the pricing of options on assets with stochastic volatilities one option pricing problem that has hitherto been unsolved is the pricing of a european call on an asset that has a stochastic volatility this paper examines this problem the option price is determined in series form for the case in which the stochastic volatility is independent of the stock price numerical solutions are also produced for the case in which the volatility is correlated with the stock price it is found that the black scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity one option pricing problem that has hitherto remained unsolved is the pricing of a european call on a stock that has a stochastic volatility from the work of merton 12 garman 6 and cox ingersoll and ross 3 the differential equation that the option must satisfy is known the solution of this differential equation is independent of risk preferences if a the volatility is a traded asset or b the volatility is uncorrelated with aggregate consumption if either of these conditions holds the risk neutral valuation arguments of cox and ross 4 can be used in a straightfoward way this paper produces a solution in series form for the situation in which the stock price is instantaneously uncorrelated with the volatility we do not assume that the volatility is a traded asset also a constant correlation between the instantaneous rate of change of the volatility and the rate of change of aggregate consumption can be accommodated the option price is lower than the blackscholes b s 1 price when the option is close to being at the money and higher when it is deep in or deep out of the money the exercise prices for which overpricing by b s takes place are within about ten percent of the security price this is the range of exercise prices over which most option trading takes place so we may in general expect the b s price to overprice options this effect is exaggerated as the time to maturity increases one of the most surprising implications of this is that if the b s equation is used to determine the implied volatility of a near the money option the longer the time to maturity the lower the implied volatility numerical solutions for the case in which the volatility is correlated with the stock price are also examined the stochastic volatility problem has been examined by merton 13 geske 7 johnson 10 johnson and shanno 11 eisenberg 5 wiggins 16 and

inequality and violent crime abstract we investigate the robustness and causality of the link between income inequality and violent crime across countries first we study the correlation between the gini index and homicide and robbery rates within and between countries second we examine the partial correlation by considering other crime determinants third we control for the endogeneity of inequality by isolating its exogenous impact on these crime rates fourth we control for measurement error in crime rates by modeling it as both unobserved country effects and random noise finally we examine the robustness of this partial correlation to alternative measures of inequality the panel data consist of nonoverlapping 5 year averages for 39 countries during 1965 95 for homicides and 37 countries during 1970 94 for robberies crime rates and inequality are positively correlated within countries and particularly between countries and this correlation reflects causation from inequality to crime rates even after controlling for ot

generalized parameter functions for option pricing we extend the benchmark nonlinear deterministic volatility regression functions of dumas et al 1998 to provide a semi parametric method where an enhancement of the implied parameter values is used in the parametric option pricing models besides volatility skewness and kurtosis of the asset return distribution can also be enhanced empirical results using closing prices of the s p 500 index call options in one day ahead out of sample pricing tests strongly support our method that compares favorably with a model that admits stochastic volatility and random jumps moreover it is found to be superior in various robustness tests our semi parametric approach is an effective remedy to the curse of dimensionality presented in nonparametric estimation and its main advantage is that it delivers theoretically consistent option prices and hedging parameters the economic significance of the approach is tested in terms of hedging where the evaluation and estimation loss functions are aligned

help wanted economists crime and public policy beginning with gary w becker s 1968 article on crime and punishment economists have contributed important theoretical insights and empirical findings to the study of criminal behavior but the influence of economists on crime relevant research and over policy debates remains negligible this essay summarizes some basic data on the causes of crime the social costs and benefits of incarceration and replenishing social capital work on crime by economists should become influential in setting research agendas and shaping policy debates but economists will have to roll up their sleeves complexify their models and confront a real world prisoner s dilemma or two

pricing hang seng index options around the asian financial crisis a garch approach abstract this paper investigates how well the hang seng index options the most important class of option contracts traded in hong kong are priced using the garch approach we calibrated the garch parameters using the call and put option data and used them to price options in the subsequent weeks we found the garch model performs very well in comparison with the black scholes model even after allowing for a smile smirk adjustment its superior performance was also evident both before and during the recent asian financial turmoil

crime and victimization an economic perspective the recent upward trend in crime rates of developing countries has spurred widespread public concern about personal and proprietary insecurity in some countries the questions of crime violence and victimization are attracting more attention from academics and policy makers than traditional economic problems the objective of this paper is to examine the main issues related to crime and victimization from an economic perspective for this purpose the paper combines a review of the main results established in the literature with original research on the causes of crime and the risk factors of victimization the first section provides a review of the estimates of the costs of crime the main theoretical and empirical research on its causes and the relative advantages of official and survey data on crime the second section presents original work on the main causes of violent crime from a cross country perspective the empirical work starts with a basic model of the economic determinants of homicide and robbery rates in turn this empirical model is extended along five dimensions 1 deterrence factors 2 illegal drug related activities 3 demographic issues 4 income and ethnic polarization and 5 social capital the third section reviews recent case studies of latin american cities that rely on survey data to assess the empirical determinants of the probability of victimization these studies focus on three types of risk factors 1 individual characteristics 2 household characteristics and 3 community characteristics the main conclusions from the previous sections are summarized in section four

how important is the correlation between returns and volatility in a stochastic volatility model empirical evidence from pricing and hedging in the s p 500 index options market abstract this paper examines the importance of allowing for correlation between returns and volatility in a continuous time stochastic volatility option pricing model specifically it tests the closed form stochastic volatility model of heston review of financial studies 6 1993 327 343 that allows for non zero correlation in terms of pricing and hedging options on the s p 500 index it is found that non zero correlation in the stochastic volatility model leads to significant improvements in mispricing of out of the money options and overall pricing performance compared to if correlation is constrained to be zero in terms of hedging non zero correlation results in significantly lower hedging errors for out of the money options

forecasting stock return variance toward an understanding of stochastic implied volatilities we examine the behavior of measured variances from the options market and the underlying stock market under the joint hypotheses that markets are informationally efficient and that option prices are explained by a particular asset pricing model forecasts from time series models of the stockreturn process should not have predictive content given the market forecast as embodied in option prices both in sample and out of sample tests suggest that this hypothesis can be rejected using simulations we show that biases inherent in the procedure we use to imply variances cannot explain this result thus we provide evidence inconsistent with the orthogonality restrictions of option pricing models that assume that variance risk is unpriced these results also have implicationsfor optimal variance forecast rules

garch vs stochastic volatility option pricing and risk management this paper examines the out of sample performance of two common extensions of the black scholes framework namely a garch and a stochastic volatility option pricing model the models are calibrated to intraday ftse 100 option prices we apply two sets of performance criteria namely out of sample valuation errors and value at risk oriented measures when we analyze the fit to observed prices garch clearly dominates both stochastic volatility and the benchmark black scholes model however the predictions of the market risk from hypothetical derivative positions show sizable errors the fit to the realized profits and losses is poor and there are no notable differences between the models overall we therefore observe that the more complex option pricing models can improve on the black scholes methodology only for the purpose of pricing but not for the value at risk forecasts author s abstract

shadow economies size causes and consequences using various methods the size of the shadow economy in 76 developing transition and oecd countries is estimated average size varies from 12 percent of gdp for oecd countries to 23 percent for transition countries and 39 percent for developing countries increasing taxation and social security contributions combined with rising state regulations are driving forces for the increase of the shadow economy especially in oecd countries according to some findings corruption has a positive impact on the size of the shadow economy and a growing shadow economy has a negative effect on official gdp growth

pricing individual stock options using both stock and market index information abstract when it comes to individual stock option pricing most applications consider a univariate framework from a theoretical point of view this is unsatisfactory as we know that the expected return of any asset is closely related to the exposure to the market risk factors to address this we model the evolution of the individual stock returns together with the market index returns in a flexible bivariate model in line with theory the model parameters are estimated using both historical returns and aggregated option data from the index and the individual stocks we assess the model performance by pricing a large set of individual stock options on 26 major us stocks over a long time period including the global financial crisis our results show that the losses from using a univariate formulation amounts to 11 on average when compared to our preferred bivariate specification

uses and abuses of estimates of the underground economy ered valuable by at least a part of society narcotics production and distribution prostitution gambling these activities can be large in some countries and should be counted in the national accounts of all countries although they rarely are their omission affects the comparability of data across countries the incomes generated by illegal activities are rarely taxed many other activities such as those associated with the subsistence or informal sectors are estimated rather than measured and are generally not taxed because of the low value they generate to those who engage in them in conclusion there are many reasons beside the ones discussed in this paper why the measurements of national output may not be complete about two decades ago a few economists became convinced that many normal economic activities that should be measured and taxed were taking place underground or in the shadow thus presumably escaping the attention of the statistical offices of the tax authorities and more generally of the government regulators some of these economists also claimed that like alice in wonderland these hidden activities were growing in a ridiculous fashion see gutmann 1977 and feige 1979 by the late 1970s the role of government had grown enormously so that the level of taxation and the tax rates had risen sharply and regulations had proliferated in many countries see tanzi and schuknecht 1997 these developments had created strong incentives for individuals and enterprises to go underground to avoid taxes and regulatory restrictions thus a good case could be made that what came to be called the underground economy was a phenomenon to worry about newspaper articles were ready to accept the

what causes violent crime this study uses panel data of intentional homicide and robbery rates for a sample of developed and developing countries for the period 1970 1994 based on information from the united nations world crime surveys to analyze the determinants of national crime rates both across countries and over time a simple model of the incentives to commit crimes is proposed which explicitly considers possible causes of the persistence of crime over time criminal inertia a panel data based gmm methodology is used to estimate a dynamic model of national crime rates this estimator controls for unobserved country speci ce ects the joint endogeneity of some of the explanatory variables and the existence of some types of measurement errors a icting the crime data the results showthat increases in income inequality raise crime rates crime tends to be countercyclical and criminal inertia is signi cant 2002 elsevier science b v all rights reserved

an empirical comparison of continuous time models of implied volatility indices abstract we explore the ability of alternative popular continuous time diffusion and jump diffusion processes to capture the dynamics of implied volatility indices over time the performance of the various models is assessed under both econometric and financial metrics to this end data are employed from major european and american implied volatility indices and the rapidly growing cboe volatility futures market we find that the addition of jumps is necessary to capture the evolution of implied volatility indices under both metrics mean reversion is of second order importance though the results are consistent across the various metrics markets and construction methodologies

violent crime does social capital matter this paper examines empirically the effect of some commonly used indicators of social capital such as the prevalence of trust on community members and the participation in voluntary secular and religious organizations on the incidence of violent crimes this is a cross country study whose basic sample consists of 39 developed and developing countries and whose dependent variable is the national intentional homicide rate the paper identifies and deals with three challenges in the empirical estimation of the effect of social capital on the incidence of violent crimes the omittedvariable problem is dealt with by including income inequality and economic growth as additional determinants of a country s violent crime rate the joint endogeneity or reverse causation problem is accounted for by using instrumental variables for social capital in the crime regression the specificity problem that is the potentially opposite effects of group specific and society wide social capital is noted and addressed only indirectly by emphasizing the results applied to the social capital indicators that have application for society as a whole the main result of the paper is that only the component of social capital measured by trust on community members has the effect of reducing the incidence of violent crimes the results regarding measures of other indicators of social capital are rather unclear this may be due to a combination of limited samples inability to fully control for reverse causation and most likely the opposite effects that society wide and group specific social capital may have on violent crime lederman and menendez are economists with the office of the chief economist for latin america and the caribbean of the world bank loayza is a senior economist with the research department of the central bank of chile and he is currently on leave from the development economics research group of the world bank the opinions expressed herein should not be attributed to the world bank the authors are grateful to ed glaeser jeff grogger gale johnson sanjay marwah steve messner nicholas sambanis and an anonymous referee for invaluable comments and suggestions the authors are responsible for any remaining errors

accurate minimum capital risk requirements a comparison of several approaches in this paper we estimate for several investment horizons minimum capital risk requirements for short and long positions using the unconditional distribution of three daily indexes futures returns and a set of short and long memory stochastic volatility and garch type models we consider the possibility that errors follow a t student distribution in order to capture the kurtosis of the returns series the results suggest that accurate modelling of extreme observations obtained for long and short trading investment positions is possible with an autoregressive stochastic volatility model moreover modelling futures returns with a long memory stochastic volatility model produces in general excessive volatility persistence and consequently leads to large minimum capital risk requirement estimates finally the models predictive ability is assessed with the help of out of sample conditional tests

value at risk models for dutch bond portfolios this study investigates the consequences of dynamics in the term structure of dutch interest rates for the accurateness of value at risk models therefore value at risk measures are calculated using both historical simulation variance covariance and monte carlo simulation methods for a ten days holding period the best results were obtained for a combined variance covariance monte carlo method using a term structure model with a normal distribution and garch specification term structure models with a t distribution or with cointegration performed much worse 2000 elsevier science b v all rights reserved jel classification e43 g28

an empirical model comparison for valuing crack spread options in this paper we investigate the pricing of crack spread options particular emphasis is placed on the question of whether univariate modeling of the crack spread or explicit modeling of the two underlyings is preferable therefore we contrast a bivariate garch volatility model for cointegrated underlyings with the alternative of modeling the crack spread directly conducting an empirical analysis of crude oil heating oil and crude oil gasoline crack spread options traded on the new york mercantile exchange the more simplistic univariate approach is found to be superior with respect to option pricing performance

dynamic deterrence theory economic theories of deterrence have primarily been built on static models a common and serious shortcoming of the existing dynamic deterrence models is the assumption of a twoperiod structure that ignores recidivism the aims of this paper are to formulate and solve a general dynamic deterrence model that incorporates recidivistic behaviour to explore its implications and to derive some testable predictions the analysis shows how the value and the intensity of engaging in illegal activity change over time highlights the weaknesses of twoperiod deterrence models and compares the deterrent effectiveness of increasing the likelihood of punishment versus the severity of punishment finally the recidivistic model provides a structural foundation for the widely used stochastic process models of crime in operations research and criminology

estimations of the economic model of crime using aggregate and individual level data much has happened in the economics of crime since becker s 1 seminal paper of two decades ago the theory has been refined by among others ehrlich 10 11 12 block and lind 4 5 block and heinke 3 and schmidt and witte 30 attempts to test the model empirically began immediately the most cited including ehrlich 10 11 12 sjoquist 31 carr hill and stern 7 phillips and votey 26 witte 38 and myers 22 23 interest continues with recent work including layson 19 sandelin and skogh 29 ehrlich and brower 13 cover and thistle 9 viscusi 36 and tauchen witte and griesinger 33 there has been some controversy however concerning the type of data more suitable to the estimation of the economic model of crime most of the work has used aggregate data in which the unit of observation is a political jurisdiction but the use of aggregate data has been sharply criticized the alternative is individual data few attempts have been made to use individual data probably because an ideally constructed data set representative of a general population would be far too costly for most research budgets most of the studies that have been done have used data on releasees from prison or other criminal justice programs they are in effect recidivism studies based on the economic model of crime

a pedagogical treatment of bilateral monopoly most economists are familiar with the concept of bilateral monopoly an upstream monopolist sells its output to a single downstream buyer that may also be a monopolist in its output market the theory of bilateral monopoly has a rich history that can be traced to the writings of cournot 10 and menger 31 over the 150 or so years that the problem has been under consideration however economists have offered a variety of solutions ranging from a completely determinate intermediate good price and output to a completely indeterminate solution within a specified range interestingly this historical divergence of opinion concerning the correct outcome under bilateral monopoly still persists a clear consensus has not yet emerged surprisingly this lack of unanimity exists despite the fact that bowley 5 provided the theoretically correct solution in 1928 2 even more surprising however is the apparent popularity of the incorrect solution a recent survey of the population of intermediate microeconomic texts on the authors bookshelves revealed that over 80 percent of the current treatments of this topic are in error 3 table i presents the results of that survey those authors who present a correct analysis of bilateral monopoly recognize that optimality requires joint profit maximization this leads them to the correct conclusion regarding the determinate quantity of the intermediate product exchanged of the five treatments we have classified

nobel lecture the economic way of looking at behavior an important step in extending the traditional theory of individual rational choice to analyze social issues beyond those usually considered by economists is to incorporate into the theory a much richer class of attitudes preferences and calculations while this approach to behavior builds on an expanded theory of individual choice it is not mainly concerned with individuals it uses theory at the micro level as a powerful tool to derive implications at the group or macro level the lecture describes the approach and illustrates it with examples drawn from my past and current work