Maximum Likelihood Estimation of Latent Affine Processes

This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. The equivalent of Bayes' rule is derived for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. Likelihood functions can consequently be evaluated directly by Fourier inversion. An application to daily stock returns over 1953-96 reveals substantial divergences from EMM-based estimates: in particular, more substantial and time-varying jump risk.

The Market for Crash Risk

This paper examines the equilibrium when negative stock market jumps (crashes) can occur, and investors have heterogeneous attitudes towards crash risk. The less crash-averse insure the more crash-averse through the options markets that dynamically complete the economy. The resulting equilibrium is compared with various option pricing anomalies reported in the literature: the tendency of stock index options to overpredict volatility and jump risk, the Jackwerth (2000) implicit pricing kernel puzzle, and the stochastic evolution of option prices. The specification of crash aversion is compatible with the static option pricing puzzles, while heterogeneity partially explains the dynamic puzzles. Heterogeneity also magnifies substantially the stock market impact of adverse news about fundamentals.

Testing Option Pricing Models

This paper discusses the commonly used methods for testing option pricing models, including the Black-Scholes, constant elasticity of variance, stochastic volatility, and jump-diffusion models. Since options are derivative assets, the central empirical issue is whether the distributions implicit in option prices are consistent with the time series properties of the underlying asset prices. Three relevant aspects of consistency are discussed, corresponding to whether time series-based inferences and option prices agree with respect to volatility, changes in volatility, and higher moments. The paper surveys the extensive empirical literature on stock options, options on stock indexes and stock index futures, and options on currencies and currency futures.

U.S. Stock Market Crash Risk, 1926-2006

This paper applies the Bates (RFS, 2006) methodology to the problem of estimating and filtering time- changed Lévy processes, using daily data on U.S. stock market excess returns over 1926-2006. In contrast to density-based filtration approaches, the methodology recursively updates the associated conditional characteristic functions of the latent variables. The paper examines how well time-changed Lévy specifications capture stochastic volatility, the "leverage" effect, and the substantial outliers occasionally observed in stock market returns. The paper also finds that the autocorrelation of stock market excess returns varies substantially over time, necessitating an additional latent variable when analyzing historical data on stock market returns. The paper explores option pricing implications, and compares the results with observed prices of options on S&P 500 futures.

Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in thePHLX Deutschemark Options

An efficient method is developed for pricing American options on combination stochastic volatility/jump-diffusion processes when jump risk and volatility risk are systematic and nondiversifiable, thereby nesting two major option pricing models. The parameters implicit in PHLX-traded Deutschemark options of the stochastic volatility/jump- diffusion model and various submodels are estimated over 1984-91, and are tested for consistency with the $/DM futures process and the implicit volatility sample path. The parameters implicit in options are found to be inconsistent with the time series properties of implicit volatilities, but qualitatively consistent with log- differenced futures prices. No economically significant implicit expectations of exchange rate jumps were found in full-sample estimation, which is consistent with the reduced leptokurtosis of$/DM weekly exchange rate changes over 1984-91 relative to earlier periods.

Interfaces and Grain Boundaries of Lamellar Phases

Interfaces between lamellar and disordered phases, and grain boundaries within lamellar phases, are investigated employing a simple Landau free energy functional. The former are examined using analytic, approximate methods in the weak segregation limit, leading to density profiles which can extend over many wavelengths of the lamellar phase. The latter are studied numerically and exactly. We find a change from smooth chevron configurations typical of small tilt angles to distorted omega configurations at large tilt angles in agreement with experiment.Comment: 9 pages, 6 figures 9 pages, 6 figure

Doing Business under Canadian Environmental Law

In recent years, the role of the environmental risk management has become increasingly significant to multinational corporations. Corporations from the United States and elsewhere are now undertaking aggressive assessments of environmental regulatory compliance, and are incorporating environmental due diligence into transactions such as mergers, acquisitions, joint ventures, and divestitures. The first step toward assessing compliance often involves interpretation of complex, vaguely written environmental statutes and regulations. Matters are made more difficult by the fact that each governmental structure is different, and environmental controls inevitably will be administered in ways unfamiliar to foreign companies, even in countries which have emulated the United States\u27 system of environmental regulation. This article provides an overview of environmental requirements in Canada, primarily from the viewpoint of one already familiar with the United States regulatory framework. The article begins with an introduction to Federal laws and to the interrelationships between Federal and Provincial law and enforcement. It then focuses in greater detail on environmental laws in Ontario. That province is second only to Canada as the largest trading partner of the United States. American businesses conduct an increasingly diverse array of operations in Ontario, including manufacturing, real estate development, and capital investment, all of which come under extensive environmental regulation. Ontario is also the most industrialized province of Canada, and accounts for approximately one-half of the total volume of hazardous waste generated in Canada

Doing Business under Canadian Environmental Law

In recent years, the role of the environmental risk management has become increasingly significant to multinational corporations. Corporations from the United States and elsewhere are now undertaking aggressive assessments of environmental regulatory compliance, and are incorporating environmental due diligence into transactions such as mergers, acquisitions, joint ventures, and divestitures. The first step toward assessing compliance often involves interpretation of complex, vaguely written environmental statutes and regulations. Matters are made more difficult by the fact that each governmental structure is different, and environmental controls inevitably will be administered in ways unfamiliar to foreign companies, even in countries which have emulated the United States\u27 system of environmental regulation. This article provides an overview of environmental requirements in Canada, primarily from the viewpoint of one already familiar with the United States regulatory framework. The article begins with an introduction to Federal laws and to the interrelationships between Federal and Provincial law and enforcement. It then focuses in greater detail on environmental laws in Ontario. That province is second only to Canada as the largest trading partner of the United States. American businesses conduct an increasingly diverse array of operations in Ontario, including manufacturing, real estate development, and capital investment, all of which come under extensive environmental regulation. Ontario is also the most industrialized province of Canada, and accounts for approximately one-half of the total volume of hazardous waste generated in Canada