the two underlying assets. Analytic expressions for the values of spread puts and calls in a Black-Scholes environment are not known, and various numerical algorithms must be used. This article presents an accurate and efficient approach for pricing European-style spread options on equities, foreign currencies, and commodities. The key to the approach is to recognize that the joint density of the terminal prices of the underlying assets can be factored into the product of univariate marginal and conditional densities, and that an analytic expression for the integral of the option payoffs over the conditional density is available. The remaining integration amounts to valuing the payoff function given by the results of the first integration. This payoff function is approximated by a portfolio of ordinary puts and calls, and valued accordingly. The approach is more accurate than existing bivariate binomial schemes, and fast enough for practical applications. It also allows for accurate and efficient computation of the partial derivatives of the option price, i.e., the Greek letter risks.

Option Value, Uncertainty, and the Investment Decision

The options-based approach to studying irreversible investment under uncertainty emphasizes that the opportunity cost of investment includes the value of the option to wait that is extinguished when an investment is undertaken. Thus, the investment decision is affected by the determinants of the value of this option. We extend and generalize a standard model of irreversible investment by introducing a second fully reversible technology, and also incorporate partial reversibility by allowing capital to be abandoned at a cost. As in the existing literature, we find that the threshold value of the “underlying asset” (in our case, demand) at which investment takes place is increasing in the uncertainty of demand. We also find that the value of the option and thus the threshold value of the option value multiple at which investment takes place may be either increasing or decreasing in the uncertainty of demand. In addition, we find that for the case in which capital is used to replace the reversible technology, the threshold value of the option value multiple is insensitive to the degree of reversibility of capital.

OPTION PRICING: A NEW APPROACH TO MINE VALUATION

Uncertainty is an important feature of many investments, but it is especially important for mineral properties. Mine properties often entail large investments and fixed commitments. Managers in the mining industry often view price uncertainty as undesirable, due to the possibility that the price of the mined commodity will fall to a level that prevents the firm from recovering its investment and fixed costs. This paper identifies pitfalls in conventional valuation methods and outlines a new approach to valuation based on option pricing theory and dynamic programming. In the process, it identifies generic strategies for organizing mine production in ways that allow the owner to benefit from the uncertainty in mineral prices.

Study of Real Options with Exogenous Competitive Entry to Analyze Dispute Resolution Ladder Investments in Architecture, Engineering, and Construction Projects

Architecture, engineering, and construction industry participants often find it pragmatic to implement a project-specific dispute resolution ladder (DRL) as a managerial tool to assist in the prompt resolution of claims and change orders (CCOs) that might arise during the project construction phase. This project-specific DRL consists of a single or multiple alternative dispute resolution (ADR) techniques that require capital expenditures to cover the expenses incurred by the owner’s/contractor’s employees and third-party neutrals. If a project-specific DRL is properly chosen, then the capital expenditures are outweighed by the expected benefits from the DRL implementation; namely, prompt resolution of the CCOs without incurring excessive cost overruns on an already financially stressed project budget, as well as avoiding the escalation of the claims to a dispute that requires long protracted litigation for final settlement. Typically, the decision as to which ADR techniques to include in the project-speci...

VaR: The state of play

Abstract Since “Value at Risk” (VaR) received its first wide introduction in the July 1993 Group of Thirty report, the number of users of—and uses for—VaR have increased dramatically. However, VaR itself has been evolving. In this article, we will first review some of the important refinements in VaR that have appeared—improved speed of computation, improved accuracy, and improved stress testing. We then look at the “next steps” (which we refer to as “Beyond VaR”), in which we review extensions to standard VaR, the emergence of “risk contribution” measures, and alternatives to standard VaR (including Extreme Value Theory [EVT] and Coherent Risk Measures).

Option Trading Costs Are Lower than You Think

Conventional estimates of the costs of taking liquidity in equity options markets are large. This presents a puzzle, which we resolve by taking seriously the implication of models of dynamic limit order markets that the bid-ask midpoint can be a poor proxy for the true value of a security, conditional on the occurrence of a trade. Changes in option prices can be predicted using publically available information, and a large proportion of option trades exploit this high-frequency predictability to take liquidity at low cost, buying and selling immediately before option prices are expected to change. Conventional measures of effective spreads and price impact do not account for this execution timing but can be adjusted to do so. For the average trade, effective spreads that take account of trade timing are one-third smaller than the conventionally measured effective spreads; for trades that reflect execution timing, they are four times smaller. Conventional measures of price impact overstate it by a factor of more than two. These findings have striking implications for the profitability of options trading strategies that involve taking liquidity. Our main results are robust to recent changes in option market structure.