a multiobjective approach to vendor selection abstract purchases from vendors involve significant costs for many firms decisions related to these purchases include the selection of vendors and the determination of order quantities to be placed with the selected vendors such decisions are frequently multiobjective in nature that is they are evaluated by more than one criterion at least 23 criteria for various vendor selection problems have been identified in this article we present a multiobjective approach to systematically analyze the inherent tradeoffs involved in multicriteria vendor selection problems the approach is motivated by and demonstrated with an actual purchasing problem facing a division of a fortune 500 company

digital contracts simple tools for pricing complex derivatives this article presents a simple unified approach for valuing a variety of financial assets using digital contracts three types of digitals are used a digital option paying either one dollar or nothing a digital share paying nothing or converting into one share of the underlying asset and a first touch digital paying one dollar the first time that the price of the underlying stock moves into some specified region it is shown how the values of these three types of digitals can be determined for a wide variety of payoff events and how they can be combined to price complex contracts copyright 2000 by university of chicago press

a simplified jump process for common stock returns the specification of a statistical distribution which accurately models the behavior of stock returns continues to be a salient issue in financial economics with the introduction of arithmetic and geometric brownian motion models much attention has recently focused on a poisson mixture of distributions as an appropriate specification of stock returns for example see 12 3 8 10 5 and 1 consistent with empirical evidence these models yield leptokurtic security return distributions and furthermore the specification has much economic intuition in particular one may always decompose the total change in stock price into normal and abnormal components the normal change may be due to variation in capitalization rates a temporary imbalance between supply and demand or the receipt of any other information which causes marginal price changes this component is modelled as a lognormal diffusion process the abnormal change is due to the receipt of any information which causes a more than marginal change in the price of the stock and is usually modeled as a poisson process

variance risk premium dynamics the role of jumps using high frequency stock market data and synthetic variance swap rates this paper identifles and investigates the temporal variation in the market variance risk premium the variance risk is manifest in two salient features of flnancial returns stochastic volatility and jumps the pricing of these two separate components is analyzed in a general semiparametric framework the key empirical results imply that investors fears of future jumps are especially sensitive to recent jump activity and that their willingness to pay for protection against jumps increase signiflcantly immediately after the occurrence of jumps this in turn suggests that time varying risk aversion as previously documented in the literature is primarily driven by large or extreme market moves the dynamics of risk neutral jump intensity extracted from deep out of the money put options conflrms these flndings jel c51 c52 g12 g13

learning and time varying macroeconomic volatility abstract this paper presents a dsge model in which agents learning about the economy can endogenously generate time varying macroeconomic volatility economic agents use simple models to form expectations and need to learn the relevant parameters their gain coefficient is endogenous and is adjusted according to past forecast errors the model is estimated using likelihood based bayesian methods the endogenous gain is jointly estimated with the structural parameters of the system the estimation results show that private agents appear to have often switched to constant gain learning with a high constant gain during most of the 1970s and until the early 1980s while reverting to a decreasing gain later on as a result the model can generate a pattern of volatility which is increasing in the 1970s and falling in the second half of the sample with a decline that can roughly match the magnitude of the so called great moderation in the 1984 2007 period the paper also documents how a failure to incorporate learning into the estimation may lead econometricians to spuriously find time varying volatility in the exogenous shocks even when these have constant variance by construction

digital contracts and price manipulation corporate insiders holding derivative contracts on their firm s stock have an incentive to engage in stock price manipulation i examine several derivative contracts susceptible to manipulation and the price impact of the insiders strategic behavior digital contracts the basic building blocks for valuing complex financial derivatives are vulnerable to manipulation the impact of the strategies from holding digital contracts is consistent with an implied volatility skew and volatility clustering even seemingly innocuous derivatives such as ordinary bull spreads generate these manipulation incentives this has strong implications for corporate policy since firms often use option spreads in their stock repurchase programs

cautious risk takers investor preferences and demand for active management actively managed mutual funds have distinct return distributions from their passive benchmarks and our theoretical analysis using tail sensitive risk preferences suggests that active value and growth funds may serve to reduce downside risk and capture upside potential respectively furthermore tail sensitivity measures estimated from the empirical pricing kernel have significant explanatory power for active fund flows even after controlling for business cycles and market wide sentiment finally active funds unlike their passive counterparts have exposures to option strategies hedging downside risk or capturing upside potential

static hedging of exotic options this paper develops static hedges for several exotic options using standard options the method relies on a relationship between european puts and calls with different strike prices the analysis allows for constant volatility or for volatility smiles or frowns

the skew risk premium in the equity index market we develop a new method for measuring moment risk premiums we find that the skew premium accounts for over 40 of the slope in the implied volatility curve in the s p 500 market skew risk is tightly related to variance risk in the sense that strategies designed to capture the one and hedge out exposure to the other earn an insignificant risk premium this provides a new testable restriction for asset pricing models trying to capture in particular disaster risk premiums we base our results on a general trading strategy by replicating contracts that swap implied for realized conditional asset moments

recovering probability distributions from option prices this article derives underlying asset risk neutral probability distributions of european options on the s p 500 index nonparametric methods are used to choose probabilities that minimize an objective function subject to requiring that the probabilities are consistent with observed option and underlying asset prices alternative optimization specifications produce approximately the same implied distributions a new and fast optimization technique for estimating probability distributions based on maximizing the smoothness of the resulting distribution is proposed since the crash the risk neutral probability of a three four standard deviation decline in the index about 36 percent 46 percent over a year is about 10 100 times more likely than under the assumption of lognormality recently the increasing popularity of derivatives and some highly publicized failures to control risk have led to increased efforts to find reasonable methods to measure the sensitivity of large institutional derivatives portfolios to extreme events merely because such events are rare is not sufficient to ignore them since on the few occasions when they do occur significant amounts of money can change hands potentially wiping out profits accumulated over long prior periods a key assumption behind methods of estimation is the joint probability distribution of constituent underlying asset returns this has long been a concern of financial economists since probability assumptions are critical to much of their research during the last quarter century heretofore probability distributions of stock market returns have typically been estimated from historical time series unfortunately common hypotheses may not capture the probability of extreme events and the events of interest are rare or may not be present in the historical record even though they are clearly possible

the subjective and objective evaluation of incentive stock options owners of incentive options invariably hold undiversified portfolios this paper derives a model for the subjective and objective values of such options the subjective value the value to the holder is less than the market value because the option is held in an undiversified portfolio and because it is exercised suboptimally from the market perspective the objective value is the cost to the firm of issuing the option and lies between the market and subjective values this value recognizes the suboptimal exercise but not the undiversified discount the model which is the black scholes model with modified parameters is simple to use

the non optimality of proposed monetary policy rules under timeless perspective commitment abstract in a near canonical forward looking model the timeless perspective form of commitment typically provides outcomes that are on average superior to those resulting from discretion the specific condition that appears in the literature is however not optimal from the relevant perspective

a model of credit risk optimal policies and asset prices this article studies an economy with borrowers firms or individuals under costly default borrowers defaulting under adverse economic conditions may despite incurring default costs emerge as wealthier than nonborrowers asset substitution is generally not pronounced although a larger risk exposure by borrowers may also occur and then binary options emerge as useful credit derivatives the asset value dynamics are endogenously determined and shown to exhibit stochastic mean and volatility in contrast to many credit risk models in equilibrium the market level is increased decreased in economic downturns upturns by the presence of credit risk

option pricing with discrete time jump processes in this paper we propose new option pricing models based on class of models with jumps contained in the levy type based models nig levy schoutens 2003 merton jump merton 1976 and duan based model duan et al 2007 by combining these different classes of models with several volatility dynamics of the garch type we aim at taking into account the dynamics of financial returns in a realistic way the associated risk neutral dynamics of the time series models is obtained through two different specifications for the pricing kernel we provide a characterization of the change in the probability measure using the esscher transform and the minimal entropy martingale measure we finally assess empirically the performance of this modelling approach using a dataset of european options based on the s p 500 and on the cac 40 indices our results show that models involving jumps and a time varying volatility provide realistic pricing and hedging results for options with different kinds of time to maturities and moneyness these results are supportive of the idea that a realistic time series model can provide realistic option prices making the approach developed here interesting to price options when option markets are illiquid or when such markets simply do not exist

mean variance theory in complete markets two paradigms in the pricing of risky assets are the complete markets model of arrow and debreu and mean variance pricing as embodied in the capital asset pricing model capm the former is primarily of theoretical interest in fact prior to the recent work of banz and miller 1978 and breeden and litzenberger 1978 there was little thought or hope of practical applications on the other hand the hegemony of the capm is due mostly to its apparent ease of applicability and to a lesser extent its empirical justification in a competitive market with no taxes transactions costs or institutional constraints on portfolio holdings the allocation of the available assets will be pareto optimal the end of period distribution of wealth or the consumption goods however will typically be pareto optimal only when there is available an arrow debreu security for each contingency since by definition a pareto superior reallocation is weakly preferred by all investors a complete set of arrow debreu markets should naturally arise provided they are not too costly to establish the complete markets model of arrow and debreu and the meanvariance capital asset pricing model capm are two paradigms of risky asset markets this paper provides an integration of these two theories we prove that the standard meanvariance separation theorem obtains in a complete market only if all investors have quadratic utility in addition the familiar capm pricing relation can hold for all assets in a complete market only if arbitrage opportunities exist on the positive side we show that the validity of this relation for the primary assets in a complete market is unaffected by the distribution of returns on the created financial assets

the role of the variance premium in jump garch option pricing models abstract we develop a discrete time option pricing model incorporating a variance dependent pricing kernel of christoffersen et al 2013 under an economic framework allowing for dynamic volatility and jump intensity based on the model we examine the role of the variance premium and jump risk premium in explaining s p 500 index option prices and returns according to the results the variance premium is equally important as the jump risk premium in explaining the empirical option data whereas the incorporation of the jump risk premium improves the model fit on option prices the incorporation of the variance premium improves the fit on option returns in particular the variance premium can explain both 1 month holding period returns of 2 month maturity straddles which are significantly negative and call returns which decrease according to moneyness the model incorporating the jump risk premium only has a limitation in explaining the above two stylized returns the outperformance of the model incorporating the variance premium on option returns stems from its ability to capture the wedge between physical and risk neutral volatilities

an evaluation of vendor selection models from a total cost of ownership perspective abstract many different vendor selection models have been published in the purchasing literature however there has been no systematic approach to compare the relative efficiency of the systems in this paper we propose to use the concept of total cost of ownership as a basis for comparing vendor selection models we illustrate the comparison with a real life data set of the purchasing problem of ball bearings at cockerill sambre a belgian multinational company in the steel industry from a total cost of ownership perspective mathematical programming models outperform rating models and multiple item models generate better results than single item models for this specific case study

optimal pricing and inventory strategies with multiple price markdowns over time abstract we study a multiple period discount problem for products that undergo several price cuts over time in the high technology sector electronic component suppliers are often able to offer pre announced price cuts to buyers due to technological innovation that allows them to produce existing components at lower costs in this context suppliers are primarily concerned with the optimal pricing decisions for the components over their life spans in order to achieve the highest possible revenues accordingly the buying firms i e manufacturers or retailers also need to identify the corresponding optimal retail prices and order quantity for the finished products that utilize the components for which discounts are offered frequently in this research we develop a multiple period price discount model that addresses this issue extant research in the price discount literature focuses on supply chains pricing and inventory decisions in the presence of a single price discount the proposed model in contrast offers a systematic decision tool for identifying the optimal strategies throughout a product s life span our results show that a decentralized supply chain characterized by multi period discounts over a product s life typically achieves 75 percent supply chain efficiency we undertake a series of numerical experiments based on the model and discuss their managerial implications

a theory of volatility spreads this study formalizes the departure between risk neutral and physical index return volatilities termed volatility spreads theoretically the departure between risk neutral and physical index volatility is connected to the higher order physical return moments and the parameters of the pricing kernel process this theory predicts positive volatility spreads when investors are risk averse and when the physical index distribution is negatively skewed and leptokurtic our empirical evidence is supportive of the theoretical implications of risk aversion exposure to tail events and fatter left tails of the physical index distribution in markets where volatility is traded

the concave cost supply problem abstract this paper is divided in two parts in the first part we consider the case where several providers feed a single manufacturing unit periodically in order to satisfy a given demand the cost incurred when a provider feeds the manufacturing unit is a concave function of the quantity delivered furthermore each provider either delivers a quantity that lies between a minimum and maximum value or do not deliver anything we are introducing some properties of an optimal solution and derive a heuristic algorithm from these properties a numerical example illustrates this approach in the second part of the paper we consider the case where several providers feed periodically several manufacturing units in order to satisfy given demands a heuristic algorithm is proposed the results provided by this algorithm are compared with the optimal solution in the case when the costs are linear for a strictly positive quantity and equal to zero otherwise

generalized risk premia abstract this paper develops an optimal trading strategy explicitly linked to an agent s preferences and assessment of the distribution of asset returns the price of this strategy is a portfolio of implied moments and its expected excess returns naturally accommodate compensation for higher order moment risk variance risk and the equity premium approximate it to first order and it nests cross sectional asset pricing models such as the linear capital asset pricing model capm an empirical study in the us index market compares the investment behavior of an agent with recursive long run risk preferences to one who merely uses an identically independently distributed time series model and takes market prices as given the two agents exhibit very similar behavior during crises and can be distinguished mostly during calm periods

who buys and who sells options the role of options in an economy with background risk abstract in this paper we derive an equilibrium in which some investors buy call put options on the market portfolio while others sell them since investors are assumed to have similar risk averse preferences the demand for these contracts is not explained by differences in the shape of utility functions rather it is the degree to which agents face other non hedgeable background risks that determines their risk taking behavior in the model we show that investors with low or no background risk have a concave sharing rule i e they sell options on the market portfolio whereas investors with high background risk have a convex sharing rule and buy these options journal of economic literature classification numbers d52 d81 g11 g13

the value of interest rate stabilization policies when agents are learning we examine the expectational stability e stability of rational expectations equilibrium under optimal interest rate rules in the context of the standard new keynesian model of the monetary transmission mechanism we focus on the case where the monetary authority adds interest rate stabilization to its other objectives of inflation and output stabilization we consider both the case where the monetary authority lacks a commitment technology and as well as the case of full commitment we show that for both cases optimal interest rate rules yield rational expectations equilibria that are e stable for a wide range of empirically plausible parameter values this finding stands in contrast to the findings of evans and honkapohja 2002 2003ab for optimal monetary policy rules in environments where interest rate stabilization is not part of the central bank s objective function

a simple formula for the expected rate of return of an option over a finite holding period under conditions consistent with the black scholes formula a simple formula is developed for the expected rate of return of an option over a finite holding period possibly less than the time to expiration of the option under these conditions surprisingly the expected future value of a european option even prior to expiration is shown equal to the current black scholes value of the option except that the expected future value of the stock at the end of the holding period replaces the current stock price in the black scholes formula and the future value of a riskless invesment of the striking price replaces the striking price an extension of this result is used to approximate moments of the distribution of returns from an option portfolio

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

changes of numeraire for pricing futures forwards and options a change of numeraire argument is used to derive a general option parity or equivalence result relating american call and put prices and to obtain new expressions for futures and forward prices the general parity result unifies and extends a number of existing results the new futures and forward pricing formulas are often simpler to compute in multifactor models than existing alternatives we also extend previous work by deriving a general formula relating exchange options to ordinary call options a number of applications to diffusion models including stochastic volatility stochastic interest rate and stochastic dividend rate models and jump diffusion models are examined a self financing portfolio is called a numeraire if security prices measured in units of this portfolio admit an equivalent martingale measure the most commonly used numeraire is the reinvested short rate process the corresponding equivalent martingale measure is the risk neutral measure geman el karoui and rochet 1995 show that other numeraires can simplify many asset pricing problems in this article we build on their results and using the reinvested asset price as the numeraire unify and extend the literature on option parity or equivalence results relating american call and put prices for asset and futures options the same numeraire change is used to obtain new pricing formulas for futures and forwards that are often simpler to compute in multifactor models finally we use a numeraire change to simplify exchange option pricing extending a similar result in geman el karoui and rochet to dividend paying assets the change of numeraire method is most intuitive in the context of foreign currency derivative securities as discussed by grabbe 1983 an american call option to buy 1 dm with dollar price process s for k dollars is equivalent to an american put option to sell k dollars with dm price process k s for a strike price of 1 dm the dollar price of the call must therefore equal the product of the current exchange rate s0 and the dm price of the put the call price is computed using the dollar value of a u s i am grateful to kerry back the editor and costis skiadas for their many helpful suggestions thanks also to peter demarzo matt jackson naveen khanna david marshall robert mcdonald jim moser phyllis payette and an anonymous referee for their comments this article subsumes schroder 1992

diversification under supply uncertainty supply chain management is becoming an increasingly important issue especially when in most industries the cost of materials purchased comprises 40 60 of the total sales revenue despite the benefits cited for single sourcing in the popular literature there is enough evidence of industries having two three sources for most parts in this paper we address the operational issue of quantity allocation between two uncertain suppliers and its effects on the inventory policies of the buyer based on the type of delivery contract a buyer has with the suppliers we suggest three models for the supply process model i is a one delivery contract with all of the order quantity delivered either in the current period with probability or in the next period with probability 1 model ii is also a one delivery contract with a random fraction of the order quantity delivered in the current period the portion of the order quantity not delivered is cancelled model iii is similar to model ii with the remaining quantity delivered in the next period we derive the optimal ordering policies that minimize the total ordering holding and penalty costs with backlogging we show that the optimal ordering policy in period n for each of these models is as follows for x a n order nothing for vi n x a n use only one supplier and for x vi n order from both suppliers for the limiting case in the single period version of model i we derive conditions under which one would continue ordering from one or the other or both suppliers for model ii we give sufficient conditions for not using the second more expensive supplier when the demand and yield distributions have some special form for the single period version of models ii and iii with equal marginal ordering costs we show that the optimal order quantities follow a ratio rule when demand is exponential and yields are either normal or gamma distributed

learning about monetary policy rules abstract we study macroeconomic systems with forward looking private sector agents and a monetary authority that is trying to control the economy through the use of a linear policy feedback rule we use stability under recursive learning a la evans and honkapohja learning and expectations in macroeconomics princeton university press princeton new jersey 2001 as a criterion for evaluating monetary policy rules in this context we find that considering learning can alter the evaluation of alternative policy rules

the price of a smile hedging and spanning in option markets the volatility smile changed drastically around the crash of 1987 and new option pricing models have been proposed to accommodate that change deterministic volatility models allow for more flexible volatility surfaces but refrain from introducing additional risk factors thus options are still redundant securities alternatively stochastic models introduce additional risk factors and options are then needed for spanning of the pricing kernel we develop a statistical test based on this difference in spanning using daily s p 500 index options data from 1986 95 our tests suggest that both in and out of the money options are needed for spanning the findings are inconsistent with deterministic volatility models but are consistent with stochastic models that incorporate additional priced risk factors such as stochastic volatility interest rates or jumps article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

note an acquisition policy for a single item multi supplier system in this paper we consider the problem of developing an acquisition policy specifically given a set of potential qualified suppliers from whom should the firm buy the product in what quantities and how often we provide properties of the optimal solution and relate them to the approach of using a single source as advocated by jit the solution procedure provides the periodic order quantity from each supplier the order size and the firm cycle time as well as how many times per cycle we should order from each supplier we show that the maximum error of our solution can be made as small as desired

a nonlinear factor analysis of s p 500 index option returns growing evidence suggests that extraordinary average returns may be obtained by trading equity index options and that at least part of this abnormal performance is attributable to volatility and jump risk premia this paper asks whether such priced risk factors are alone sufficient to explain these average returns to provide an answer in as general as possible a setting i estimate a flexible class of nonlinear models using all s p 500 index futures options traded between 1986 and 2000 the results show that priced factors contribute to these expected returns but are insufficient to explain their magnitudes particularly for short term out of the money puts in a recent paper c oval and shumway 2001 examine the returns on deltahedged option positions focusing on the at the money straddle and find average returns close to minus 3 per week since over short time horizons these positions are approximately invariant to movements in the underlying index coval and shumway argue that their capm betas should be near zero and their expected returns close to the risk free rate they conclude that large deviations from the capm are the norm which they suggest is evidence that some other systematic factor such as stochastic volatility might be priced by the market similar conclusions are made by jackwerth 2000 who finds risk adjusted profitability from selling puts and by bakshi and kapadia 2003 who find that the volatility risk premium contributes significantly to higher prices for calls and puts buraschi and jackwerth 2001 concur suggesting that more than one priced risk factor is necessary to explain option prices a less direct set of evidence is the now standard observation that the black scholes implied volatilities of equity index options are upward biased predictors of future realized volatility numerous studies such as fleming ostdiek and whaley 1995 and christensen and prabhala 1998 document that implied volatilities of short term at the money equity index options are on average several percentage points higher than the volatilities realized over the option s

cumulative prospect theory option returns and the variance premium the variance premium and the pricing of out of the money otm equity index options are major challenges to standard asset pricing models we develop a tractable equilibrium model with cumulative prospect theory cpt preferences that can overcome both challenges the key insight is that the variance premium can be written as the expected return on a portfolio of otm call and put options and the probability weighting feature of cpt can explain the puzzlingly low returns observed for these options using gmm on a sample of u s index option returns between 1996 and 2010 we show that the cpt model ts well observed option prices and therefore the variance premium in a dynamic setting probability weighting and time varying equity return volatility combine to match the observed time series pattern of the variance premium

diversification under yield randomness in inventory models abstract in this paper we consider the case of random yield and diversification in two different inventory models it is assumed that two sources suppliers exist who ship an amount which is a random function of the amount requisitioned since they may charge different prices and their reliability in terms of the variance of the yield random variable may be different diversification may be more desirable than using a single supplier we analyze this problem for both the eoq model and the newsboy model analytic results for the optimal order quantities and the minimum cost are obtained for the eoq model convexity of the objective function is also discussed we develop the necessary conditions for the newsboy model and propose an approximate solution technique the concavity of the expected profit function is shown numerical examples are provided for both models

escaping nash inflation an ordinary differential equation ode gives the mean dynamics that govern the convergence to self confirming equilibria of self referential systems under discounted least squares learning another ode governs escape dynamics that recurrently propel away from a self confirming equilibrium in a model with a unique self confirming equilibrium the escape dynamics make the government discover too strong a version of the natural rate hypothesis the escape route dynamics cause recurrent outcomes close to the ramsey commitment inflation rate in a model with an adaptive government

the crash of ʼ87 was it expected the evidence from options markets transactions prices of s p 500 futures options over 1985 1987 are examined for evidence of expectations prior to october 1987 of an impending stock market crash first it is shown that out of the money puts became unusually expensive during the year preceding the crash second a model is derived for pricing american options on jump diffusion processes with systematic jump risk the jump diffusion parameters implicit in options prices indicate that a crash was expected and that implicit distributions were negatively skewed during october 1986 to august 1987 both approaches indicate no strong crash fears during the 2 months immediately preceding the crash attempts to explain what caused the stock market crashes around the world in october 1987 have suffered from the paucity of major economic developments occurring around that time that could have triggered the crashes shifting expectations regarding monetary policy foreign investors fears of a dollar decline increasing riskiness of assets none of these appeared major enough if present at all to explain the magnitude of the crashes and although portfolio insurance strategies could conceivably magnify the effects of a jump in fundamentals the initiating jump in fundamentals appears to be lacking

an exact algorithm for the capacitated total quantity discount problem in this paper we analyze the procurement problem of a company that needs to purchase a number of products from a set of suppliers to satisfy demand the suppliers offer total quantity discounts and the company aims at selecting a set of suppliers so to satisfy product demand at minimum purchasing cost the problem known as total quantity discount problem tqdp is strongly np hard we study different families of valid inequalities and provide a branch and cut approach to solve the capacitated variant of the problem capacitated tqdp where the quantity available for a product from a supplier is limited a hybrid algorithm called help heuristic enhancement from lp is used to provide an initial feasible solution to the exact approach help exploits information provided by the continuous relaxation problem to construct neighborhoods optimally searched through the solution of mixed integer subproblems a streamlined version of the proposed exact method can optimally solve in a reasonable amount of time instances with up to 100 suppliers and 500 products and largely outperforms an existing approach available in the literature and cplex 12 2 that frequently runs out of memory before completing the search

robust stability of monetary policy rules under adaptive learning recent research has explored how minor changes in expectation formation can change the stability properties of a model duffy and xiao 2007 evans and honkapohja 2009 this article builds on this research by examining an economy subject to a variety of monetary policy rules under an endogenous learning algorithm proposed by marcet and nicolini 2003 the results indicate that operational versions of optimal discretionary rules are not robustly stable as in evans and honkapohja 2009 in addition commitment rules are not robust to minor changes in expectational structure and parameter values

an empirical test of pricing kernel monotonicity summary a large class of asset pricing models predicts that securities which have high payoffs when market returns are low tend to be more valuable than those with high payoffs when market returns are high more generally we expect the projection of the stochastic discount factor on the market portfolio that is the discounted pricing kernel evaluated at the market portfolio to be a monotonically decreasing function of the market portfolio numerous recent empirical studies appear to contradict this prediction the non monotonicity of empirical pricing kernel estimates has become known as the pricing kernel puzzle in this paper we propose and apply a formal statistical test of pricing kernel monotonicity we apply the test using 17 years of data from the market for european put and call options written on the s p 500 index statistically significant violations of pricing kernel monotonicity occur in a substantial proportion of months suggesting that observed non monotonicities are unlikely to be the product of statistical noise copyright 2014 john wiley sons ltd

a recovery that we can trust deducing and testing the restrictions of the recovery theorem how reliable is the recovery theorem of ross 2015 we explore this question in the context of options on the 30 year treasury bond futures allowing us to deduce restrictions that link the physical and risk neutral return distributions our empirical results undermine the implications of the recovery theorem first we reject an implicit assumption of the recovery theorem that the martingale component of the stochastic discount factor is identical to unity second we consider the restrictions between the physical and risk neutral return moments when the recovery theorem holds and reject them in both forecasting regressions and generalized method of moments estimations received november 7 2016 editorial decision july 24 2017 by editor stijn van nieuwerburgh authors have furnished an internet appendix which is available on the oxford university press web site next to the link to the final published paper online

understanding index option returns this paper studies the returns from investing in index options previous research documents significant average option returns large capm alphas and high sharpe ratios and concludes that put options are mispriced we propose an alternative approach to evaluate the significance of option returns and obtain different conclusions instead of using these statistical metrics we compare historical option returns to those generated by commonly used option pricing models we find that the most puzzling finding in the existing literature the large returns to writing out of themoney puts is not even inconsistent with the black scholes model moreover simple stochastic volatility models with no risk premia generate put returns across all strikes that are not inconsistent with the observed data at the money straddle returns are more challenging to understand and we find that these returns are not inconsistent with explanations such as jump risk premia peso problems and estimation risk

optimal procurement strategies for online spot markets abstract spot markets have emerged for a broad range of commodities and companies have started to use them in addition to their traditional long term procurement contracts forward contracts in comparison to forward contracts spot markets offer products at essentially negligible lead time but typically command a higher expected price for this added flexibility while also exhibiting substantial price uncertainty in our research we analyze the resulting procurement challenge and quantify the benefits of using spot markets from a supply chain perspective we develop and solve mathematical models that determine the optimal order quantity to purchase via forward contracts and the optimal quantity to purchase via spot markets we analyze the most general situation where commodities can be both bought and sold via a spot market and derive closed form results for this case we compare the obtained results to the reference scenario of pure contract sourcing and we include results for situations where the use of spot markets is restricted to either buying or selling only our approaches can be used by decision makers to determine optimal procurement strategies based on key parameters such as demand and spot price volatilities correlation between demand and spot prices and risk aversion the results of our analysis demonstrate that significant profit improvements can be achieved if a moderate fraction of the commodity demand is procured via spot markets the results also show that companies who use spot markets can offer a higher expected service level but that they might experience a higher variability in profits than companies who do not use spot markets we illustrate our analytical results with numerical examples throughout the paper

option prices implied price processes and stochastic volatility this paper characterizes all continuous price processes that are consistent with current option prices this extends derman and kani 1994 dupire 1994 1997 and rubinstein 1994 who only consider processes with deterministic volatility our characterization implies a volatility forecast that does not require a specific model only current option prices we show how arbitrary volatility processes can be adjusted to fit current option prices exactly just as interest rate processes can be adjusted to fit bond prices exactly the procedure works with many volatility models is fast to calibrate and can price exotic options efficiently using familiar lattice techniques

the fine structure of asset returns an empirical investigation we investigate the importance of diffusion and jumps in a new model for asset returns in contrast to standard models we allow for jump components displaying finite or infinite activity and variation empirical investigations of time series indicate that index dynamics are devoid of a diffusion component which may be present in the dynamics of individual stocks this leads to the conjecture confirmed on options data that the risk neutral process should be free of a diffusion component we conclude that the statistical and risk neutral processes for equity prices are pure jump processes of infinite activity and finite variation

soft dollars and the brokerage industry large investors frequently receive some type of research service in retumr for sending an equity trade to a specific brokerage firm the commissions so directed are associated with the term soft dollars a survey of institutional managers and analysis of their trading records reveal something about the effects of soft dollars on the structure of the brokerage industry the use of soft dollars has had significant effects on order flows to diferent types of brokers

a theory of the nominal term structure of interest rates a model of the nominal term structure of interest rates is developed that has a positive and stationary process for the interest rate and delivers closed form expressions for the prices of discount bonds and european options on bonds unlike the one state variable version of the cox ingersoll and ross 1985 model this model even in its one state variable version allows the term premium to change sign as a function of the state and the term to maturity and also allows for shapes of the yield curve that are observed in the u s data but that are disallowed in the cox ingersoll and ross model article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

shared resource capacity expansion decisions for multiple products with quantity discounts abstract when multiple products compete for the same storage space their optimal individual lot sizes may need to be reduced to accommodate the storage needs of other products this challenge is exacerbated with the presence of quantity discounts which tend to entice larger lot sizes under such circumstances firms may wish to consider storage capacity expansion as an option to take full advantage of quantity discounts this paper aims to simultaneously determine the optimal storage capacity level along with individual lot sizes for multiple products being offered quantity discounts either all units discounts incremental discounts or a mixture of both by utilizing lagrangian techniques along with a piecewise linear approximation for capacity cost our algorithms can generate precise solutions regardless of the functional form of capacity cost i e concave or convex the algorithms can incorporate simultaneous lot sizing decisions for thousands of products in a reasonable solution time we utilize numerical examples and sensitivity analysis to understand the key factors that influence the capacity expansion decision and the performance of the algorithms the primary characteristic that influences the capacity expansion decision is the size of the quantity discount offered but variability in demand and capacity per unit influence the expansion decision as well furthermore we discover that all units quantity discounts are more likely to lead to capacity expansion compared to incremental quantity discounts our analysis illuminates the potential for significant savings available to companies willing to explore the option of increasing storage capacity to take advantage of quantity discount offerings for their purchased products

intertemporal asset pricing with heterogeneous beliefs abstract we examine the behaviour of the interest rate asset prices and asset holdings in an economy with heterogeneous rationally updated beliefs about the expected rate of production growth the equilibrium interest rate is a weighted average of the interest rates that would prevail in economies populated by homogeneous agents with the beliefs of the respective agents in the heterogeneous model the weights are given by the fractions of total wealth held financial innovation affects the dynamics of allocations and prices but preserves the aggregate output process and the structure of equilibrium asset prices also display the wealth weighted average characterization journal of economic literature classification numbers c60 d52 d91 g12

interest rate control and nonconvergence to rational expectations this paper investigates the feasibility of a monetary policy aimed at pegging the nominal rate of interest it shows that under general conditions such a policy would produce the well known cumulative process despite the fact that there exists a well behaved rational expectations equilibrium with no tendency for inflation to accelerate or decelerate the cumulative process shows up as the failure of learning to converge to rational expectations specifically the paper shows first in a conventional is lm model with an expectations augmented phillips curve and then in a micro based finance constraint model that if people follow any learning rule based on experience that satisfies a weak condition then the sequence of temporary equilibria under a policy of interest pegging cannot converge the nonconvergent path that will be observed accords with the familiar cumulative process in that inflation accelerates if the market rate of interest has been pegged below the natural rate

equilibrium analysis of portfolio insurance a martingale approach is used to characterize general equilibrium in the presence of portfolio insurance insurers sell to noninsurers in bad states and general equilibrium requires that the risk premium rises to induce noninsurers to increase their holdings we show that portfolio insurance increases price volatility causes mean reversion in asset returns raises the sharpe ratio and volatility in bad states and causes volatility to be correlated with volume we also explain why out of the money sp that is the demand for an absolute level of price protection is equivalent to a demand for put options 1 we show that a similar argument can be used in a

why do option returns change sign from day to night abstract average delta hedged returns for standard poor s 500 index options are large 0 7 per day when we decompose these option returns into intraday and overnight components average close to open returns are 1 per day and open to close returns are positive 0 3 a similar return pattern holds for all maturity and moneyness categories and equity options these positive intraday returns are particularly difficult to explain however our results are consistent with option prices failing to account for the well known fact that stock volatility is substantially higher intraday than overnight these findings help explain price formation in the options market

functional ross recovery theoretical results and empirical tests abstract recently ross 2015 showed that the real world probability distribution of a discrete markovian state variable can be recovered from observed option prices the so called recovery theorem follows from perron frobenius matrix theory when the pricing kernel is transition independent in this paper we generalize the recovery theorem to continuous state spaces using perron frobenius operator theory building on our theoretical results we devise a nonparametric approach to empirically estimate the recovered pricing kernel and probability density in closed form using s p 500 index options we analyze recovered pricing kernels empirically and find evidence that ross recovery is misspecified

single versus multiple supplier sourcing strategies successful supply chain management necessitates an effective sourcing strategy to combat uncertainties in both supply and demand in particular supply disruption results in excessive downtime of production resources upstream and downstream supply chain repercussions and eventually a loss in the market value of the firm in this paper we analyze single period single product sourcing decisions under demand uncertainty our approach integrates product prices supplier costs supplier capacities historical supplier reliabilities and firm specific inventory costs a unique feature of our approach is the integration of a firm specific supplier diversification function we also extend our analysis to examine the impact of minimum supplier order quantities our results indicate that single sourcing is a dominant strategy only when supplier capacities are large relative to the product demand and when the firm does not obtain diversification benefits in other cases we find that multiple sourcing is an optimal sourcing strategy we also characterize a non intuitive trade off between supplier minimum order quantities costs and supplier reliabilities finally we examine the robustness of our results through an extensive numerical analysis of the key parameters of our model

a simple recursive forecasting model abstract we compare the performance of alternative recursive forecasting models a simple constant gain algorithm used widely in the learning literature both forecasts well out of sample and also provides the best fit to the survey of professional forecasters

approximating the asset pricing kernel this article tests a simple consumption based asset pricing model by approximating the true asset pricing kernel using low order orthonormal polynomials based on the model s state variables approximated kernels based solely on next period s consumption growth are not rejected by overall measures of model fit but they produce statistically and economically large pricing errors approximated kernels based on two quarters of future consumption growth and technology shocks have substantially improved overall fit in particular the best of these kernels are capable of eliminating the small firm effect a conventional approach to examining the implications of dynamic asset pricing models is to assume that markets are complete the economy is in equilibrium and that the unique state price deflator can be interpreted as the intertemporal marginal rate of substitution of a representative consumer given assumptions about the form of this unobservable utility function and on the observability of aggregate consumption the model can be tested by examining the conditional or unconditional covariation of estimated intertemporal marginal rates of substitution with measured asset returns the fact that this method of testing dynamic models requires strong assumptions is in and of itself not particularly troubling however the fact that these attempts have been almost uniformly inconsistent with the data on asset returns and consumption is problematic for example when the utility function is assumed to be time and state separable the absolute and relative levels of the real returns on risk free and risky securities see for example mehra and prescott 1985 and weil 1989 are inconsistent with the model s predictions the primary finding from a large literature testing consumption based models is that measured consumption is too smooth to rationalize the observed level and variability of asset returns for reasonable parameterizations of time separable utility functions an alternate approach pursued in this paper is to approximate the stateprice deflator or asset pricing kernel using orthonormal polynomials in a

recurrent hyperinflations and learning we use a model of boundedly rational learning to account for the observations of recurrent hyperinflations in the 1980 s in a standard monetary model we replace the assumption of full rational expectations by a formal definition of quasi rational learning the model under learning matches some crucial stylized facts observed during the recurrent hyperinflations experienced by several countries in the 1980 s remarkably well we argue that despite being a small departure from rational expectations quasi rational learning does not preclude falsifiability of the model it does not violate reasonable rationality requirements and it can be used for policy evaluation

why does implied risk aversion smile implied risk aversion estimates reported in the literature are strongly u shaped this article explores different potential explanations for these smile patterns i preference aggregation both with and without stochastic volatility and jumps in returns ii misestimation of investors beliefs caused by stochastic volatility jumps or a peso problem and iii heterogeneous beliefs the results reveal that preference aggregation and misestimation of investors beliefs caused by stochastic volatility and jumps are unlikely to be the explanation for the smile although a peso problem can account for the smile the required probability of a market crash is unrealistically large heterogeneous beliefs cause sizable distortions in implied risk aversion but the degree of heterogeneity required to explain the smile is implausibly large jel g12 g13 in a representative agent economy equilibrium asset prices reflect the agent s preferences and beliefs rubinstein 1994 showed that any two of the following imply the third i the representative agent s preferences ii his subjective probability assessments and iii the state price density therefore essentially any state price density can be reconciled with the distribution of asset prices by using an appropriate set of preferences for the representative agent building on this insight a number of papers have derived estimates of the representative agent s risk aversion from the state price density and the subjective probability density ao t sahalia and lo 2000 jackwerth 2000 and rosenberg and engle 2002 report implied risk aversion estimates that have similar shapes with some differences they all found that implied risk aversion varies strongly across s p 500 index values and is u shaped around the futures price jackwerth 2000 and rosenberg and engle 2002 even obtained negative risk aversion estimates for a range of index values centered around the futures price the aim of this article is to explore different potential explanations for the implied risk aversion smile by investigating the properties of implied

returns of claims on the upside and the viability of u shaped pricing kernels abstract when the pricing kernel is u shaped then expected returns of claims with payout on the upside are negative for strikes beyond a threshold determined by the slope of the u shaped kernel in its increasing region and have negative partial derivative with respect to strike in the increasing region of the kernel using returns of i s p 500 index calls ii calls on major international equity indexes iii digital calls iv upside variance contracts and v a theoretical construct that we denote as kernel call we find broad support for the implications of u shaped pricing kernels a possible theoretical reconciliation of our empirical findings is explored through a model that accommodates heterogeneity in beliefs about return outcomes and short selling

robust strategies for natural gas procurement abstract in order to serve their customers natural gas local distribution companies ldcs can select from a variety of financial and non financial contracts the present paper is concerned with the choice of an appropriate portfolio of natural gas purchases that would allow a ldc to satisfy its demand with a minimum tradeoff between cost and risk while taking into account risk associated with modeling error we propose two types of strategies for natural gas procurement dynamic strategies model the procurement problem as a mean risk stochastic program with various risk measures naive strategies hedge a fixed fraction of winter demand the hedge is allocated equally between storage futures and options we propose a simulation framework to evaluate the proposed strategies and show that i when the appropriate model for spot prices and its derivatives is used dynamic strategies provide cheaper gas with low risk compared to naive strategies ii in the presence of a modeling error dynamic strategies are unable to control the variance of the procurement cost though they provide cheaper cost on average based on these results we define robust strategies as convex combinations of dynamic and naive strategies the weight of each strategy represents the fraction of demand to be satisfied following this strategy a mean variance problem is then solved to obtain optimal weights and construct an efficient frontier of robust strategies that take advantage of the diversification effect

options short sales and market completeness this paper presents empirical evidence that trading in options contributes to both transactional and informational efficiency of the stock market by reducing the effect of constraints on short sales the significantly higher average level of short interest exhibited by optionable stocks supports the argument that options facilitate short selling we also find significant effects on option prices related to the short interest in the underlying stock we then present evidence that options also increase information efficiency earlier work that is replicated and extended here has suggested that short sale constraints cause stock prices to underweight negative information options appear to reduce that effect

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

monetary policy expectations and commitment commitment in monetary policy leads to equilibria that are superior to those from optimal discretionary policies a number of interest rate reaction functions and instrument rules have been proposed to implement or approximate commitment policy we assess these rules in terms of whether they lead to a rational expectations equilibrium that is both locally determinate and stable under adaptive learning by private agents a reaction function that appropriately depends explicitly on private sector expectations performs particularly well on both counts

systematic risk and the price structure of individual equity options this study demonstrates the impact of systematic risk on the prices of individual equity options the option prices are characterized by the level and slope of implied volatility curves and the systematic risk is measured as the proportion of systematic variance in the total variance using daily option quotes on the s and p 100 index and its 30 largest component stocks we show that after controlling for the underlying asset s total risk a higher amount of systematic risk leads to a higher level of implied volatility and a steeper slope of the implied volatility curve thus systematic risk proportion can help differentiate the price structure across individual equity options the author 2008 published by oxford university press on behalf of the society for financial studies all rights reserved for permissions please email journals permissions oxfordjournals org oxford university press

incorporating quantity discounts and their inventory impacts into the centralized purchasing decision multi site organizations must balance conflicting forces to determine the appropriate degree of purchasing centralization for their respective supplies the ability to garner quantity discounts represents one of the primary reasons that organizations centralize procurement this paper provides methodologies to calculate optimal order quantities and compute total purchasing and inventory costs when products have quantity discount pricing procedures for both all units and incremental quantity discount schedules are provided for four different strategic purchasing configurations scenarios complete decentralization centralized pricing with decentralized purchasing centralized purchasing with local distribution and centralized purchasing and warehousing for ordering decisions under local distribution procedures to determine optimal order quantities and costs are presented in a precise form that could be easily implemented into spreadsheets by practicing managers for the more complicated multi echelon scenarios we introduce a single cycle policy with a tailored aggregation refinement step that performs very well under experimentation when compared to a conservative bound