microstructure noise realized variance and optimal sampling a recent and extensive literature has pioneered the summing of squared observed intra daily returns realized variance to estimate the daily integrated variance of financial asset prices a traditional object of economic interest we show that in the presence of market microstructure noise realized variance does not identify the daily integrated variance of the frictionless equilibrium price however we demonstrate that the noise induced bias at very high sampling frequencies can be appropriately traded off with the variance reduction obtained by high frequency sampling and derive a mean squared error mse optimal sampling theory for the purpose of integrated variance estimation we show how our theory naturally leads to an identification procedure which allows us to recover the moments of the unobserved noise this procedure may be useful in other applications finally using the profits obtained by option traders on the basis of alternative variance forecasts as our economic metric we find that explicit optimization of realized variance s finite sample mse properties results in accurate forecasts and considerable economic gains copyright 2008 wiley blackwell

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

estimation of an asymmetric stochastic volatility model for asset returns a stochastic volatility model may be estimated by a quasi maximum likelihood procedure by transforming to a linear state space form the method is extended to handle correlation between the two disturbances in the model and applied to data on stock returns

commonality in product design cost saving valuation change and cannibalization abstract offering a variety of products is important for a firm to attract different consumer segments however high product variety increases production and distribution costs modular product design and parts commonality are approaches used to counter this trend in cost and still offer a variety of products this paper develops a model to examine when modular products should be introduced and how much modularity to offer the model looks at a market consisting of a high segment and a low segment customers choose the product that maximizes their surplus which is defined as the product s utility minus its price presence of commonality affects the utility of a product greater commonality decreases production cost but makes the products more indistinguishable from one another this makes the product more desirable for the low segment but less desirable for the high segment the firm s objective is to design the products and set the prices so as to maximize its profit

determinacy of equilibrium in stationary economies with both finite and infinite lived consumers abstract we consider the determinacy of perfect foresight equilibrium near steady state equilibria of stationary infinite horizon economies the work of t j kehoe and d k levine econometrica 53 1985 433 453 is generalized by the inclusion of both infinite lived agents and overlapping generations of finite lived agents and the inclusion of production and non depreciating pure rents we show that indeterminacy is possible in robust examples and that the dimension of the indeterminacy can be as large as the number of goods per period we also discuss extreme cases in which determinacy is guaranteed

stochastic volatility and dsge models abstract this paper argues that a specification of stochastic volatility commonly used in dsge models may not be appropriate because the level of a process with this specification does not have any moments we suggest three ways to overcome the problem

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

least squares inference on integrated volatility and the relationship between efficient prices and noise the expected value of sums of squared intraday returns realized variance gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for joint inference on integrated variance noise moments and price noise relations in the iid noise case we derive the asymptotic variance of the and noise variance estimators and show that they are consistent the joint estimation approach is particularly attractive as it reveals important characteristics of the noise process which can be related to liquidity and market efficiency the analysis of dependence between the price and noise processes provides an often missing link to market microstructure theory we find substantial differences in the noise characteristics of trade and quote data arising from the effect of distinct market microstructure frictions this article has supplementary material online

measuring uncertainty and its impact on the economy we propose a new framework for measuring uncertainty and its effects on the economy based on a large var model with errors whose stochastic volatility is driven by two common unobservable factors representing aggregate macroeconomic and financial uncertainty the uncertainty measures can also influence the levels of the variables so that contrary to most existing measures ours reflect changes in both the conditional mean and volatility of the variables and their impact on the economy can be assessed within the same framework moreover identification of the uncertainty shocks is simplified with respect to standard var based analysis in line with the favar approach and with heteroskedasticity based identification finally the model which is also applicable in other contexts is estimated with a new bayesian algorithm which is computationally efficient and allows for jointly modeling many variables while previous var models with stochastic volatility could only handle a handful of variables empirically we apply the method to estimate uncertainty and its effects using us data finding that there is indeed substantial commonality in uncertainty sizable effects of uncertainty on key macroeconomic and financial variables with responses in line with economic theory

pricing european currency options a comparison of the modified black scholes model and a random variance model we use the modified black scholes model and a random variance option pricing model to study prices of european currency options traded in geneva the options which cannot be exercised early include calls and puts on the dollar swiss franc exchange rate in the empirical analysis we examine the model fit and the biases with respect to the strike price time to maturity and volatility there is some evidence of mispricing and there are small gains available by trading with the random variance model

a general equilibrium analysis of price controls and subsidies on food in mexico abstract in this paper we present a general equilibrium model that permits a thorough analysis of the effects of government pricing policies in particular we study the effects of price controls and subsidies on agricultural and food items in mexico we analyze alternative policies for reducing the government deficit by cutting subsidies and increasing indirect taxes our results indicate that although food subsidies need to be reduced maintaining some subsidies would have a favorable impact on income distribution

leverage effects and stochastic volatility in spot oil returns a bayesian approach with var and cvar applications abstract crude oil markets have been quite volatile and risky in the past few decades due to the large fluctuations of oil prices we contribute to the current debate by testing for the existence of the leverage effect when considering daily spot returns in the wti and brent crude oil markets and by studying the direct impact of the leverage effect on measures of risk such as var and cvar more specifically we model spot crude oil returns using stochastic volatility sv models with various distributions of the errors we find that the introduction of the leverage effect in the traditional sv model with normally distributed errors is capable of adequately estimating risk for speculative oil suppliers in both the wti and brent markets our results also show that financial regulators model choice both on the supply and on the demand side would not be affected by the introduction of leverage focusing instead on firm s internal risk management our results show that the introduction of leverage would be useful for firms who are on the demand side for oil who use var for risk management and who are particularly worried about the magnitude of the losses exceeding var while wanting to minimize the opportunity cost of capital using the same logic firms who are on the supply side would be better off not considering the leverage effect

the impact of the volatility of monetary policy shocks this paper studies the impact of the volatility of monetary policy using a structural vector auroregression svar model enriched along two dimensions first it allows for time varying variance of monetary policy shocks via a stochastic volatility specification second it allows a dynamic interaction between the level of the endogenous variables in the var and the time varying volatility the analysis establishes that the nominal interest rate output growth and inflation fall in reaction to an increase in the volatility of monetary policy the analysis also develops a dynamic stochastic general equilibrium model enriched with stochastic volatility to monetary policy that generates similar responses and provides a theoretical underpinning of these findings

a non linear filtering approach to stochastic volatility models with an application to daily stock returns this paper develops a new model for the analysis of stochastic volatility sv models since volatility is a latent variable in sv models it is difficult to evaluate the exact likelihood in this paper a non linear filter which yields the exact likelihood of sv models is employed solving a series of integrals in this filter by piecewise linear approximations with randomly chosen nodes produces the likelihood which is maximized to obtain estimates of the sv parameters a smoothing algorithm for volatility estimation is also constructed monte carlo experiments show that the method performs well with respect to both parameter estimates and volatility estimates we illustrate our model by analysing daily stock returns on the tokyo stock exchange since the method can be applied to more general models the sv model is extended so that several characteristics of daily stock returns are allowed and this more general model is also estimated copyright 1999 john wiley sons ltd

doubts and variability a robust perspective on exotic consumption series in order for consumption based asset pricing models to reconcile data on returns with that on consumption researchers have resorted to augmenting the consumption series in exotic ways when an agent s consumption series is subject to changes in volatility we show that concerns for model misspecication can induce fears of both disasters and long run risk we appeal to this pessimistic view to explain why introducing stochastic volatility in the presence of model uncertainty helps generate a more plausible unconditional market price of risk and time variation in the conditional market price of risk our analysis is based on a parameterization derived from bayesian estimation of our stochastic volatility model using us consumption data

estimation methods for stochastic volatility models a survey abstract although stochastic volatility sv models have an intuitive appeal their empirical application has been limited mainly due to difficulties involved in their estimation the main problem is that the likelihood function is hard to evaluate however recently several new estimation methods have been introduced and the literature on sv models has grown substantially in this article we review this literature we describe the main estimators of the parameters and the underlying volatilities focusing on their advantages and limitations both from the theoretical and empirical point of view we complete the survey with an application of the most important procedures to the s p 500 stock price index

market segmentation self selection and product line design the purpose of this paper is to develop a theory of market segmentation based on consumer self selection the extant theory is based on the third degree price discrimination model of pigou central assumptions of which are that the firm can directly address individual segments and isolate them by using consumer self selection i am relaxing these assumptions in the context of a monopolist designing a product line i show that this relaxation has significant implications for how the products and prices are chosen and what they look like in particular segments may be aggregated even though there are no economies of scale furthermore consumer self selection enables us to model cannibalization and competition among firms

stock prices and volume the authors undertake a comprehensive investigation of price and volume co movement using daily new york stock exchange data from 1928 to 1987 they adjust the data to take into account well known calendar effects and long run trends to describe the process they use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume four empirical regularities are found 1 positive correlation between conditional volatility and volume 2 large price movements are followed by high volume 3 conditioning on lagged volume substantially attenuates the leverage effect and 4 after conditioning on lagged volume there is a positive risk return relation article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

the time varying volatility of macroeconomic fluctuations we investigate the sources of the important shifts in the volatility of us mac roeconomic variables in the postwar period to this end we propose the esti mation of dsge models allowing for time variation in the volatility of the structural innovations we apply our estimation strategy to a large scale model of the business cycle and find that shocks specific to the equilibrium condition of investment account for most of the sharp decline in volatility of the last two decades jel c51 e32

a maximum likelihood approach for non gaussian stochastic volatility models a maximum likelihood approach for the analysis of stochastic volatility models is developed the method uses a recursive numerical integration procedure that directly calculates the marginal likelihood only conventional integration techniques are used making this approach both flexible and simple experimentation shows that the method matches the performance of the best estimation tools currently in use new stochastic volatility models are introduced and estimated the model that best fits recent stock index data is characterized by a highly non gaussian stochastic volatility innovation distribution this model dominates a model that includes an autoregressive conditional heteroscedastic effect in the stochastic volatility process and a model that includes a stochastic volatility effect in the conditional mean

modelling the dynamics of bitcoin and litecoin garch versus stochastic volatility models abstractwe examine and compare a large number of generalized autoregressive conditional heteroskedastic garch and stochastic volatility sv models using series of bitcoin and litecoin price retu

how do oil price shocks affect the output volatility of the u s energy mining industry the roles of structural oil price shocks abstract this paper focuses on how explicit structural shocks that characterize the endogenous character of international oil price change affect the output volatility of the u s crude oil and natural gas mining industries to this end we employ a modified structural vector autoregressive model svar to decompose real oil price changes into four components u s supply shocks non u s supply shocks aggregate demand shocks and oil specific demand shocks mainly driven by precautionary demand the results indicate that output volatility of the u s crude oil and natural gas mining industry has significantly negative responses to u s supply shocks aggregate demand shocks and oil specific demand shocks while lacks significant response to non u s supply shocks variance decomposition and historical decomposition confirm that u s supply shocks occupy most explaining variations in output volatility among the four structural oil shocks moreover the oil specific demand shocks explain more variation than that of aggregate demand shocks for the crude oil mining industry but the opposite is true for the natural gas mining industry

arch models properties estimation and testing abstract the aim of this survey paper is to provide an account of some of the important developments in the autoregressive conditional heteroskedasticity arch model since its inception in a seminal paper by engle 1982 this model takes account of many observed properties of asset prices and therefore various interpretations can be attributed to it we start with the basic arch models and discuss their different interpretations arch models have been generalized in different directions to accommodate more and more features of the real world we provide a comprehensive treatment of many of the extensions of the original arch model next we discuss estimation and testing for arch models and note that these models lead to some interesting and unique problems there have been numerous applications and we mention some of these as we present different models the paper includes a glossary of the acronyms for the models we describe

stock returns and volatility an empirical study of the uk stock market abstract attempts to quantify the relationship between stock returns and volatility have produced conflicting conclusions in recent u s studies our paper examines this issue in the u k context for the first time using daily weekly fortnightly and monthly returns on the financial times all share index from january 1965 to december 1989 volatility estimates are obtained from monthly sample variances and arch models expected returns are shown to have had a positive though not statistically significant relationship with expected volatility the relationship between the unexpected components of the returns and volatility series is less clear we find evidence for a negative relationship but only when volatility expectations are represented by standard deviations

inflation uncertainty and labour market conditions in the us recent inflation dynamics in the united states us questioned the role of driving forces of inflation in the long run although the us recorded one of the longest economic recovery periods and the

product development decisions a review of the literature this paper is a review of research in product development which we define as the transformation of a market opportunity into a product available for sale our review is broad encompassing work in the academic fields of marketing operations management and engineering design the value of this breadth is in conveying the shape of the entire research landscape we focus on product development projects within a single firm we also devote our attention to the development of physical goods although much of the work we describe applies to products of all kinds we look inside the black box of product development at the fundamentaldecisions that are made by intention or default in doing so we adopt the perspective of product development as a deliberate business process involving hundreds of decisions many of which can be usefully supported by knowledge and tools we contrast this approach to prior reviews of the literature which tend to examine the importance of environmental and contextual variables such as market growth rate the competitive environment or the level of top management support

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

a new approach to identifying the real effects of uncertainty shocks this article introduces the use of the sign restrictions methodology to identify uncertainty shocks we apply our methodology to a class of vector autoregression models with stochastic volatility t

were there regime switches in u s monetary policy working paper 2004 14 june 2004 abstract a multivariate model identifying monetary policy and allowing for simultaneity and regime switching in coefficients and variances is confronted with u s data since 1959 the best fit is with a model that allows time variation in structural disturbance variances only among models that also allow for changes in equation coefficients the best fit is for a model that allows coefficients to change only in the monetary policy rule that model allows switching among three main regimes and one rarely and briefly occurring regime the three main regimes correspond roughly to periods when most observers believe that monetary policy actually differed and the differences in policy behavior are substantively interesting though statistically ill determined the estimates imply monetary targeting was central in the early 80s but was also important sporadically in the 70s the changes in regime were essential neither to the rise in inflation in the 70s nor to its decline in the 80s jel classification e52 e47 c53 key words counterfactuals lucas critique policy rule monetary targeting simultaneity volatility model comparison i the debate over monetary policy change in an influential paper clarida gali and gertler 2000 cgg presented evidence that us monetary policy changed between the 1970 s and the 1980 s indeed that in the 70 s it was drastically worse they found that the policy rule apparently followed in the 70 s was one that when embedded in most stochastic general equilibrium models would imply non uniqueness of the equilibrium and hence vulnerability of the economy to sunspot fluctuations of arbitrarily large size their estimated policy rule for the later period on the other hand eliminated this indeterminacy these results are a possible explanation of the volatile and rising inflation of the 70 s and of its subsequent decline the cgg analysis has two important weaknesses one is that it fails to account for stochastic volatility us macroeconomic variables and particularly the federal funds rate have gone through periods of tranquility and of agitation with forecast error variances varying greatly from period to period ignoring such variation does not lead to inconsistent estimates of model parameters when the forecasting equations themselves are constant but it strongly biases toward a finding of changed parameters tests of the stability of the forecasting equations the other weakness is that the cgg analysis rests on powerful and implausible identifying assumptions they require that we accept that the response of the monetary authority to expected future inflation and output does not depend on the recent history of inflation money growth or output it is hard to understand why this should be so especially in the 70 s when monetarism was a prominent theme in policy debates congress was requiring reports from the fed of projected time paths of monetary aggregates and financial markets were reacting sensitively to weekly money supply numbers the requirement for existence and uniqueness of equilibrium in dynamic models is that the monetary policy rule show a more than unit response of interest rates to the sum of the logs of all nominal variables that appear on the right hand side of the reaction function if we force a particular measure of expected future inflation to proxy for all the nominal variables that actually appear independently in the reaction function we are bound to get distorted conclusions on the one hand because expected future inflation will be a noisy measure of the full set of nominal influences on policy we might get downward bias in our estimates from the usual errorsin variables effect on the other hand to the extent that expected future inflation like most expected future values shows less variation than current nominal variables we could find a mistaken scaling up of coefficients

designing a family of development intensive products faced with fragmented markets saturated and demanding customers and global competition firms increasingly must design and offer a line of innovative quality differentiated products to target customers with differing willingness to pay wtp in this context designing a special class of products that we term development intensive products dips for which the fixed costs of development far outweigh the unit variable costspresents some unique managerial challenges examples of such development intensive offerings abound in a number of industries including the pharmaceutical information and entertainment sectors of the economy our contributions in this paper are threefold a to show that managerial insights from the traditional approach to product line design developed for unit variable cost intensive products do not carry over to dips b to present new mechanisms and managerial guidelines for designing a family of products for which development costs cannot be ignored and c to illustrate the insights with an extended industry example we find that the design approach based on degrading or subtracting value from a high end product to obtain a subsumed low end edition shown in the literature to be an effective approach for designing unit cost intensive products can be inappropriate for dips this limitation of value subtraction has implications for the number of variants and the sequence in which they are developed as an alternative to a subsumed product design strategy we propose and examine the overlapped product design approach in which a low end product is not completely subsumed within its high end counterpart but differentiated on additional vertical quality dimensions our results both explain the recent challenges of firms with subsumed low end products and guide them in designing a product line to successfully address emerging low end market segments

commonality decisions when designing for multiple markets abstract it is well established that a manufacturer s commonality decisions between related products are driven by trade offs between cost savings from standardization and demand effects of customization prior research has examined these trade offs in the context of product line design for a single geography where cannibalization is a primary concern however the insights from a single market may not readily apply when serving related products for different geographies where cannibalization ceases to be a concern the downside of commonality for geographically separated markets arises from a mismatch in customer preferences which results in disutilities in this paper we model the trade off between the consumer side disutilities and the cost side scale economies in the presence of demand uncertainty and derive the optimal extent of commonality between products for both the markets in the context of two product development strategies i primary market centric design pmd and ii design for multiple markets dfm our insights from analytical and numerical analysis show that when consumers are very picky and market uncertainty is low the dfm strategy outperforms the pmd strategy counter to the practice of introducing primary market centric products into emerging markets our study demonstrates the need for more customization especially in small but uncertain markets our research has important implications for automakers in integrating the diversity in tastes while making commonality decisions for multiple markets

the stochastic volatility in mean model with time varying parameters an application to inflation modeling this article generalizes the popular stochastic volatility in mean model to allow for time varying parameters in the conditional mean the estimation of this extension is nontrival since the volatility appears in both the conditional mean and the conditional variance and its coefficient in the former is time varying we develop an efficient markov chain monte carlo algorithm based on band and sparse matrix algorithms instead of the kalman filter to estimate this more general variant the methodology is illustrated with an application that involves u s u k and germany inflation the estimation results show substantial time variation in the coefficient associated with the volatility highlighting the empirical relevance of the proposed extension moreover in a pseudo out of sample forecasting exercise the proposed variant also forecasts better than various standard benchmarks

assortment planning and inventory decisions under a locational choice model we consider a single period assortment planning and inventory management problem for a retailer using a locational choice model to represent consumer demand we first determine the optimal variety product location and inventory decisions under static substitution and show that the optimal assortment consists of products equally spaced out such that there is no substitution among them regardless of the distribution of consumer preferences the optimal solution can be such that some customers prefer not to buy any product in the assortment and such that the most popular product is not offered we then obtain bounds on profit when customers dynamically substitute using the static substitution for the lower bound and a retailer controlled substitution for the upper bound we thus define two heuristics to solve the problem under dynamic substitution and numerically evaluate their performance this analysis shows the value of modeling dynamic substitution and identifies conditions in which the static substitution solution serves as a good approximation