the economic determinants of interest rate option smiles we address three questions relating to the interest rate options market what is the shape of the smile what are the economic determinants of the shape of the smile do these determinants have predictive power for the future shape of the smile and vice versa we investigate these issues using daily bid and ask prices of euro interest rate caps floors we find a clear smile pattern in interest rate options the shape of the smile varies over time and is affected in a dynamic manner by yield curve variables and the future uncertainty in the interest rate markets it also has information about future aggregate default risk our findings are useful for the pricing hedging and risk management of these derivatives

decentralized organizational learning an experimental investigation we experimentally study decentralized organizational learning our objective is to understand how learning members of an organization cope with the con founding effects of the simultaneous learning of others we test the predictions of a stylized rational agent model of organizational learning that provides sharp predictions as to how learning members of an organization might cope with the simultaneous learning of others as a function of fundamental variables e g firm size and the discount factor while the problem of learning while others are learning is quite difficult we find support for the comparative static predictions of the models unique symmetric equilibrium jel c72 d23 d83 if one s own actions are embedded in an ecology of the actions of many others who are simultaneously learning and changing it is not easy to understand what is going on the relationship between the actions of individuals in the organization and overall organiza tional performance is confounded by simultaneous learning of other actors

an experiment on the value of structural information in a 2 2 repeated game abstract in a repeated 2 2 cooperation game providing subjects with little information impedes cooperation providing subjects with little more information prior to playing the game leads to almost sure cooperation this result stands in contrast to predictions from adaptive as well as almost optimal learning rules

analytical evaluation of volatility forecasts estimation and forecasting for realistic continuous time stochastic volatility models is hampered by the lack of closed form expressions for the likelihood in response andersen bollerslev diebold and labys econometrica 71 2003 579 625 advocate forecasting integrated volatility via reduced form models for the realized volatility constructed by summing high frequency squared returns building on the eigenfunction stochastic volatility models we present analytical expressions for the forecast efficiency associated with this reduced form approach as a function of sampling frequency for popular models like garch multifactor affine and lognormal diffusions the reduced form procedures perform remarkably well relative to the optimal infeasible forecasts

a two person game of information transmission we consider a statistical decision problem faced by a two player organization whose members may not agree on outcome evaluations and prior probabilities one player is specialized in gathering information and transmitting it to the other who takes the decision this process is modeled as a game qualitative properties of the equilibria are analyzed the impact of improving the quality of available information on the equilibrium welfares of the two individuals is studied better information generally may not improve welfare we give conditions under which it will

answering the skeptics yes standard volatility models do provide accurate forecasts a voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using arch and stochastic volatility models while most of these studies have documented highly significant in sample parameter estimates and pronounced intertemporal volatility persistence traditional ex post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts contrary to this contention we show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications new methods for improved ex post interdaily volatility measurements based on high frequency intradaily data are also discussed

evolutionary stability in games of communication abstract this paper identifies evolutionarily stable outcomes in games in which one player has private information and the other takes a payoff relevant action the informed player can communicate at little cost outcomes satisfying a set valued evolutionary stability condition must exist and be efficient in common interest games when there is a small cost associated with using each message the outcome preferred by the informed player is stable the paper introduces a nonequilibrium set valued stability notion of entry resistant sets for games with partial common interest the no communication outcome is never an element of an entry resistant set journal of economic literature classification numbers c72 d82

option pricing when the variance changes randomly theory estimation and an application in this paper we examine the pricing of european call options on stocks that have vari ance rates that change randomly we study continuous time diffusion processes for the stock return and the standard deviation parameter and we find that one must use the stock and two options to form a riskless hedge the riskless hedge does not lead to a unique option pricing function because the random standard deviation is not a traded security one must appeal to an equilibrium asset pricing model to derive a unique option pricing function in general the option price depends on the risk premium associated with the random standard deviation we find that the problem can be simplified by assuming that volatility risk can be diversified away and that changes in volatility are uncorrelated with the stock return the resulting solution is an integral ofthe black scholes formula and the distribution function for the variance of the stock price we show that accurate option prices can be computed via monte carlo simulations and we apply the model to a set of actual prices

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

models of stock returns a comparison in this paper a discrete mixture of normal distributions is proposed to explain the observed significant kurtosis fat tails and significant positive skewness in the distribution of daily rates of returns for a sample of common stocks and indexes stationarity tests on the parameter estimates of this discrete mixture of normal distributions model revealed significant differences in the mean estimates that can explain the observed skewness and significant differences in the variance estimates that can explain the observed kurtosis an alternative explanation for the observed fat tails is the symmetric student model the result of a comparison between the models is that the discrete mixture of normal distributions model has substantially more descriptive validity than the student model for many years both financial economists and statisticians have been concerned with the description of stock market returns the form of the distribution of stock returns is a crucial assumption for mean variance portfolio theory theoretical models of capital asset prices and the prices of contingent claims for example understanding the behavior of the variance is essential to option pricing models empirical tests of asset pricing models and the efficient markets hypothesis draw statistical inferences that are also conditional on distributional assumptions the most convenient assumption for financial theory and empirical methods is that the distribution of security rates of return be multivariate normal with parameters that are stationary over time since the normal distribution is stable under addition any arbitrary portfolio of stocks will also be normally distributed with the additional assumption of risk aversion mean variance theory follows furthermore the assumptions of normality and parameter stationarity are required for most of the econometric techniques typically used in empirical research tests of the normality hypothesis on the daily returns of the dow jones industrial stocks by fama 121 revealed more kurtosis fatter tails than that predicted from a sample of independent and identically distributed normal variates fama concluded from this evidence that the distribution of price changes conforms better to the stable paretian distribution with characteristic exponent

approximate option valuation for arbitrary stochastic processes abstract we show how a given probability distribution can be approximated by an arbitrary distribution in terms of a series expansion involving second and higher moments this theoretical development is specialized to the problem of option valuation where the underlying security distribution if not lognormal can be approximated by a lognormally distributed random variable the resulting option price is expressed as the sum of a black scholes price plus adjustment terms which depend on the second and higher moments of the underlying security stochastic process this approach permits the impact on the option price of skewness and kurtosis of the underlying stock s distribution to be evaluated

interest rate volatility and the term structure a two factor general equilibrium model we develop a two factor general equilibrium model of the term structure the factors are the short term interest rate and the volatility of the short term interest rate we derive closed form expressions for discount bonds and study the properties of the term structure implied by the model the dependence of yields on volatility allows the model to capture many observed properties of the term structure we also derive closed form expressions for discount bond options we use hansen s generalized method of moments framework to test the cross sectional restrictions imposed by the model the tests support the two factor model there are essentially two approaches to the modeling of the term structure of interest rates in continuous time the equilibrium approach pioneered by

the term structure of volatility implied by foreign exchange options this paper illustrates regression and kalman filtering methods for estimating the time varying term structure of volatility expectations revealed by options prices short and long term expectations are estimated for four currencies using daily phlx options prices from 1985 to 1989 throughout this period there were important differences between shortand long term expectations the slope of the term structure changed frequently and there were significant variations in long term volatility expectations the expectation estimates can be used to value otc options to improve hedging strategies and to test the hypothesis that the options market overreacts

meaning and credibility in cheap talk games i define neologism proofness a refinement of perfect bayesian equilibrium in cheap talk games it applies when players have a preexisting common language so that an unexpected message s literal meaning is clear and only credibility restricts communication i show that certain implausible equilibria are not neologism proof in some games no equilibrium is journal of economic literature classification numbers d83 d82 c73

signal jamming models of fraudulent misreporting and economic prospects an experimental investigation abstract this study uses experimental methodology to examine how the frequency and magnitude with which managers commit fraud varies with economic prospects boom middle and bust the experimental design is based on signal jamming equilibrium sje models of fraud in which managers make potentially inaccurate public reports and investors bid on shares under sje managers always exaggerate reports by a fixed amount up to the maximum possible report independent of the truth shareholders can perfectly correct managers reports except for the maximum possible report in contrast the results of the experiment show four robust deviations from sje predictions 1 managers exaggerate and shareholders correct reports according to dominated mixed strategies with probabilities significantly less than one 2 managers exaggerate more frequently and by more when outcomes are poor 3 shareholders adjust low reports by less than high reports and 4 shareholders correct relatively high reports by more in booms than busts even though managers reporting strategies are invariant to economic prospects

transaction data tests of s p 100 call option pricing this paper examines the pricing of s p 100 calls using 14 months of transactions data we find that market prices of s p 100 calls differ systematically from black scholes values the biases in black scholes model prices are both statistically and economically significant and correspond to biases that arise if market prices incorporate a stochastically changing volatility of the index

the informational content of implied volatility implied volatility is widely believed to be informationally superior to historical volatility because it is the markets forecast of future volatility but for s p 100 index options the most actively traded contract in the united states we find implied volatility in aggregate and across subsamples separated by maturity and strike price implied volatility has virtually no correlation with future volatility and it does not incorporate the information contained in recent observed volatility article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

valuation of power options under heston s stochastic volatility model abstract we derive semi analytic solutions for power option prices under the heston model specifically the pricing formula is shown to be valid whenever the power of the underlying asset price has a finite moment unlike the majority of stochastic volatility models there remains a significant problem to check the existence of moments of assets prices of order higher than one fortunately the moment explosion property under the heston model is examined systematically in andersen and piterbarg 2000 incorporating with their results we present explicit formulas for moment generating function of log price and for power option prices under the circumstances when the corresponding moments are finite in case that the corresponding moment explodes we provide two numerical methods to derive prices of power put and capped power call options in spite of a simple idea numerical examples show that the approximations are extremely accurate and efficient

an examination of firms employment costs the existence of quasi fixed costs of work may affect firms desired employee hours and number of workers which has important implications for the estimation of labour supply parameters firm level data from the 1982 employment opportunity pilot project is used to estimate the importance to firms of employee quasi fixed costs related to searching hiring training and firing specifically this paper examines how these costs affect number of workers and hours per worker turnover and vacancies to the extent that the costs are determined by the firm s presumably exogenous industrial classification an attempt is made to control for biases due to employee heterogeneity as well results show that higher costs are associated with lower turnover fewer vacancies and longer hours as predicted by a model of labour demand

displaced diffusion option pricing this paper develops a new option pricing formula that pushes the underlying source of risk back to the risk of individual assets of the firm the formula simultaneously encompasses differential riskiness of the assets of the firm their relative weights in determining the value of the firm the effects of firm debt and the effects of a dividend policy with both constant and random components although this setting considerably generalizes the black scholes 1 analysis it nonetheless produces a formula via riskless arbitrage arguments that given estimated inputs is as easy to use as the black scholes formula

information time option pricing theory and empirical evidence abstract with a stochastic time change from calendar time to information time we derive a parsimonious option pricing formula with stochastic volatility as a risk neutral poisson sum of merton s 1973 prices over the option s information time maturity domain the formula contains two unobservable parameters information arrival intensity and information time asset volatility with stochastic volatility induced by random information arrival when the information arrival rate intensifies the option price increases and vice versa we test the formula in pricing hedging and excess profits capture empirically using currency and the s p 500 futures options transaction data

on jumps in common stock prices and their impact on call option pricing the black scholes call option pricing model exhibits systematic empirical biases the merton call option pricing model which explicitly admits jumps in the underlying security return process may potentially eliminate these biases we provide statistical evidence consistent with the existence of lognormally distributed jumps in a majority of the daily returns of a sample of nyse listed common stocks however we find no operationally significant differences between the black scholes and merton model prices of the call options written on the sampled common stocks

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

the stochastic volatility in mean model empirical evidence from international stock markets in this paper we present an exact maximum likelihood treatment for the estimation of a stochastic volatility in mean svm model based on monte carlo simulation methods the svm model incorporates the unobserved volatility as an explanatory variable in the mean equation the same extension is developed elsewhere for autoregressive conditional heteroscedastic arch models known as the arch in mean arch m model the estimation of arch models is relatively easy compared with that of the stochastic volatility sv model however efficient monte carlo simulation methods for sv models have been developed to overcome some of these problems the details of modifications required for estimating the volatility in mean effect are presented in this paper together with a monte carlo study to investigate the finite sample properties of the svm estimators taking these developments of estimation methods into account we regard sv and svm models as practical alternatives to their arch counterparts and therefore it is of interest to study and compare the two classes of volatility models we present an empirical study of the intertemporal relationship between stock index returns and their volatility for the united kingdom the united states and japan this phenomenon has been discussed in the financial economic literature but has proved hard to find empirically we provide evidence of a negative but weak relationship between returns and contemporaneous volatility which is indirect evidence of a positive relation between the expected components of the return and the volatility process copyright 2002 john wiley sons ltd

an experiment to evaluate bayesian learning of nash equilibrium play abstract we report on an experiment designed to evaluate the empirical implications of jordan s model of bayesian learning in games of incomplete information a finite example is constructed in which the model generates unique predictions of subjects choices in nearly all periods when the true game defined by players private information was one with a unique equilibrium in pure strategies the experimental subjects play converged to the equilibrium as jordan s theory predicts even when the subjects had not attained complete information about one another but when there were two pure strategy equilibria the theory s predictions were not consistent with observed behavior journal of economic literature classification numbers d83 c72 c92

new insights into smile mispricing and value at risk the hyperbolic model the authors investigate a new basic model for asset pricing the hyperbolic model which allows an almost perfect statistical fit of stock return data after a detailed introduction into the theory they use secondary market data to compare the hyperbolic model to the classical black scholes model the authors study implicit volatilities the smile effect and pricing performance exploiting the full power of the hyperbolic model they construct an option value process from a statistical point of view by estimating the implicit risk neutral density function from option data finally the authors present some new value at risk calculations leading to new perspectives to cope with model risk copyright 1998 by university of chicago press

stochastic volatility option pricing this paper examines alternative methods for pricing options when the underlying security volatility is stochastic we show that when there is no correlation between innovations in security price and volatility the characteristic function of the average variance of the price process plays a pivotal role it may be used to simplify fourier option pricing techniques and to implement simple power series methods we compare these methods for the alternative mean reverting stochastic volatility models introduced by stein and stein 1991 and heston 1993 we also examine the biases in the black scholes model that are eliminated by allowing for stochastic volatility and we correct some errors in the stein and stein 1991 analysis of this issue empirical evidence on underlying asset prices and on their derivatives strongly suggests that asset price volatility is stochastic the pricing of options under this condition is therefore an important problem in this paper we study alternative option pricing methods that account for stochastic volatility we are particularly concerned with power series methods which we show to be quite accurate and easy to implement for alternative volatility specifications we point out their relation with recently proposed exact methods this permits a precise assessment of the approximation involved in the simple power series approach and of the impact of stochastic volatility on option prices following garman 1976 stochastic volatility option prices must satisfy a bivariate fundamental partial differential equation pde in the two state variables security price and volatility since volatility is not spanned by assets in the econ omy the volatility risk may not be eliminated by arbitrage methods therefore its market price explicitly enters into the pde the associated risk premium is owen graduate school of management vanderbilt university nashville tn 37203 and universita di siena facolta di scienza economiche e bancarie 53100 siena italy respectively part of this research was supported from a grant from the dean s fund and the financial markets research center at the owen school of management vanderbilt university some of this research was completed while roma was visiting the anderson graduate school of management ofthe university of california at los angeles we thank participants of the finance accounting and economics workshop at the owen school of management vanderbilt university for useful comments we appreciate the suggestions of roger huang craig lewis ron masulis and walter torous we thank joanne ball for editorial

common factors and local factors implications for term structures and exchange rates this paper studies a multi factor two country term structure and exchange rate model when a diversification effect for an international bond portfolio is expected it shows that the diversification gain calls upon certain restrictions on the process of the stochastic discount factor in a factor structured economy existence of local factors is shown to be a necessary condition for the gains from investing in foreign bonds further the exchange rate risk premia are shown to be a function of the differentials of the risk premia of the factors in bond returns empirical results reveal the tendency for investors to respond sensitively to rare shocks which is shown to be a potential solution to the forward premium puzzle

option valuation and hedging strategies with jumps in the volatility of asset returns we develop a model in which the volatility of risky assets is subject to random and discontinuous shifts over time we derive prices of claims contingent on such assets and analyze options based trading strategies to hedge against the risk of jumps in the return volatility unsystematic and systematic events such as takeovers major changes in business plans or shifts in economic policy regimes may drastically alter firms risk profiles our model captures the effect of such events on options markets lumpy arrival of information has long been recognized as a phenomenon of considerable importance in financial markets following merton 1976 1 much of the literature on contingent claims valuation under discontinuous information arrival has studied the case where jumps occur in asset values in this article we model the discontinuous resolution of uncertainty in a new way we allow for the volatility of an asset s return to change randomly and discretely we then derive and analyze valuation equations for claims contingent on such an asset we also show how certain traded options together with the underlying stock and a riskless bond can be used to insure against jumps in the volatility of an asset s returns stock price movements in our model fluctuate randomly between low and high volatility regimes discontinuous changes in the volatility of stock prices may be a result of significant changes in a firm s operating and financial structure its competitive environment or its corporate plan reorganizations caused by takeovers and mergers may also occasion such volatility shifts changes in uncertainty in our model could also be systematic and a result of aggregate supply shocks or shifts in economic policies and political regimes our model can also be interpreted as a model of a market where from time to time firms face the release of an important piece of information that may affect their stock prices significantly the market participants may be aware

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

a hybrid stock trading system using genetic network programming and mean conditional value at risk abstract this paper describes a hybrid stock trading system based on genetic network programming gnp and mean conditional value at risk model gnp cvar the proposed method combining the advantages of evolutionary algorithms and statistical model has provided useful tools to construct portfolios and generate effective stock trading strategies for investors with different risk attitudes simulation results on five stock indices show that model based on gnp and maximum sharpe ratio portfolio performs the best in bull market and that based on gnp and the global minimum risk portfolio performs the best in bear market the portfolios constructed by markowitz s mean variance model performs the same as mean cvar model it is clarified that the proposed system significantly improves the function and efficiency of original gnp which can help investors make profitable decisions

the pricing of stock index options in a general equilibrium model this paper analyzes the pricing of stock index options in a simple general equilibrium model in this model the volatility of the stock index and the spot rate of interest are functions of a stochastic variable the paper investigates the biases that arise when using the black scholes model with the assumed volatility and interest rate dynamics it is shown that the model can in principle explain the biases observed in empirical work on stock index options

the risk premium of volatility implicit in currency options this article provides an empirical investigation of the risk neutral variance process and the market price of variance risk implied in the foreign currency options market there are three principal contributions first the parameters of heston s mean reverting square root stochastic volatility model are estimated using dollar mark option prices from 1987 to 1992 second it is shown that these implied parameters can be combined with historical moments of the dollar mark exchange rate to deduce an estimate of the market price of variance risk these estimates are found to be nonzero time varying and of sufficient magnitude to imply that the compensation for variance risk is a significant component of the risk premia in the currency market finally the out of sample test suggests that the historical variance and the hull and white implied variance contain no more information than that imbedded in the heston implied variance

implied volatilities and transaction costs using data that contain bid and ask quotes for both options and stocks the analysis investigates the constant volatility assumption of the black scholes model the analysis adjusts for bid ask spreads and finds evidence that is inconsistent with the constant volatility assumption instead the results reveal a strong negative correlation between volatility and stock price and they suggest that using a nonconstant volatility model such as the cev model would be more appropriate to price long term options finally transaction costs associated with the dynamic hedge tend to increase with an option s maturity but decrease as a percentage of the option s price

a theoretical comparison between integrated and realized volatility in this paper we provide both qualitative and quantitative measures of the precision of measuring integrated volatility by realized volatility for a fixed frequency of observation we start by characterizing for a general diffusion the difference between realized and integrated volatility for a given frequency of observation then we compute the mean and variance of this noise and the correlation between the noise and the integrated volatility in the eigenfunction stochastic volatility model of meddahi 2001a this model has as special cases log normal affine and garch diffusion models using previous empirical results we show that the noise is substantial compared with the unconditional mean and variance of integrated volatility even if one employs five minute returns we also propose a simple approach to capture the information about integrated volatility contained in the returns through the leverage effect we show that in practice the leverage effect does not matter copyright 2002 john wiley sons ltd

experimental evidence on the evolution of the meaning of messages in sender receiver games an experiment this paper experimentally investigates the evolution of message meanings when talk is cheap we consider communication between a privately informed sender and a receiver when the sender s message does not affect payoffs directly sender receiver games introduced by jerry green and nancy stokey 1980 and vincent p crawford and joel sobel 1982 provide the simplest stylized environment in which communication is essential communication is the only way to link the receiver s action to the sender s private information in addition sender receiver games have been widely used to study communication in accounting economics finance and political science intuition strongly suggests that effective communication will evolve when the players interests are closely aligned however there is always a nash equilibrium in which the sender randomizes uniformly across all messages such babbling equilibria are proper roger b myerson 1978 blume 1994 and even strategic stability elon kohlberg and jeanfrancois mertens 1986 does not rule out uninformative equilibria in general in response a literature developed that formulates equilibrium selection criteria by appealing to the existence of a commonly understood language matthew rabin 1990 steven a matthews et al 1991 joseph farrell 1993 that can be used to formulate credible deviations from equilibrium unfortunately the selection criteria from this literature are frequently strong enough to remove all equilibria from consideration in addition these arguments are vulnerable to stiglitz s observation in koo cho and david m kreps 1987 that successful deviations from equilibrium may induce further deviations which in turn may undermine the credibility of the original deviations both problems can be avoided by a dynamic approach as in rabin and sobel 1996 we also adopt a dynamic perspective but do not require messages to have a priori meanings instead distinct meanings may emerge endogenously this is important for communication across cultures and for language change 2 we are guided by recent results of blume department of economics university of iowa iowa city ia 52242 dejong department of accounting university of iowa iowa city ia 52242 kim department of economics sung kyun kwan university seoul 110 745 korea sprinkle department of accounting university of wisconsin madison wi 53706 we thank joyce berg vince crawford robert forsythe joel horowitz deirdre mccloskey forrest nelson larry samuelson gene savin joel sobel and especially two anonymous referees for their advice and suggestions we benefitted from comments and discussions resulting from presentations at the 1994 summer meetings of the econometric society the 1996 social learning workshop at suny stony brook the io me gt workshop at the university of iowa the university of bonn the university of bielefeld the center for economic research at tilburg university ohio state university seoul national university and texas a m university we are grateful for financial support from the college of business administration at the university of iowa the ira b mcgladrey institute and the national science foundation

small dimension pde for discrete asian options abstract this paper presents an efficient method for pricing discrete asian options in presence of smile and non proportional dividends using an homogeneity property we show how to reduce an n 0 dimensional problem to a one or two dimensional one we examine different numerical specifications of our dimension reduced pde using a crank nicholson method interpolation method grid boundaries time and space steps as well as the extension to the case of non proportional discrete dividends using a jump condition we benchmark our results with quasi monte carlo simulation and a multi dimensional pde

ict and productivity growth in the united kingdom this paper develops new estimates of investment in and output of information and communication technology ict these new estimates imply that gdp growth has been significantly understated particularly since 1994 a growth accounting approach is employed to measure the contribution of ict to the growth of both aggregate output and aggregate input on both counts the contribution of ict has been rising over time from 1989 to 1998 ict output contributed a fifth of overall gdp growth since 1989 55 per cent of capital deepening the growth of capital per hour worked has been contributed by ict capital since 1994 this proportion has risen to 90 per cent ict capital deepening accounts for 25 per cent of the growth of labour productivity over 1989 98 and 48 per cent over 1994 8 but even when output growth is adjusted for the new ict estimates both labour productivity and tfp growth are still found to slow down after 1994

an analytical approximation formula for european option pricing under a new stochastic volatility model with regime switching abstract in this paper an analytical approximation formula for pricing european options is obtained under a newly proposed hybrid model with the volatility of volatility in the heston model following a markov chain the adoption of which is motivated by the empirical evidence of the existence of regime switching in real markets we first derive the coupled pde partial differential equation system that governs the european option price which is solved with the perturbation method it should be noted that the newly derived formula is fast and easy to implement with only normal distribution function involved and numerical experiments confirm that our formula could provide quite accurate option prices especially for relatively short tenor ones finally empirical studies are carried out to show the superiority of our model based on s p 500 returns and options with the time to expiry less than one month

work sharing and overtime this paper deals with the employment effects of reduced working time when firms endogenous response of overtime is considered the analysis distinguishes between fixed and profit maximizing levels of output as well as between interior and corner solutions it is shown that under plausible assumptions a reduction in working time is quite likely to be counterproductive as an employment promoting measure i introduction a reduction in working time has been proposed as a method of increasing employment through work sharing such proposals however often seem to build on an oversimplified view of the world where little consideration is given to various possible repercussions most economists therefore seem rather sceptical towards such proposals for more or less critical discussions see e g hart sloane 1979 charpin 1984 brunstad holm 1984 calmfors 1985 hoel 1986 1987 hoel vale 1986 and dreze 1987 none of these papers however takes into account that actual working time will differ from normal working time to the extent that there is overtime work the aim of this paper is to analyse how endogenous responses of overtime may affect the outcome with respect to employment of reducing the normal working time although overtime work currently accounts for only a minor proportion of total working time around three per cent in sweden we believe this to be an important channel since a major reduction in working time will represent a nonmarginal change which is likely to produce significant changes in established practices our results add to the doubts that a reduction in working time increases employment there has been some recent work on the relationship between normal working time and overtime cf hart 1984 fitzroy hart 1985

adaptive learning models of consumer behavior abstract in a model of dynamic duopoly optimal price policies are characterized assuming consumers learn adaptively about the relative quality of the two products a contrast is made between belief based and reinforcement learning under reinforcement learning consumers can become locked into the habit of purchasing inferior goods such lock in permits the existence of multiple history dependent asymmetric steady states in which one firm dominates in contrast belief based learning rules must lead asymptotically to correct beliefs about the relative quality of the two brands and so in this case there is a unique steady state

cheap talk and the fed a theory of imprecise policy announcments this paper examines the problem faced by the federal reserve in announcing its private information about its future policies because it would like to manipulate expectations and pursue a time inconsistent policy the fed cannot reveal its policy objectives precisely and credibly it can however communicate some information about its goals through the cheap talk mechanism of vincent crawford and joel sobel making announcements that are imprecise and only giving ranges within which these goals may lie copyright 1989 by american economic association

option pricing when the variance is changing the monte carlo method is used to solve for the price of a call when the variance is changing stochastically

on the number of state variables in options pricing in this paper we investigate the methodological issue of determining the number of state variables required for options pricing after showing the inadequacy of the principal component analysis approach which is commonly used in the literature we adopt a nonparametric regression technique with nonlinear principal components extracted from the implied volatilities of various moneyness and maturities as proxies for the transformed state variables the methodology is applied to the prices of s p 500 index options from the period 1996 2005 we find that in addition to the index value itself two state variables approximated by the first two nonlinear principal components are adequate for pricing the index options and fitting the data in both time series and cross sections

learning and communication in sender receiver games an econometric investigation this paper compares the performance of stimulus response sr and belief based learning bbl using data from game theory experiments the environment extensive form games played in a population setting is novel in the empirical literature on learning in games both the sr and bbl models fit the data reasonably well in common interest games with history while the test results accept sr and reject bbl in games with no history and in all but one of the divergent interest games estimation is challenging since the likelihood function is not globally concave and the results may be subject to convergence bias

the rationality of early exercise decisions evidence from the s p 100 index options market this study provides a comprehensive empirical analysis of the early exercise bistoty of sp but we show that a substantal number of these decisions are clearly irratonal since it would bave been possible to realize a larger riskless net cash jlow by seuling unlike p us studies of early exercise our tests of efflciency and the rationat decions tbatpresumably lead to eficient markets are model independet we also provide evidence concerning the relatve significance of dividends and the wild card to index optonpricing models and introduce and document the importance of the opton to exercise and avoid the indirect costs oftbe spread we alsofind evidence of a significant day of tbe week exercise effect and present some likely explanations for that effect

stock price volatility mean reverting diffusion and noise abstract using weekly call option prices on twenty five stocks over a ten year period 1975 1985 and calls on the s p 500 stock index futures we find that ex ante market volatility follows a mixed mean reverting diffusion with noise process changes in volatility are correlated across stocks and a marketwide volatility effect is found strong forces pull the volatility back to its long term value the findings suggest the development of new option pricing models

models of labour services and estimates of total factor productivity this article examines the manner in which labour services are modelled in the aggregate production function concentrating on the relationship between numbers employed and average hours worked it argues that numbers employed and hours worked are not perfect substitutes and that conventional estimates of total factor productivity which by using total hours worked as the measure of labour services assume they are perfect substitutes will be biased when there are marked changes in average hours worked the relevance of the theoretical argument is illustrated using data for the united states and the united kingdom

labour utilization and statutory non wage costs the purpose of this paper is to develop a theoretical framework in which to analyse the effects of statutory non wage costs on labour utilization the theoretical analysis of statutory non wage costs has been hampered by the complexity of the various schemes operated by different countries most countries have a social security contribution scheme that is partly fixed with respect to labour utilization and partly variable in this paper a contribution system that incorporates some typical elements of such schemes is analysed a framework is developed that seeks to determine how variations in statutory non wage costs might alter the employer s cost minimizing combination of utilization and employment if the statutory fixed component of labour costs could be reduced then the cost of an additional hour of overtime would increase relative to the cost of an hour s work from a new employee thus shifting the optimizing combination many types of statutory non wage payments are made in different countries but the majority of these can be fitted within a framework that has three main elements a a payment that is fixed irrespective of earnings or hours of work these may be payroll taxes or redundancy payments contributions or in some cases may be negative as for example regional employment premium in the united kingdom b an element that varies with total earnings for example rates of social insurance contribution c a payment that is fixed once earnings rise above a given ceiling most social insurance schemes take this regressive form payment of national insurance in the united kingdom for example for a period

conditional volatility and the informational efficiency of the phlx currency options market abstract the relative performance of implied and historical volatility predictors is compared for four exchange rates from 1985 to 1991 for three currencies arch models estimated up to 1989 show that phlx implied volatilities provide specifications for daily conditional variances which can not be significantly improved by using past returns this result is consistent with the informational efficiency of the philadelphia currency options market out of sample forecasts of the average volatility over four week periods are evaluated for 1990 and 1991 once more the implied predictors are superior to historical predictors

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

hedging options under transaction costs and stochastic volatility in this paper we consider the problem of hedging contingent claims on a stock under transaction costs and stochastic volatility extensive research has clearly demonstrated that the volatility of most stocks is not constant over time as small changes of the volatility can have a major impact on the value of contingent claims hedging strategies should try to eliminate this volatility risk we propose a stochastic optimization model for hedging contingent claims that takes into account the effects of stochastic volatility transaction costs and trading restrictions simulation results show that our approach could improve performance considerably compared to traditional hedging strategies

option values under stochastic volatility theory and empirical estimates abstract this paper numerically solves the call option valuation problem given a fairly general continuous stochastic process for return volatility statistical estimators for volatility process parameters are derived and parameter estimates are calculated for several individual stocks and indices the resulting estimated option values do not differ dramatically from black scholes values in most cases although there is some evidence that for longer maturity index options black scholes overvalues out of the money calls in relation to in the money calls

cheap talk coordination and evolutionary stability abstract asymmetric information games where the informed player can send a costless message sender receiver games typically have equilibria where meaningful communication occurs we therefore know such cheap talk can matter still even when there is no conflict of interest there are also equilibria where no information transmission occurs this paper shows that for a class of games with perfectly coinciding interests modeled as asymmetric contests where players are unsure of which role they will have only meaningful communication is evolutionarily stable journal of economic literature classification numbers c70 c72 d82

variances of security price returns based on high low and closing prices in a recent paper garman and klass 1980 studied the problem of estimating capital asset price volatility parameters developing an idea first introduced by parkinson 1980 they argue that improved volatility measures can be obtained by taking into account the daily high low and opening prices in addition to the traditionally used closing prices this paper is concerned mainly with testing the empirical validity of different volatility estimators based on high low and closing prices

communication between rational agents abstract conventional game theoretic solution concepts never guarantee meaningful communication in cheap talk games i define a solution concept which does guarantee communication in some games i assume full rationality without imposing equilibrium conditions but add a natural behavioral assumption about how agents use language agents have a propensity to speak the truth and to believe others speak the truth but use the game s strategic incentives to check whether such behavior and beliefs are rational i also define and prove the existence of an equilibrium version of the concept and present examples where its predictions seem more natural than farrell s neologism proof equilibrium

index options the early evidence index options became the most important traded contracts during their first year of existence two contracts namely those on the s p100 and the major markets index have a trading volume which typically surpasses the trading volume in all individual stock option contracts in this paper we examine the pricing of the options on the s p100 and the major markets index using intra day prices we find the options frequently violate the arbitrage boundary put call parity and are substantially mispriced relative to theoretical values our results suggest that tests of option pricing models may be more difficult than previously realized due to nonsynchronous prices even using real time data from the exchanges

option arbitrage and strategy with large price changes abstract arbitrage pricing theorems are derived for options on stocks with jumps as a well as local movements the resulting valuation formulas depend on observable variables only closed form valuation expressions are obtained in the case of large positive and negative jumps these results translate into a simple algebra for characterizing the risk of arbitrage and investment portfolios a continuous time formulation of the infinite variance hypothesis leads to isomorphic pricing expressions

valuation of american futures options theory and empirical tests this paper reviews the theory of futures option pricing and tests the valuation principles on transaction prices from the s p 500 equity futures option market the american futures option valuation equations are shown to generate mispricing errors which are systematically related to the degree the option is in the money and to the option s time to expiration the models are also shown to generate abnormal risk adjusted rates of return after transaction costs the joint hypothesis that the american futures option pricing models are correctly specified and that the s p 500 futures option market is efficient is refuted at least for the sample period january 28 1983 through december 30 1983 futures option contracts now trade on every major futures exchange and on a wide variety of underlying futures contracts the chicago mercantile exchange the chicago board of trade the new york futures exchange and the commodity exchange now collectively have more than twenty options written on futures contracts where the underlying spot commodities are financial assets such as stock portfolios bonds notes and eurodollars foreign currencies such as west german marks swiss francs and british pounds precious metals such as gold and silver livestock commodities such as cattle and hogs and agricultural commodities such as corn and soybeans moreover new contract applications are before the commodity futures trading commission and should be actively trading in the near future with the markets for these new contingent claims becoming increasingly active it is appropriate that the fundamentals of futures option valuation be reviewed and tested black 5 provides a framework for the analysis of commodity futures options although his work is explicitly directed at pricing european options on forward contracts it applies to european futures contracts as well if the riskless rate of interest is constant during the futures option life 1 the options currently

pricing of index options when interest rates are stochastic an empirical test abstract this paper tests amin and jarrow s amin and jarrow 1992 version of merton s merton 1973 stochastic interest rate option pricing formula for stock options in their model the interest rate dynamics are given by the heath et al 1992 term structure model the empirical results using data on european stock index options from the swedish option market show that the amin and jarrow model clearly outperforms the black and scholes 1973 model furthermore the time to maturity bias found in tests of the black and scholes model disappears when the options are priced with the amin and jarrow model

total factor productivity an unobserved components approach this work examines the presence of unobserved components in the time series of total factor productivity tfp which is an idea central to modern macroeconomics the main approaches in both the study of economic growth and the study of business cycles rely on certain properties of the different components of the time series of tfp in the study of economic growth the neoclassical growth model explains growth in terms of technical progress as measured by the secular component of tfp while in the study of business cycles the real business cycle approach explains short run fluctuations in the economy as determined by temporary movements in the production function which are reflected by the cyclical component of the time series of the same variable the econometric methodology employed in the estimation of these different components is the structural time series approach developed by harvey 1989 harvey and shephard 1993 and others an application to the time series of tfp for the 1948 2002 us priva

option pricing and implicit volatilities abstract this paper demonstrates that black scholes implied volatilities can be used to value options in many situations where the assumptions of the black scholes model are violated including i alternative stock processes ii stochastic interest rates and iii market frictions given its computational simplicity this procedure provides an attractive alternative to the more complex models with a direct estimation procedure

learning mixed equilibria we study learning processes for finite strategic form games in which players use the history of past play to forecast play in the current period in a generalization of fictitious play we assume only that players asymptotically choose best responses to the historical frequencies of opponents past play this implies that if the stage game strategies converge the limit is a nash equilibrium in the basic model plays seems unlikely to converge to a mixed strategy equilibrium but such convergence is natural when the stage game is perturbed in the manner of harsanyi s purification theorem journal of economic literature classification number c72

a risk reserve model for hedging in incomplete markets abstract this paper presents a new approach to the pricing and hedging problem for contingent claims in incomplete markets we assume that traders wish to maximize the expected final payoff of the hedging portfolio and the claims and we avoid the use of utility functions instead we model how traders are punished when taking excessive risks in practice to do so we introduce an extra reserve bank account which earns a smaller rate of return than a standard deposit bank account the reserve account should always contain a minimal amount of money which depends on the risk that the trader s portfolio is exposed to we focus on a specific example which uses option price sensitivities the greeks to specify the risk the resulting optimization problem can then be solved in a rather explicit form and we show how the solution naturally leads to bid ask spreads prices which depend on the trader s current position and implied volatility smiles

nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active cboe option classes from august 23 1976 through august 31 1978

a bayesian approach to modeling stock return volatility for option valuation new measures of stock return volatility are developed to increase the precision of stock option price estimates with bayesian statistical methods volatility estimates for a given stock are developed using prior information on the cross sectional patterns in return volatil ities for groups of stocks sorted on size financial leverage and trading volume call option values computed with the bayesian procedure generally improve prediction accuracy for market prices of call options relative to those computed using implied volatility standard historical volatility or even the actual ex post volatility that occurred during each option s life although the bayesian methods produce biased call price estimators they do reduce the systematic tendency of standard pricing approaches to overprice underprice options on high low volatility stocks little bias improvement is observed with respect to the time to maturity and moneyness of the call options

the valuation of american options for a class of diffusion processes we present an integral equation approach for the valuation of american style derivatives when the underlying asset price follows a general diffusion process and the interest rate is stochastic our contribution is fourfold first we show that the exercise region is determined by a single exercise boundary under very general conditions on the interest rate and the dividend yield second based on this result we derive a recursive integral equation for the exercise boundary and provide a parametric representation of the american option price third we apply the results to models with stochastic volatility or stochastic interest rate and to american bond options in one factor models for the cases studied explicit parametric valuation formulas are obtained finally we extend results on american capped options to general diffusion prices numerical schemes based on approximations of the optimal stopping time such as approximations based on a lower bound or on a combination of lower and upper bounds are shown to be valid in this context

hedging derivative securities and incomplete markets an e arbitrage approach given a european derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based we solve the optimal replication problem find a self financing dynamic portfolio strategy involving only the underlying securities that most closely approximates the payoff function at maturity by applying stochastic dynamic programming to the minimization of a mean squared error loss function under markov state dynamics we derive recursive expressions for the optimal replication strategy that are readily implemented in practice the approximation error or e of the optimal replication strategy is also given recursively and may be used to quantify the degree of market incompleteness to investigate the practical significance of these e arbitrage strategies we consider several numerical examples including path dependent options and options on assets with stochastic volatility and jumps