A tale of two volatilities

We show that there are two distinct ways to make volatility stochastic that are differentiated by their consequences for skewness. Most models in the literature have adopted the relatively tractable methodology of using stochastic time changes to engineer stochastic volatility. Unfortunately, this is also the one that can conflict with the relationship occasionally observed in markets between volatility and skewness. Research enhancing the tractability of the second approach to stochastic volatility based on scaling is called for.     

Wages and prices in Europe: A test of the German leadership thesis

Zusammenfassung L?hne und Preise in Europa. Ein Test der These von der Vorherrschaft der Bundesrepublik. — Die Autoren prüfen die These, da das Europ?ische W?hrungssystem (EWS) der Bundesrepublik zur Führung bei der Inflationsbek?mpfung verhalf. Dabei werden zwei Ans?tze verwendet. Bei dem ersten wird die Bedeutung der deutschen Inflationserwartungen für die Erwartungen in anderen EWS-L?ndern untersucht, beim zweiten die Kointegration zwischen der Inflation in Deutschland und der in anderen EWS-L?ndern. Zur Kontrolle werden einerseits die Daten aus der Zeit vor Errichtung des EWS verwendet und andererseits die Daten des Vereinigten K?nigreichs, das am Wechselkursmechanismus des EWS nicht partizipierte. Die Ergebnisse sind zwar in mancher Hinsicht günstig, k?nnen aber nicht endgültig eine deutsche Führungsrolle im EWS best?tigen. Mit Hilfe der Kointegrationstechniken wird au\erdem gezeigt, da\ die Kaufkraftparit?t für das EWS nicht kennzeichnend war.

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Résumé Les revenus et les prix en Europe: Un test de la thèse de la prédominance allemande. — Cette étude a l’intention de vérifier la thèse que le système monétaire européen (SME) a fait se former la prédominance allemande dans la lutte contre l’inflation. Il y a deux tests. D’abord, on a examiné l’importance des expectations de l’inflation allemande pour les expectations aux autres pays du SME, puis on a examiné la cointégration de l’inflation en RFA avec celle aux autres pays. On emploie deux systèmes de contr?le: les données avant la fondation du SME et les données pour la Grande Bretagne qui n’a pas été membre du SME. Les résultats étant favorables à beaucoup d’autres aspects ne peuvent pas confirmer le r?le prédominant de la RFA dans le SME. En utilisant des techniques de cointégration on a aussi trouvé que la parité du pouvoir d’achat n’a pas caractérisé le SME.

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Resumen Salarios y precios en Europa : un test de la tesis del lidemgo alemán. — En este trabajo se examina la tesis que el Sistema Monetario Europeo (SME) constituye un vehículo para el liderazgo alemán en materia de política antiinflacionaria. Se emplean dos enfoques. En uno de ellos se estudia la relevancia de las expectativas inflacionarias en Alemania para las expectativas en otros países miembros del SME, en el otro se examina empirícamente la cointegraci?n entre la inflatión en Alemania y la de otros países del SME. Para ello se utilizan dos controles: datos para el período anterior al SME y datos para el Reino Unido, país no miembro del SME. Los resultados, si bien favorables en relatión a ciertos aspectos, no conf?rman en última instancia la tesis del liderazgo aleman en el SME. Asimismo, se demuestra que, utilizando técnicas de cointegración, el SME no está caracterizado por la paridad del poder de compra.

     

A two price theory of financial equilibrium with risk management implications

Financial primitives are introduced to define acceptable loss exposures when demands and supplies are defined on differing event spaces. Acceptable loss exposures are modeled by a convex cone of random variables containing the nonnegative random variables. The resulting financial equilibrium defines in general a two price economy. Analytical procedures for identifying the two prices are described. The size of the two price economy is fundamentally determined by the financial system that determines the size of the cone of acceptable losses. There are implications for accounting and risk management as liabilities would typically be valued at ask while assets are valued at bid with no data available on bidirectional prices for anything. Marking to market in such financial economies is at best marking to two price economies.     

Time Changes for Lévy Processes

The goal of this paper is to consider pure jump Lévy processes of finite variation with an infinite arrival rate of jumps as models for the logarithm of asset prices. These processes may be written as time-changed Brownian motion. We exhibit the explicit time change for each of a wide class of Lévy processes and show that the time change is a weighted price move measure of time. Additionally, we present a number of Lévy processes that are analytically tractable, in their characteristic functions and Lévy densities, and hence are relevant for option pricing.     

Stochastic Volatility for Lévy Processes

Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean-reverting square root process. The model for the mean-reverting time change is then generalized to include non-Gaussian models that are solutions to Ornstein-Uhlenbeck equations driven by one-sided discontinuous Lévy processes permitting correlation with the stock. Positive stock price processes are obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating these processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. In general mean-corrected exponentiation performs better than employing the stochastic exponential. It is observed that the mean-corrected exponential model is not a martingale in the filtration in which it is originally defined. This leads us to formulate and investigate the important property of martingale marginals where we seek martingales in altered filtrations consistent with the one-dimensional marginal distributions of the level of the process at each future date.     

AN ECONOMETRIC ANALYSIS OF EQUITY COSTS AND RISK PREMIUMS IN THE ELECTRIC UTILITY INDUSTRY: 1971–1985

This paper develops a varying parameter econometric model that estimates the cost of equity of individual utility firms from 1971 to 1985. The equity costs estimated in this framework can be analyzed in terms of their statistical precision. The paper also examines, theoretically and empirically, the relationship between the econometric estimates of the equity risk premiums and the risk-free interest rates. The data do not support the hypothesis that risk premiums are independent of interest rates. Also, the relationship appears to vary over time. These results invalidate the risk premium approach in which equity costs are estimated by adding a constant, historical average risk premium to the prevailing interest rates.     

Option Pricing With V. G. Martingale Components1

European call options are priced when the uncertainty driving the stock price follows the V. G. stochastic process (Madan and Seneta 1990). the incomplete markets equilibrium change of measure is approximated and identified using the log return mean, variance, and kurtosis. an exact equilibrium interpretation is also provided, allowing inference about relative risk aversion coefficients from option prices. Relative to Black-Scholes, V. G. option values are higher, particularly so for out of the money options with long maturity on stocks with high means, low variances, and high kurtosis.     

Exchange rate sensitivity of US bilateral trade flows

The traditional way of assessing the impact of currency depreciation on the trade balance has been to estimate the elasticity of trade volume to relative prices. To this end, most previous studies used aggregate trade data. To avoid aggregation biases potentially hidden in aggregate data, recent studies have relied on bilateral trade data. Since import and export price data is not available on bilateral level, this study proposes an alternative way of assessing the impact of currency depreciation on bilateral trade flows. The models are applied between the US and her 19 industrial trading partners using recent advances in time-series modeling.