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

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

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

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

cereals demand in the sahel and potential impacts of regional cereals protection abstract recent policy debate in the sahel has focused on a regional protection zone for cereals this paper discusses crosscountry evidence of consumption patterns and the sensitivity of these to policy variables and considers potential income distribution and efficiency impacts of a rice tariff increase a tariff would hurt the poor in the short term because the poor depend to a large extent on rice as a fast food purchased from street vendors the trend toward rice consumption is a long term structural phenomenon linked to urbanization rather than to short term price changes maize and millet sorghum are substitutes in consumption which should serve to encourage development of maize in the guinean zone to help assure sahel food security in drought years

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

jump risks and the intertemporal capital asset pricing model the specification of the stochastic process for stock prices is an important assumption underlying most equilibrium and option pricing models in modern finance this is particularly true of the continuous time capital asset pricing models where it is assumed that asset prices follow diffusion processes with continuous sample paths see merton 1973a breeden 1979 grossman and shiller 1982 the extent to which the implications of these models generalize to discontinuous sample paths is an unanswered question in theoretical finance however the answer to this question is of more than just theoretical interest since accumulated empirical evidence appears to be inconsistent with the continuous sample path assumption see rosenberg 1972 oldfield rogalski and jarrow 1977 rosenfeld 1982 one purpose of this paper is to provide some answers to this question we do this by extending merton s 1973a intertemporal asset pricing model in the special case of a constant investment opportunity set to include discontinuous sample paths for asset prices the constant investment opportunity set assumption is imposed because we are interested in obtaining sufficient conditions under which an instantaneous capital asset pricing model capm results the extension of our model to a stochastic opportunity set is discussed briefly in the text this paper investigates an economy where stock prices follow a jump diffusion process the first part of the analysis derives a sufficient condition under which an instantaneous capm will characterize equilibrium expected returns the sufficient condition is that the jump component of a stock s return must be unsystematic and diversifiable in the market portfolio the second part of the paper is an empirical investigation of the satisfaction of this condition the evidence is seen to be inconsistent with the satisfaction of this hypothesis that is the market portfolio appears to contain a jump component

option prices as predictors of equilibrium stock prices the black scholes option pricing model modified for dividend payments is used to calculate jointly implied stock prices and implied standard deviations a comparison of the implied stock prices with observed stock prices reveals that the implied prices contain information regarding equilibrium stock prices that is not fully reflected in observed stock prices the implications of this finding are discussed this study investigates the role of call option prices as predictors of the equilibrium prices of their underlying stocks using the black scholes 3 bs model previous tests of the bs model have shown that the formula is highly successful in explaining the observed market prices of options see black and scholes 2 galai 8 chiras and manaster 6 and macbeth and merville 12 according to the model the option price is a function of the current value of the underlying stock the instantaneous variance of the stock s rate of return the time to maturity of the option the risk free rate of interest and the exercise price of the option 1 given an observed option price and known values of all input parameters to the bs model except the stock price one can determine the price of the underlying stock that equates the observed option price to its calculated value it follows from the underlying logic of the model that the implied price is the value of the underlying stock for which a continuously revised option bond portfolio would be a perfect substitute for the stock hence if options are actually priced according to the model implied stock prices will be the option market s assessment of equilibrium stock values previous empirical studies have assumed that observed stock prices are the relevant stock prices for option valuation however just as stock prices may differ in the short run from one exchange to another i e nyse midwest

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

arbitrage continuous trading and margin requirements this paper studies the impact that margin requirements have on both the existence of arbitrage opportunities and the valuation of call options in the context of the blackscholes economy margin restrictions are shown to exclude continuous trading arbitrage opportunities and with two additional hypotheses still to allow the black scholes call model to apply the black scholes economy consists of a continuously traded stock with a price process that follows a geometric brownian motion and a continuously traded bond with a price process that is deterministic continuous trading security market models constitute a significant area of continuing reesearch in financial economics these models form the basis of the option pricing methodology see merton 16 for a review and current intertemporal asset pricing models see merton 15 breeden 3 and cox ingersoll and ross 5 given the importance of these models it is of no surprise that there has been significant academic concern see dybvig 9 cox ingersoll and ross 4 p 341 and ingersoll 13 pp 13 25 over the discovery of a continuous trading strategy by harrison and kreps 10 called the doubling strategy that generates a sure dollar from a zero investment the existence of this doubling strategy violates a basic premise of the option pricing methodology the premise of no arbitrage opportunities given this violation the question naturally arises as to whether the option pricing methodology is internally consistent fortunately harrison and pliska 11 showed that the exclusion of arbitrage opportunities and the doubling strategy does not invalidate the familiar derivation of the black scholes call option formula the exogenous exclusion of these doubling strategies is somewhat arbitrary however types of constraints that exclude continuous trading arbitrage opportunities were studied by kreps 14 harrison and kreps 10 and dybvig 9 these papers provide constraints that are unsatisfactory from an institutional point of view since they have no market analogue margin requirements on the other hand have a market analogue one purpose of this paper is to show that margin requirements also exclude continuous trading arbitrage opportunities to make this argument self contained we first provide a unified framework that synthesizes the previously stated results our assertion concerning margin re

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

prices and health identifying the effects of nutrition exercise and medication choices on blood pressure biomedical studies suggest that a person s behavior matters to health but these studies usually treat human choice as exogenous this study shows that individual choices on nutrient intake exercise and use of medication are influenced by exogenous food prices wages and non labor income using these exogenous variables as instruments for endogenous behavior makes a big difference in the estimated impact of nutrient intake exercise and medication on blood pressure for example application of instrumental variables methods changes the impact of sodium on blood pressure from positive to negative and significant in his 1993 nobel prize speech economic historian robert fogel documented how dramatic improvements in human health and lifespan over the last century have increased labor productivity and economic growth these health improvements were largely ascribed to better nutrition and to an enhanced ability of consumers to transform nutrition information into desired health states at the same time fogel called for joint use of biomedical and economic techniques of analysis so that the consequences of better nutrition for human well being can be more deeply probed the combined techniques would yield insights otherwise unobtainable when relying on one of the disciplines alone fogel s plea for combined techniques rarely has been heeded either in the biomedicine or in the health economics literature biomedical studies adhere strictly to a mind body dualism

using option prices to estimate realignment probabilities in the european monetary system the case of sterling mark abstract this paper describes a procedure for estimating the market s perceived probability distribution of future exchange rates from the prices of risk reversals strangles and other currency options and uses the procedure to estimate the risk neutral ex ante probability of a realignment of the pound sterling the procedure for estimating the realignment probabilities relies on the jump diffusion model of exchange rate behavior and the resulting option pricing formula by fitting this model to market option price data i retrieve the unobserved parameters of the jump diffusion process i then use these parameter estimates to estimate the ex ante probability distribution of exchange rates and thus the realignment probabilities

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 measuring the risk of common stocks implied by options prices a note this paper examines the implied standard deviation isd estimated from transactons data on options using the black scholes pricing model it was found that the distribution of the isd is symmetric though not normal also the isd based on the last daily observation deviates significantly from the daily average isd it is suggested that the daily average is a more reliable estimate of the standard deviation

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

tests of two models for valuing call options on stocks with dividends roll has recently formulated an option pricing model which allows dividend payments on the underlying stock this paper compares the performance of the exact roll model with a modified but inexact black scholes model the results indicate that the roll model prices are significantly closer to actual market prices

substitution between goods and leisure in a developing country the paper explores the substitutability between goods female leisure and male leisure we find that goods and leisure are not separable we then adapt the almost ideal demand system aids to include leisure in the system in the same manner as commodities the model is not sensitive to variations in the assumption of total time available for each individual s work and leisure results from sri lanka indicate the marginal propensity to consume leisure is quite high especially in rural areas this finding has important implications for transfer programs designed to raise food consumption a somewhat surprising complementarity between male and female leisure was also observed a number of goods were found to be complements to both male and female leisure

the maximum likelihood estimation of security price volatility theory evidence and application to option pricing the market requires efficient estimation of the assuming security price dynamics are governed by a diffusion process and given the publicly most available form of data this paper provides the maximum likelihood estimator of security price volatility a monte carlo simulation compares the small sample properties of this and other proposed security price volatility estimators the resultant maximum likelihood estimator of the black scholes call option price formulation is also derived for small sample sizes a monte carlo simulation study facilitates comparison with other proposed estimation procedures also the statistically most powerful confidence intervals for the blackscholes call option price are constructed we would like to thank the participants of the statistics department seminar and finance department workshop at the university of michigan for their helpful comments we are especially grateful to fred hoppe adrian tschoegl and an anonymous referee for their insightful suggestions any remaining errors are our responsibility

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

nutrient demand and the allocation of time evidence from guam this paper presents an econometric study of nutrient intake in guam which explicitly accounts for household time allocation and household capital variables the empirical framework is based on a household production model of nutrient consumption food expenditure and the allocation of time between labour leisure and food preparation activities the study finds evidence that 1 capital and wage variables have significant impacts on households nutrient demands 2 income wage and educational status have very different effects on the nutrient choices of low calorie households than on the nutrient choices of high calorie households and 3 a family s participation in the food stamp programme leads to higher levels of food expenditure but this impact is attributable to the purchase of more costly taste characteristics in food rather than to the purchase of more nutritious foods

the effect of the value of time on food consumption patterns in developing countries evidence from sri lanka this study shows that the opportunity cost of women s time can affect household food consumption patterns in developing countries demand equations for rice bread and the ratio of bread to total cereal consumption are estimated for urban sri lankan households the demand specification which is based on the new household economics includes as explanatory variables the woman s estimated market wage and the household s full income and alternatively observed income wages are estimated using the heckman procedure to correct for sample selection bias

comparative performance of the black scholes and roll geske whaley option pricing models the original black scholes bs 2 european call option pricing model does not take account of divided payments on the underlying stock and does not allow for the possibility of early exercise that may be optimal when the stock pays dividends black 1 has suggested that the original bs model can be modified to take account of dividends and sharpe 14 predicts that this modified or pseudo american bs approach while not exact is probably sufficient for many listed options

a simple approach to interest rate option pricing a simple introduction to contingent claim valuation of risky assets in a discrete time stochastic interest rate economy is provided taking the term structure of interest rates as exogenous closed form solutions are derived for european options written on 1 treasury bills 2 interest rate forward contracts 3 interest rate futures contracts 4 treasury bonds 5 interest rate caps 6 stock options 7 equity forward contracts 8 equity futures contracts 9 eurodollar liabilities and 10 foreign exchange contracts article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

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

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

the calculation of implied variances from the black scholes model a note black and scholes 2 have derived a model for the equilibrium price of a european stock purchase option according to the black and scholes model equilibrium option prices are a function of the time to maturity of the option the exercise price the current price of the underlying stock the risk free rate of interest and the instantaneous variance of the stock s rate of return of these five variables only the first four can be directly observed the instantaneous variance of the stock s return can only be estimated recently severdl authors 3 4 5 6 10 11 rather than estimating a variance from past data have attempted to employ the black scholes option pricing formula to derive an implied variance an implied variance is the value of the instantaneous variance of the stock s return which when employed in the blackscholes formula results in a model price equal to the market price u nfortunately the implied variance cannot be calculated explicitly and previous researchers have used numerical methods such as the newton raphson method and its variants 8 however for many options no values of implied variance could be found to justify the observed option prices in this note necessary and sufficient conditions for the existence of a positive implied variance are given an algorithm is presented which converges monotonically and quadratically to the unique implied variance when it exists the most valuable feature of this algorithm is that it provides a starting value for the first iteration of the newton raphson procedure if one applies the newton raphson procedure without the correct starting value solutions that do exist can be overlooked the option pricing formula of black and scholes is

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

the valuation of american call options and the expected ex dividend stock price decline abstract this study focuses on the ex dividend stock price decline implicit within the valuation of american call options on dividend paying stocks the roll 1977 american call option pricing formula and the observed structure of cboe call option transaction prices are used to infer the expected ex dividend stock price decline as a proportion of the amount of the dividend the relative decline is shown to be not meaningfully different from one confirming some recent evidence from studies which examined stock prices in the days surrounding ex dividend

further results on the constant elasticity of variance call option pricing model the black scholes 4 call option model is a member of the class of constant elasticity of variance call option models proposed by cox 6 while the black scholes model assumes that the volatility or instantaneous variance of return is constant through time the other members of the class allow the volatility to change with the stock price this property is of interest because empirical evidence suggests that returns to common stock are heteroscedastic and also that volatilities implied from the black scholes model and market prices of call options are not constant

the relationship between arbitrage and first order stochastic dominance this paper joins together two fields of research in financial economics the first field studies stochastic dominance while the second field studies arbitrage pricing the two fields are linked together through the derivation and the proof of a characterization theorem the characterization theorem gives necessary and sufficient conditions for the existence of arbitrage opportunities in terms of the existence of two assets one of which first order stochastically dominates the other and the price of a particular contingent claim examples are provided to demonstrate the theorem s content this paper joins together two fields of research in financial economics the first field studies portfolio choice from the perspective of stochastic dominance see hadar and russell 5 6 hanoch and levy 7 levy and kroll 13 the second field studies arbitrage pricing its characterization and implications see ross 15 kreps 12 harrison and kreps 8 harrison and pliska 9 in these fields it is well known that the existence of arbitrage opportunities implies first order stochastic dominance and that the converse does not hold this paper provides a set of conditions under which the converse is true given complete markets the existence of an arbitrage opportunity is characterized in terms of the existence of two traded assets one of which stochastically dominates the other along with one additional condition the additional condition is roughly that state contingent prices must be zero over the states where the first asset dominates the second the theorem has a qualification however it is applicable only in markets which are complete not in the arrow debreu sense but in a weaker sense in the sense that all contingent claims on the primary assets must trade in many applications especially with respect to continuous trading models this condition is usually satisfied see duffie 2 and harrison and pliska 9 in the case of stochastically dominated assets this paper shows that the relationship of the assets to the state contingent prices is important in identifying arbitrage opportunities in this sense this paper is related to a recent paper of jagannathan 10 jagannathan studies the relationship of second order stochastic dominance not first order to call option valuation this characterization theorem relating arbitrage opportunities to stochastic dominance should provide a valuable tool in the area of stochastic dominance this theorem specifies conditions under which two assets can be compared using first order stochastic dominance on an individual basis for inclusion in the

primes and scores an essay on market imperfections this paper investigates the reported relative mispricing of primes and scores to the underlying stock given transaction costs we establish arbitrage based bounds on prime and score prices we then develop a new nonparametric statistical technique to test whether prime and score prices violate these bounds we find that prime and score prices do exceed stock prices and often by a considerable amount we demonstrate that this increased value is most likely due to the score s ability to save on the costs of dynamic hedging we also show how short sale and trust size constraints impede the ability to arbitrage price disparities in an efficient market the price of a security reflects the value of its underlying assets it should not be possible therefore to create value simply by splitting a security into different parts since the underlying assets are unchanged the packaging of the cash flows should not matter the recent introduction of primes and scores suggests that this is not always the case by separating a security s cash flows into a dividend based component the prime and an appreciation or option based component the score developers of these securities have seemingly created two assets whose value separately exceeds that of the original stock since the prime and the score are based on the same underlying asset this raises a puzzling question about the actual efficiency of securities markets this paper investigates this anomaly by examining whether primies and scores are actuauy mispriced and if so why given the costs of transacting in the prime score and stock we establish bounds on prime and score prices that are consistent with no arbitrage opportunities we then develop a new nonparametric statistical technique to test whether prime and score prices violate these bounds this nonparametric procedure is designed both to confront the measurement error problems plaguing the literature i e nonobservable bid ask prices and nonsimultaneous prices see phillips and smith 1980 bhattacharya 1983 and bookstaber 1981 and to avoid the estimation of round trip transaction costs commissions we find the surprising result that prime and score prices exceed the price of the underlying stock often by a considerable amount using time series data we de monstrate that significant price differentials exist for each firm in our sample

options taxes and ex dividend day behavior a novel way of estimating the expected as opposed to the actual share price fall off is developed using option prices this method is applied to the uk traded options market using data from 1979 to 1984 the results show that a the average expected fall off implicit in option prices is around 55 to 60 of the dividend and significantly different from it the fall off also varied inversely with the dividend yield which is consistent with the prediction of the tax clientele hypothesis b the estimates of the expected fall off were not significantly different from the actual fall off c finally the results imply that the usual assumption made in valuing options on dividend paying stocks that the fall off is equal to the dividend would lead to downward biased estimates of the option value

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

gender and poverty issues and policies with special reference to asian developing countries abstract recent years saw the outpouring of a theoretical and empirical literature exploring the nexus between gender and poverty in developing countries this paper which provides a critical review of the literature examines the conceptual basis for a gender focused approach to poverty alleviation reviews the relevant empirical studies and data drawn principally but not exclusively from asian developing countries and explores the role of public policies to redress gender disparity the present review argues that the conceptual basis for many gender focused policies is far from well established the empirical foundations of many conventional wisdoms as well as of popular policies remain fragile due to the dearth of reliable gender segregated data and rigorous empirical studies the paper underscores the need for more careful empirical analyses as an input to formulating sound public policy with regard to gender and poverty

the effects of data collection methods on calorie expenditure elasticity estimates a study from the dominican republic abstract using data from a nationally representative household survey in the dominican republic we find that the estimates of calorie expenditure elasticity vary widely depending upon the form of calorie variable used estimated elasticity is lower for calories purchased than for calories prepared for consumption in the home the divergence between the estimates increases at higher income levels there is a downward bias in the estimates obtained from purchase data due to some missing information on infrequent bulk purchases and greater memory lapse in recalling purchases we conclude that surveys undertaken to estimate calorie income elasticity should measure calories from consumption data if purchase data are used the period of recall should be flexible and defined by the respondent for each commodity so that infrequent purchases are captured survey methods should be standardized if elasticity estimates are to be compared across populations

fixed income linked life insurance policies with minimum guarantees pricing models and numerical results abstract we propose a pricing model for life insurance policies in which the benefits are linked to the performance of a portfolio of interest rate sensitive assets reference fund and a minimum guarantee provision is present the model is cast in the celebrated term structure framework developed by cox ingersoll and ross 1985 as for the behaviour of the investment component we analyse two polar cases in the first one the payments due on the reference fund when the contract is still alive are not reinvested while in the second case we propose a reinvestment policy we show how to obtain a closed form solution for the single premium in the no reinvestment case and how to implement a simulation approach to calculate numerically the single premium in the reinvestment case we illustrate our analysis with numerical results that help in understanding the comparative static properties of the models proposed

testing among models of intrahousehold resource allocation households are the locus for much economic decision making households function as producers investors in human and physical capital managers of risk and as consumers many resources are allocated within households and the effects of many policies depend on the dynamics of household decision making for example household decisions about allocating food among individual household members may determine who benefits from programs to improve health nutrition or welfare in many microeconomic studies the household is treated as an individual for analytical purposes in other words it is assumed that a household acts as a single entity with a single set of preferences recently however a number of economists have recognized that households are sites of conflict as well as cooperation and have begun to use new classes of models to explain how resources are allocated among household members this literature has especially improved our understanding of households in which income is not completely pooled in such a setting standard household models may offer misleading conclusions about the effects of policies on individual household members i this paper goes beyond recent surveys of intrahousehold issue by explicitly examining the assumptions predictions and empirical implications of different intrahousehold models in particular it analyzes empirical tests that distinguish among competing models by clarifying the similarities and differences among alternative models this paper also clarifies what has actually been demonstrated and what has not been demonstrated by previous empirical studies in so doing the paper points to specific topics in need of further research this paper is organized as follows section 2 analyzes the assumptions and predictions of each of the five main classes of intrahousehold resource allocation models section 3 describes empirical tests of these assumptions along with an analysis of empirical work that has been generated sections 4 and 5 discuss the questions that remain unanswered and directions for future research

labor force participation and earnings determinants for women in the special conditions of developing countries abstract little systematic analysis exists regarding hypothesized special labor market conditions for women in developing countries this study explores such conditions in nicaragua major results are i small children affect participation less than in developed countries due to child care from extended families or while on informal sector jobs and the necessity for poor mothers to work ii schooling and experience have major roles affecting work sector and earnings but the primary school return is half that cited by the world bank iii other human capital variables particularly nutrition have some impact

westernization of asian diets and the transformation of food systems implications for research and policy abstract rapid economic and income growth urbanization and globalization are leading to a dramatic shift of asian diets away from staples and increasingly towards livestock and dairy products vegetables and fruit and fats and oils while the diversification of diets away from the traditional dominance of rice with rising incomes is expected and observed current food consumption patterns are showing signs of convergence towards a western diet the diet transition is characterized by increased consumption of wheat temperate fruit and vegetables and high protein and energy dense food globalization and the consequent global interconnectedness of the urban middle class is the driving force behind the convergence of diets the rapid spread of global supermarket chains and fast food restaurants is reinforcing the above trends the growing demand for diet diversity cannot be met solely by the traditional food supply chain it requires the modernisation of the food retail sector and the vertical integration of the food supply chain in effect linking the consumers plate to the farmers plow as a consequence asian agriculture is on an irreversible path leading away from its traditional pre occupation with cereal crop production especially rice towards a production system that is becoming increasingly commercialized and diversified this paper describes the determinants and trends in the diversification and westernization of asian diets implications of the evolving demand trends for food supply and retail systems are presented the paper discusses the prospects for small farmer participation in the emerging food supply system with a particular emphasis on asian rice production systems finally the paper considers emerging challenges for food policy small holder welfare and agricultural research and development priorities

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

some urban facts of life implications for research and policy abstract this review of recent literature explores the challenges to urban food and nutrition security in the rapidly urbanizing developing world the premise of the manuscript is that the causes of malnutrition and food insecurity in urban and rural areas are different due primarily to a number of phenomena that are unique to or exacerbated by urban living these areas include a a greater dependence on cash income b weaker informal safety nets c greater labor force participation of women and its consequences for child care d lifestyle changes particularly diet and exercise patterns e greater availability of public services but questionable access by the poor f greater exposure to environmental contamination and g governance by a new possibly nonexistent set of property rights the main focus is on identifying what is different about urban areas so as to better frame the program and policy responses

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

option pricing and replication with transactions costs transactions costs invalidate the black scholes arbitrage argument for option pricing since continuous revision implies infinite trading discrete revision using black scholes deltas generates errors which are correlated with the market and do not approach zero with more frequent revision when transactions costs are included this paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision hedging errors are uncorrelated with the market and approach zero with more frequent revision the technique permits calculation of the transactions costs of option replication and provides bounds on option prices

why governments should invest more to educate girls abstract women and men often receive the same percentage increase in their wage rates with advances in schooling because these returns decline with more schooling the marginal returns for women will tend to exceed those for men especially in countries where women are much less educated the health and schooling of children are more closely related to their mother s education than father s more educated women work more hours in the market labor force broadening the tax base and thereby potentially reducing tax distortions these three conditions it is argued justify the disproportionate allocation of public expenditures toward women s education

an exact bond option formula this paper derives a closed form solution for european options on pure discount bonds assuming a mean reverting gaussian interest rate model as in vasicek 8 the formula is extended to european options on discount bond portfolios

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

the mobilization of women s labor for cash crop production a game theoretic approach in the last decade or so economists have modeled phenomena such as household labor supply fertility behavior and child survival rates using the household as the unit of analysis this paper presents data that call into question the assumption that the household is a joint decision making unit which maximizes a neoclassical household utility function the data come from a study of the mobilization of women s labor by their husbands for irrigated rice production in north cameroon the first section of this paper describes briefly the massa rice and sorghum farming system and then considers the relationship between the amount of compensation women receive from their husbands for their labor on rice production and the amount of labor they allocate to rice production the findings suggest that a bargaining model may describe the intrahousehold relations of production and distribution better than the neoclassical model the second section specifies a nash bargaining model and contrasts it with the neoclassical model of the household using the bargaining framework the third section explores in more detail possible explanations of the allocative inefficiency which seems to characterize many of the rice cultivating households

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

household behaviour and nutrition in developing countries abstract this article reviews some of the recent major research findings concerning the effect of household behaviour on food consumption and nutrition important extensions to the understanding of household behaviour have been made in the areas of the impact of income and price changes agricultural households the effects of agricultural commercialization the new household economics and particularly the effect of time as a scarce economic resource the intrahousehold allocation of food and the determinants of nutritional status this knowledge is important because the response by households affects the final impact of economic changes and government actions on the nutritional status of the population

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

on valuing american call options with the black scholes european formula empirical papers on option pricing have uncovered systematic differences between market prices and values produced by the black scholes european formula such biases have been found related to the exercise price the time to maturity and the variance we argue here that the american option variant of the black scholes formula has the potential to explain the first two biases and may partly explain the third it can also be used to understand the empirical finding that the striking price bias reverses itself in different sample periods the expected form of the striking price bias is explained in detail and is shown to be closely related to past empirical findings the black scholes european option pricing model tends to exhibit systematic empirical biases when used to value american call options the reported biases

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

general equilibrium pricing of options on the market portfolio with discontinuous returns when the price process for a long lived asset is of a mixed jump diffusion type pricing of options on that asset by arbitrage is not possible if trading is allowed only in the underlaying asset and a risk less bond using a general equilibrium framework we derive and analyze option prices when the underlying asset is the market portfolio with discontinuous returns the premium for the risk of jumps and the diffusion risks forms a significant part of the prices of the options in this economy an attempted replication of call and put options by the black scholes type of trading strategies may require substantial infusion of funds when jumps occur we study the cost and risk implications of such dynamic hedging plans article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

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

standard deviations implied in option prices as predictors of future stock price variability abstract standard deviations implied in option prices have recently been introduced as being better than average predictors of future stock price variability this article specifically studies the predictive ability of implicit standard deviations taking into account the dividend problem and the problem of optimal weighting schemes of the standard deviations when there are several options on the same stock transaction data information was used to study the importance of non simultaneities in observing stock and option prices

modelling implied volatility with ols and panel data models abstract the paper performs an empirical estimation of time varying volatility using ols regression error components and dummy variable models by regressing the implied volatility on time to maturity the strike price and a dummy both the daily ols equations and the panel data model provide more accurate estimates of black and scholes option prices than the bench mark standard deviation of log returns ft se 100 index european options are used for empirical analysis

wife s employment food expenditures and apparent nutrient intake evidence from canada the increase in women working outside the home has had important economic effects one effect involves food expenditures both in terms of patterns of eating out and the types of foods prepared in the home with consequent effects on nutrient availability this study examines the effect of wife s employment on an extensive set of variables describing food behavior the variables include the share of food in total expenditure the share of food away from home fafh in the food budget price paid per calorie and the per capita availability of twelve nutrients the results are of potential interest for food policy for nutrition education and for programs which aim to affect the nutrient composition of food eaten outside the home restaurant food fast food school meals etc in ad

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

valuation of american call options on dividend paying stocks empirical tests abstract this paper examines the pricing performance of the valuation equation for american call options on stocks with known dividends and compares it with two suggested approximation methods the approximation obtained by substituting the stock price net of the present value of the escrowed dividends into the black scholes model is shown to induce spurious correlation between prediction error and 1 the standard deviation of stock return 2 the degree to which the option is in the money or out of the money 3 the probability of early exercise 4 the time to expiration of the option and 5 the dividend yield of the stock a new method of examining option market efficiency is developed and tested

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