valuation of foreign currency options some empirical tests this paper investigates the efficiency of the market for foreign currency options with the help of a modified version of the black scholes model the evidence in the ex post tests is inconsistent with this hypothesis since we find a large number of opportunities for abnormal profits a second set of tests is conducted on an ex ante basis to determine whether these profit opportunities exist even if the execution of the strategy is delayed by one day the evidence from these tests provides more support for the hypothesis of market efficiency

the pricing of foreign currency options this study examines the assumption that the exchange rate follows a log normal probability distribution and it tests whether different stochastic specifications translate into important differences in implied option prices we investigate a class of processes which includes the log normal probability distribution as a limiting case none of the models performs particularly well the main problem appears to be that the volatility estimates from actual exchange rate data are significantly smaller than those implied by observed option prices la formation du prix des options sur des devises etrangeres cette etude examine le pos tulat que le taux de change suit une courbe de probabilite log normale et verifie si des specifications stochastiques differentes se traduisent en des diff6rences importantes dans les prix des options qui en decoulent les auteurs examinent une famille de processus dont le processus log normal est un cas limite aucun des modeles ne donne des resultats particu lierement bons le probleme principal semble etre que la volatilite des evaluations a partir des donnees sur les taux de change reel est plus faible et de maniere significative que celle des evaluations derivees des prix d options observes

improving supply chain performance and managing risk under weather related demand uncertainty we consider a manufacturer retailer supply chain for a seasonal product whose demand is weather sensitive the retailer orders from the manufacturer supplier prior to the selling season and then sells to the market we examine how a manufacturer can structure a weather linked rebate to improve his expected profit the proposed class of rebate contracts offers several advantages over many other contract structures including no required verification of leftover inventory and or markdown amounts and no adverse effect on sales effort by the retailer we provide a thorough analysis of the manufacturer s and retailer s decisions in this context we show that the weather linked rebate can take many different forms and this flexibility allows the supplier to design contracts that are pareto improving and or limit his risk in offering the contract and the retailer s risk in accepting it for weather rebates with certain characteristics the manufacturer can fully hedge his risks of offering a weather rebate by paying a risk premium we show how this can be accomplished we also show that the basic structural results extend to settings in which the two parties would like to limit their risk

flexibility and uncertainty the preserving of flexibility when faced with uncertainty is a neglected aspect of behaviour under risk yet it is an important factor in decisions to hold liquid assets or delay irreversible investment this paper formalizes the notion of flexibility in a sequential decision context and relates its value to the amount of information an agent expects to receive a rudimentary money demand model is developed embodying these ideas and the history of flexibility as an economic concept is traced choices are frequently made between alternatives that imply different degrees of future commitment between a short term investment that leaves future options open for example and a long term one that by its very nature forecloses those options the relative attractiveness of the two depends on their probability distributions of payoffs over time a basic consideration in this choice is the recognition that beliefs about the risks governing these payoffs may change current doubts may be partially resolved in the near future this prospect decreases the attractiveness of the longer term commitment in that one is able to respond less fully to new information and even if it does not directly affect the risks associated with shorter term choices enhances their appeal this paper formalizes the above remarks by establishing connections between the following two partial orderings the first is an ordering based on variability of beliefs one set of beliefs is more variable than another if more final risk is resolved at an intermediate stage the more one expects to learn by an intermediate period relative to what one knows today the more variation one is anticipating in beliefs about the final outcome the second is an ordering of current actions or positions based on flexibility one position is more flexible than another if it leaves available a larger set of future positions at any given level of cost these two orderings are incorporated in a simple sequential decision model to suggest the following behavioural principle the more variable are a decision maker s beliefs the more flexible is the position he will choose this principle potentially applies whenever i there will be opportunities to act after further information is received and ii current actions influence either the attractiveness or availability of different future actions

single period multiproduct inventory models with substitution we study a single period multiproduct inventory problem with substitution and proportional costs and revenues we consider n products and n demand classes with full downward substitution i e excess demand for class i can be satisfied using product j for i j we first discuss a two stage profit maximization formulation for the multiproduct substitution problem we show that a greedy allocation policy is optimal we use this to write the expected profits and its first partials explicitly this in turn enables us to prove additional properties of the profit function and several interesting properties of the optimal solution in a limited computational study using two products we illustrate the benefits of solving for the optimal quantities when substitution is considered at the ordering stage over similar computations without considering substitution while ordering specifically we show that the benefits are higher with high demand variability low substitution cost low profit margins or low price to cost ratio high salvage values and similarity of products in terms of prices and costs

multi resource investment strategies operational hedging under demand uncertainty abstract consider a firm that markets multiple products each manufactured using several resources representing various types of capital and labor and a linear production technology the firm faces uncertain product demand and has the option to dynamically readjust its resource investment levels thereby changing the capacities of its linear manufacturing process the cost to adjust a resource level either up or down is assumed to be linear the model developed here explicitly incorporates both capacity investment decisions and production decisions and is general enough to include reversible and irreversible investment the product demand vectors for successive periods are assumed to be independent and identically distributed the optimal investment strategy is determined with a multi dimensional newsvendor model using demand distributions a technology matrix prices product contribution margins and marginal investment costs our analysis highlights an important conceptual distinction between deterministic and stochastic environments the optimal investment strategy in our stochastic model typically involves some degree of capacity imbalance which can never be optimal when demand is known

allocation of flexible and indivisible resources with decision postponement and demand learning we consider a firm that uses two perishable resources to satisfy two demand types resources are flexible such that each resource can be used to satisfy either demand type resources are also indivisible such that the entire resource must be allocated to the same demand type this type of resource flexibility can be found in different applications such as movie theater complexes cruise lines and airlines in our model customers arrive according to independent poisson processes but the arrival rates are uncertain thus the manager can learn about customer arrival rates from earlier demand figures and potentially increase the sales by postponing the resource allocation decision we consider two settings and derive the optimal resource allocation policy for one setting and develop a heuristic policy for the other our analysis provides managerial insights into the effectiveness of different resource allocation mechanisms for flexible and indivisible resources

supply capacity acquisition and allocation with uncertain customer demands we study a class of capacity acquisition and assignment problems with stochastic customer demands often found in operations planning contexts in this setting a supplier utilizes a set of distinct facilities to satisfy the demands of different customers or markets our model simultaneously assigns customers to each facility and determines the best capacity level to operate or install at each facility we propose a branch and price solution approach for this new class of stochastic assignment and capacity planning problems for problem instances in which capacity levels must fall between some pre specified limits we offer a tailored solution approach that reduces solution time by nearly 80 over an alternative approach using a combination of commercial nonlinear optimization solvers we have also developed a heuristic solution approach that consistently provides optimal or near optimal solutions where solutions within 0 01 of optimality are found on average without requiring a nonlinear optimization solver

pricing and the news vendor problem a review with extensions in the newsvendor problem a decision maker facing random demand for a perishable product decides how much of it to stock for a single selling period this simple problem with its intuitively appealing solution is a crucial building block of stochastic inventory theory which comprises a vast literature focusing on operational efficiency typically in this literature market parameters such as demand and selling price are exogenous however incorporating these factors into the mode l can provide an excellent vehicle for examining how operational problems interact with marketing issues to influence decision making at the firm level in this paper we examine an extension of the newsvendor problem in which stocking quantity and selling price are set simultaneously we provide a comprehensive review that synthesizes existing results for the single period problem and develop additional results to enrich the existing knowledge base we also review and develop insight into a dynamic inventory extension of this problem and motivate the applicability of such models

the distribution of foreign exchange price changes trading day effects and risk measurement a comment in their 1982 study mcfarland pettit and sung 16 mps found that consecutive daily foreign exchange rates conform to neither a normal nor a nonnormal stable process and that day of the week data could be adequately described by a series of different stable distributions the authors have also documented a weekday effect in the foreign exchange market mondays and wednesdays offered higher average price changes than did thursdays and fridays in a more recent study jaffe and westerfield 9 documented negative monday returns for the currencies of the u k canada and australia in estimating the parameters of the distribution mps have utilized the fama and roll 5 6 method which assumes a symmetric distribution jaffe and westerfield 9 report only estimates of the sample moments the sample moments reported in mps s table ii part of which is reproduced in table i here reveal that most currencies especially the minor currencies the australian dollar the spanish peseta and the swedish krona have significant skewness the results indicate that the asymmetric stable paretian distribution may be more appropriate for the overall daily returns this hypothesis is consistent with

investment and capacity choice under uncertain demand this paper extends the real options literature by discussing an investment problem where a firm has to determine optimal investment timing and optimal capacity choice at the same time under conditions of irreversible investment expenditures and uncertainty in future demand after the project is installed with a certain maximum capacity this capacity is fixed as an upper boundary to the output and cannot be adjusted later on it turns out that in the framework of this once and for all decision uncertainty in future demand leads to an increase in optimal installed capacity but on the other hand it causes investment to be delayed to an extent that even small uncertainty makes waiting and accumulation of further information the optimal decision for large ranges of demand limiting the capacity which may be installed weakens this extreme effect of uncertainty

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

dynamic capacity planning using strategic slack valuation in this paper we analyze a particular aspect of capacity planning that is concerned with the active trading of production facilities for a homogenous product market we provide a theoretical rationale for the valuation and trading of these assets based on a metric of strategic slack we show that trading production assets with non additive portfolio profitability involves complex coordination with multiple equilibria and that these equilibria depend on the foresight in the planning horizon using the concept of strategic slack we have analyzed the dynamics of market structure the impact of asset trading on the level of production of the industry and to derive boundaries on the value of the traded assets moreover through computational learning the formulation is applied to a large oligopolistic electricity market showing that plant trading tends to lead to increased market concentration high prices lower production and a decrease in consumer surplus

the distribution of foreign exchange price changes trading day effects and risk measurement this study investigates the nature of price changes in a variety of major and minor foreign exchange markets the results suggest that the log of price changes over one trading day intervals seems to follow a non normal stable distribution function different measures of location and to lesser extent scale are present for different days of the week dollar denominated price changes are high on mondays and wednesdays and low on thursdays and fridays for all currencies the wednesday thursday result is consistent with the settlement procedures used in foreign exchange transactions in the dollar the friday monday result is consistent with an increase in demand for the dollar prior to the weekend this study offers some previously unavailable results on the nature of price changes in a certain set of speculative markets in particular this is a study of the distributional characteristics of daily and weekly price changes for a number of major and minor foreign exchange markets the results document the existence of non normal stable distributions for price changes in foreign exchange markets these price change distributions differ by day of the week in ways that are only partly attributable to the institutional structure of the market the results of the study are interpreted within the context of understanding how foreign exchange markets operate and within the context of prior studies of stock market data concerned with summarizing the probability distribution of price changes for different intervals including days of the week since bachelier s 1 original treatise that contained the proposition that speculative market prices follow a process that could be described by a normal distribution there have been numerous alternative attempts to describe the stochastic processes which characterize speculative market prices these studies have not resulted in any generalized description of the probability distribution of price changes in such markets indeed the evidence suggests substantial differences in the process among various types of financial instruments the failure to achieve consensus can be traced to the lack of robustness in the statistical procedures employed to estimate processes and to differences in the underlying institutional or economic arrangements which are unique to that market the possibility of differences in the information set used to assess value or differences in technology for transmitting information makes it important to secure additional

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

valuing flexibility as a complex option this paper develops an approach for valuing flexible production systems using contingent claims pricing demand curves for our model s underlying assets output products may be downward sloping in contrast with the standard option pricing assumption also our marginal production exercise costs may be increasing in addition we allow for multiple products and a production capacity constraint these elements of the model result in complex exercise decisions for the contingent claims which comprise the production system s value we illustrate our approach by valuing a flexible system that produces two products which have profit margin functions with stochastic parameters

resource flexibility with responsive pricing this article studies two types of flexibility used by firms to better respond to uncertain market conditions resource flexibility and responsive pricing we consider a situation in which a single flexible resource can be used to satisfy two distinct demand classes while the resource capacity must be decided based on uncertain demand functions the resource allocation as well as the pricing decision are made based on the realized demand functions we characterize the effects of two key drivers of flexibility demand variability and demand correlation assuming normally distributed demand curve intercepts demand variability creates opportunity costs and with fixed prices decreases the firm s profit we show that with the additional flexibility gained from responsive pricing the firm can maximize the benefits of favorable demand conditions and mitigate the effects of poor demand conditions ultimately profiting from variability positive demand correlation on the other hand remains undesirable under responsive pricing the optimal capacity of the flexible resource is always increasing in both demand variability and demand correlation this contrasts with the scenarios based on fixed prices highlighting the crucial difference that responsive pricing makes in the management of flexible resources we further quantify the value of flexibility for the firm and its customers by considering as a benchmark a firm relying on two dedicated resources the value of flexibility is most significant if the demand levels are highly variable and negatively correlated in such cases the firm benefits from demand variability due to responsive pricing while facing limited demand risk due to resource flexibility finally we endogenize the input price of the flexible resource by considering the pricing decision of the resource supplier

optimal investment strategies for flexible resources considering pricing and correlated demands we study the optimal resource investment decision faced by a two product price setting firm that operates in a monopolistic setting and employs a postponed pricing scheme the firm has the option to invest in dedicated resources as well as a more expensive flexible resource that can satisfy both products while the resource investment decision is made under demand uncertainty pricing and resource allocation decisions are postponed to the time when demand curves are realized our analysis provides the structure of the firm s optimal resource investment strategy as a function of demand parameters and investment costs and shows that the flexible resource investment decision follows athreshold policy we also show that it can be optimal for the firm to invest in the flexible resource even when demand patterns are perfectly positively correlated the reason for flexible capacity investment in this case is financial rather than risk pooling on the other hand we show that it can be optimal for the firm not to invest in the flexible resource even when demand patterns are perfectly negatively correlated the flexible resource investment decision in this case depends on the profitability of the two products based on our analysis we provide principles on the firm s optimal resource investment decision

the statistical distribution of exchange rates empirical evidence and economic implications the abundant evidence that changes in exchange rates have distributions with fatter tails than the normal distribution has led researchers to consider non normal distributions including the student the stable paretian and mixtures of distributions this paper compares the empirical fits of three non normal candidates and the normal distribution for daily changes in the logarithms of exchange rates using maximum likelihood estimation of the parameters and chi square goodness of fit tests the student and mixture of two normals provide the best fits but there is evidence that the distribution parameters may vary over time

the impact of budget constraints on flexible vs dedicated technology choice this paper studies the flexible versus dedicated technology choice and capacity investment decisions of a multiproduct firm under demand uncertainty in the presence of budget constraints the firm operates under a capital budget for financing the capacity investment and an operating budget which is uncertain in the capacity investment stage for financing the production we investigate how the tightening of the capital budget and a lower financial flexibility in the production stage the likelihood of having a sufficient operating budget shape the optimal technology choice we find that the dominant regime is one where dedicated technology should be adopted for a larger investment cost range and thus is the best response to the tighter capital budget whereas flexible technology is the best response to lower financial flexibility we identify the key roles that the capacity intensity the ratio of unit capacity cost to total unit capacity and production cost of each technology and the pooling value

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

comparative statics analysis of multiproduct newsvendor networks under responsive pricing we propose a novel analytic approach for the comparative statics analysis of multiproduct multiresource newsvendor networks under responsive pricing our approach involves exploiting the properties of the primal mathematical programming formulation and of the dual variables and linking those properties to the concept of convex orders and to properties of the underlying demand function the use of convex orders allows us to establish our main results without restriction to a specific demand distribution a major strength of our approach is that it is scalable i e it applies to newsvendor networks with any number of nonindependent i e demand or resource sharing products and resources without an exponential increase in effort as problem size increases this is unlike the current approaches commonly used in the operations management literature which typically involve a parametric analysis of the recourse problem followed by the use of jacobians and the implicit function theorem providing a rigorous framework for comparative statics analysis which can be applied to other problems that are not amenable to traditional parametric analysis is our main contribution we demonstrate this approach on the optimal capacity decision problem in multiproduct newsvendor networks under responsive pricing formulated as a two stage stochastic programming problem with recourse the firm determines the resource capacities ex ante in the first stage when demand intercepts are uncertain and makes the pricing and production decisions ex post in the second stage when demand intercepts e g market conditions are fully observed this particular problem and its variants are well studied in the operations management literature a comparative statics analysis is integral to the study of the capacity investment decision as it allows answers to important questions such as the following does the firm acquire more or less of the different resources available as demand uncertainty increases does the firm benefit from an increase in demand uncertainty using our proposed approach we establish comparative statics results on how the newsvendor s expected profit and optimal capacity decision change with demand risk in multiproduct multiresource newsvendor networks we also extend our analysis to the study of demand dependence in two product networks

empirical tests of boundary conditions for toronto stock exchange options using option and stock transaction data for the period 1978 1979 three issues were investigated first the conformance of observed prices to various boundary conditions second the evolution of the market over time as the volume of trading and the number of listed options increased and third to test the efficiency of the market it was found that violations did occur using a trading rule based on the signal of observed violations the results suggest that even after transaction costs the market was inefficient over the sample period

pricing foreign currency options under stochastic interest rates abstract in this paper we build a general framework to price contingent claims on foreign currencies using the heath et al 1987 model of the term structure closed form solutions are obtained for european options on currencies and currency futures assuming that the volatility functions determining the term structure are deterministic as such this paper provides an example of a bond price process for both the domestic and foreign economies consistent with grabbe s 1983 formulation of the same problem

equilibrium valuation of foreign exchange claims this article studies the equilibrium valuation of foreign exchange contingent claims within a continuous time lucas 1982 two country model exchange rates interest rates and in particular factor risk prices are all endogenously and jointly determined this guarantees the internal consistency of these price processes with a general equilibrium in the same model closed form valuation formulas are presented for currency options and currency futures options common to these formulas is that stochastic volatility and stochastic interest rates are admitted hedge ratios and other comparative statics are also provided analytically it is shown that most existing currency option models are included as special cases this article studies the equilibrium valuation and hedging of foreign exchange contingent claims the framework for analysis is the continuous time counterpart of the well known two country monetary model of lucas 1982 1 that is we use the modeling structure of lucas 1982 and adopt his representativeagent perfect pooling equilibrium notion rather than extending the lucas setup to a cox ingersoll and ross 1985a henceforth cir production economy as is done in nielsen and saa requejo 1993 for our purpose the lucas framework offers the desired simplicity and tractability we assume a stochastic structure for the international economy such that the resulting nominal interest rates and exchange rate dynamics exhibit similar empirically plausible features as the corresponding ones in nielsen and saa requejo 1993 for example the endogenous interest rates are positively correlated across national borders campbell and clarida 1987 and ilmanen 1995 as a predictor of future spot exchange rates the equilibrium forward exchange rate is biased in a direction consistent with the forward premium puzzle

managing flexible capacity in a make to order environment flexible capacity has been shown to be very effective to hedge against forecast errors at the investment stage in a make to order environment this flexibility can also be used to hedge against variability in customer orders in the short term for that purpose production levels must be adjusted each period to match current demands to give priority to the higher margin product or to satisfy the closest customer however this will result in swings in production inducing larger order variability at upstream suppliers and significantly higher component inventory levels at the manufacturer through a stylized two plant two product capacitated manufacturing setting we show that the performance of the system depends heavily on the allocation mechanism used to assign products to the available capacity although managers would be inclined to give priority to higher margin products or to satisfy customers from their closest production site these practices lead to greater swings in production result in higher operational costs and may reduce profits

forward contracts and futures contracts abstract this paper provides a detailed discussion of the similarities and differences between forward contracts and futures contracts under frictionless markets and continuous trading simple arbitrage arguments are invoked to value forward contracts to relate forward prices and spot prices and to relate forward prices and futures prices we also argue that forward prices need not equal futures prices unless default free interest rates are deterministic

strategic facility location capacity acquisition and technology choice decisions under demand uncertainty robust vs non robust optimization approaches abstract this paper presents a robust optimization ro modeling approach to develop insights into strategic capacity planning and resource acquisition decisions including the facility location problem and the technology choice problem the main purpose of the proposed model and numerical experiments is to examine the effects of economies of scale economies of scope and the combined effects of scale and scope under uncertain demand realizations using robust optimization the type of capacities or technology alternatives that a firm can acquire can be classified on two basic dimensions the first dimension relates to the effects of scale via distinction between labor intensive technologies and capital intensive technologies the second dimension relates to the effects of scope via distinction between product dedicated and flexible technologies moreover each product dedicated and flexible technology can have different levels of labor or capital intensity leading to the joint effects of economies of scale and economies of scope extensive computational results document how the optimal technology choice patterns depend on the cost structures and levels of model robustness specified to accommodate uncertain demand realizations the results obtained by the two stage robust optimization approach are compared to the results obtained by a non robust approach

transshipment and its impact on supply chain members performance this note extends some of the key results of dong and rudi 2004 to general demand distributions this generalization is achieved in two steps first we build on the analysis of dong and rudi to demonstrate that an inventory problem with transshipment is equivalent to a newsvendor problem with an adjusted demand then we study the impact of transshipment by comparing the adjusted demand with the original demand in addition to extending the results in the existing literature this note presents a novel approach for analyzing the impact of risk pooling

coordinating the resource investment decision for a two market price setting firm abstract we study the capacity investment decision of a two product firm that is a price setter for both products the products are of varying complexities such that the resource that can be used to produce the higher level product can also be used to produce the lower level one but not vice versa although the firm needs to make its capacity investment decision under demand uncertainty it can utilize this limited downward resource flexibility in addition to pricing to more effectively match its supply with demand as an example consider a firm that owns a main plant satisfying both end product and intermediate product demand and a subsidiary satisfying the intermediate product demand only we formulate this decision problem as a two stage stochastic programming problem with recourse and analyze the impact of coordinated decision making when the resource flexibility is taken into account in the investment decision and demand correlation on the firm s optimal investment strategy our results offer managerial principles on the firm s optimal resource investment strategy

dynamic capacity management with general upgrading this paper studies a capacity management problem with upgrading a firm needs to procure multiple classes of capacities and then allocate the capacities to satisfy multiple classes of customers that arrive over time a general upgrading rule is considered i e unmet demand can be satisfied using multistep upgrade no replenishment is allowed and the firm has to make the allocation decisions without observing future demand we first characterize the structure of the optimal allocation policy which consists of parallel allocation and then sequential rationing specifically the firm first uses capacity to satisfy the same class demand as much as possible then considers possible upgrading decisions in a sequential manner we also propose a heuristic based on certainty equivalence control to solve the problem numerical analysis shows that the heuristic is fast and delivers close to optimal profit for the firm finally we conduct extensive numerical studies to derive insights into the problem it is foun

the law of one price in the eurocurrency market abstract this paper studies the interest rate parity arbitrage condition in the eurocurrency market in the period 1967 to 1980 the results suggest that this market is relatively efficient with few opportunities for arbitrage profits turbulance associated with external shocks to this market is relatively short lived the evidence indicates that the foreign exchange and eurocurrency markets respond rapidly to monetary shocks

the probability distribution of foreign exchange price changes tests of candidate processes this study investigates empirically candidate processes for characterizing foreign exchange price changes measured over limited horizons extant empirical studies find distributions of exchange returns too long tailed and leptokurtic to satisfy normality four processes are investigated here because of their potential to model o bserved discontinuities in exchange rates and nonstationary sample moments as well as their economic appeal the results favor a mixed jump model for all six major trading currencies tested copyright 1988 by mit press

misspecification and the pricing and hedging of long term foreign currency options abstract this study examines the effects of stochastic volatility upon the pricing and hedging of long term foreign currency options the traditional method of pricing such options uses a constant volatility option model with an implicit volatility derived from a short term traded option we show that the traditional method leads to small pricing errors for short and medium term options but does a poor job in pricing long term options the traditional method also does a poor job for all maturities in determining the derivatives of the option s value with respect to the exchange rate delta and the volatility vega the errors in calculating these derivatives which are used in forming the replicating portfolio lead to large and costly errors in error hedging

tests of an american option pricing model on the foreign currency options market this paper tests the ability of the american option pricing model proposed by parkinson 18 or mason 14 to explain the pricing of the foreign currency options traded on the philadelphia stock exchange from february 28 1983 to march 26 1985 we find that the model underprices out of the money options relative to at the money and in the money options this relative underpricing is driven by an underpricing of out of the money call options of short maturity in addition the degree of relative mispricing for most categories of options is shown to be a decreasing function of the time to maturity of the options longer maturity options appear to trade at similar levels of implied volatility whether they are in at or out of the money most of these biases appear consistent with the fact that the underlying spot currency rate follows a mixed jump diffusion process as described in 17

the pricing of call and put options on foreign exchange this paper derives pricing equations for european puts and calls on foreign exchange the call and put pricing formulas are unlike the black scholes equations for stock options in that there are two relevant interest rates interest rates are stochastic and boundary constraints differ in addition it is shown that both american call and put options have values larger than their european counterparts

optimal investment in product flexible manufacturing capacity this paper presents a model and an analysis of the cost flexibility tradeoffs involved in investing in product flexible manufacturing capacity flexible capacity provides a firm with the ability to respond to a wide variety of future demand outcomes but at the expense of the increased cost of acquiring flexible manufacturing capacity as compared with dedicated or nonflexible capacity we formulate the product flexible manufacturing capacity investment decision as a two stage stochastic program in the first stage the firm must make its investment decision in manufacturing capacity before the resolution of uncertainty in product demand in the second stage after demand for products are known the firm implements its production decisions constrained by the first stage investments the main contributions of this paper are threefold first we develop a model of the firm s flexible manufacturing investment decision that conceptually captures some of the key characteristics of this complex decision probl

global facility network design in the presence of competition abstract we study the facility network design problem for a global firm that is a monopolist seller in its domestic market but faces local competition in its foreign market the global firm produces in the face of demand and exchange rate uncertainty but can postpone localization and distribution of the output until after uncertainties are resolved the competitor in the foreign market however enjoys the flexibility of postponing all production activities until after uncertainties are resolved the two firms engage in an ex post cournot competition in the foreign market we consider three potential network configurations for the global firm under a linear demand function we provide the necessary and sufficient condition that one of the three networks is the global firm s optimal choice and explore how the presence of foreign competition affects the sensitivity of the global firm s design to various cost parameters and market uncertainties

flexible production resources and capacity utilization rates a robust optimization perspective abstract this paper presents a novel application of robust optimization ro in the context of optimal choices of product dedicated and flexible capacities in a spatial setting specifically we examine the impact of acquiring flexible production technologies on a firm s overall capacity utilization rates under demand uncertainty uncorrelated negatively and positively correlated demands are considered we implement an efficient ro algorithm which can solve large samples of robust min max problems in a realistic amount of time this paper examines the impact of three critical factors that lead to different capacity utilization and resource flexibility outcomes the degree of solution robustness selected by the decision maker to accommodate uncertain demand realizations the flexible capacity costs relative to dedicated capacity costs and the level of correlation between product demands one of our results show that according to robust solutions the total capacity may not be fully utilized because of the distinction between largest in unit terms and costliest demand realizations the second result shows that increasing the proportion of flexible capacity can increase capacity utilization however our results report less than full utilization even when using flexible capacity only we show that the optimal amount of flexible capacity and its impact on overall capacity utilization rate substantially depends on demand correlation

the impact of demand aggregation through delayed component allocation in an assemble to order system we consider an assemble to order system in which multiple products are assembled from a common component and a set of product dedicated components component capacities are chosen prior to a finite horizon selling season and the common component is allocated to the products based on observed demands we propose a collection of allocation mechanisms involving varying degrees of demand aggregation ranging from a scheme under which all demands are observed prior to making the allocation decision to allocations made for each arriving demand in this context we explore the impact of the allocation scheme on sales profits and capacity decisions including the degree of capacity imbalance we find that the benefit from increased demand aggregation is closely linked to the degree of capacity imbalance profit gains from delayed allocation tend to be higher in systems in which the optimal capacity portfolio is highly unbalanced when the allocation decision is made after observing all demands we develop insights into what detailed system parameters lead to the largest gains from demand aggregation and also explore the trade offs associated with the choice of an allocation scheme when customers exhibit impatience if the allocation scheme forces them to wait to be served this paper was accepted by ananth iyer operations and supply chain management

u s war costs two parts temporary one part permanent military spending fatalities and the destruction of capital all of which are immediately felt and are often large are the most overt costs of war they are also relatively short lived but the costs of war borne by combatants and their caretakers which includes families communities and the modern welfare state tend instead to be lifelong in this paper i show that a significant component of the budgetary costs associated with u s wars is long lived one third to one half of the total present value of historical war costs are benefits distributed over the remaining life spans of veterans and their dependents even thirty years after the end of hostilities typically half of all benefits remain to be paid estimates of the costs of injuries and deaths suggest that the private burden of war borne by survivors namely the uncompensated costs of service related injuries are also large and long lived

price versus production postponement capacity and competition this article presents a comparative analysis of possible postponement strategies in a two stage decision model where firms make three decisions capacity investment production inventory quantity and price typically investments are made while the demand curve is uncertain the strategies differ in the timing of the operational decisions relative to the realization of uncertainty we show how competition uncertainty and the timing of operational decisions influence the strategic investment decision of the firm and its value in contrast to production postponement price postponement makes the investment and production inventory decisions relatively insensitive to uncertainty this suggests that managers can make optimal capacity decisions by deterministic reasoning if they have some price flexibility under price postponement additional postponement of production has relatively small incremental value therefore it may be worthwhile to consider flexible ex post pricing before production postponement reengineering while more postponement increases firm value it is counterintuitive that this also makes the optimal capacity decision more sensitive to uncertainty we highlight the different impact of more timely information which leads to higher investment and inventories and of reduced demand uncertainty which decreases investment and inventories our analysis suggests appropriateness conditions for simple make to stock and make to order strategies we also present technical sufficiency and uniqueness conditions under price postponement these results extend to oligopolistic and perfect competition for which pure equilibria are derived interestingly the relative value of operational postponement techniques seems to increase as the industry becomes more competitive

flexible service capacity optimal investment and the impact of demand correlation we consider a firm that provides multiple services using both specialized and flexible capacity the problem is formulated as a two stage single period stochastic program the firm invests in capacity before the actual demand is known and optimally assigns capacity to customers when demand is realized sample applications include a car rental company s use of mid sized cars to satisfy unexpectedly high demand for compact cars and an airline s use of business class seats to satisfy economy class demand we obtain an analytical solution for a particular case when services may be upgraded by one class the simple form of the solution allows us to compare the optimal capacities explicitly with a solution that does not anticipate flexibility given that demand follows a multivariate normal distribution we analytically characterize the effects of increasing demand correlation on the optimal solution for the case with two customer classes the effects of demand correlation are intuitive increasing correlation induces a shift from flexible to dedicated capacity when there are three or more classes there are also adjustments to the resources not directly affected by the correlation change as correlation rises these changes follow an alternating pattern for example if the optimal capacity of one resource rises then the optimal capacity of the adjacent resource falls these results make precise conjectures based on numerical experiments that have existed in the literature for some time

the value of flexibility in make to order systems the effect of demand correlation we consider a manufacturer of mass customized modular products who orders components under demand uncertainty and sets prices produces to order and trades excess components in a secondary market after this uncertainty is resolved the sequence of events reflects in a parsimonious fashion the considerable reduction in demand uncertainty between the procurement stage and the selling season typical of industries with long supply lead times and short product life cycles we prove that in contrast to conventional wisdom the value of production flexibility and expected profit increase with demand correlation if and only if commonality between the corresponding products does not exceed a threshold we also prove that the value of flexibility and expected profit may each increase or decrease with demand variability depending on demand correlations and component commonalities across the entire product line finally we prove that when demand shocks are independent the optimal product prices are positively correlated if and only if the degree of commonality between the corresponding products exceeds a threshold

forward and futures prices evidence from the foreign exchange markets empirical studies of the treasury bill markets have revealed substantial differences between the futures price and the implied forward price these differences have been attributed to taxes transaction costs and the settling up procedure employed in the futures market this paper examines the forward and futures prices in foreign exchange in an attempt to distinguish between the competing explanations empirical studies of the treasury bill market have revealed differences between the futures price or rate and the implicit forward price derived from the term structure of interest rates 1 these differences have generally been attributed to market imperfections such as taxes and transaction costs see for example arak 1 capozza and cornell 2 and rendelman and carabini 6 recently however cox ingersoll and ross 3 henceforth cir derived a model in which forward and futures prices need not be equal even in perfect markets without taxes as long as interest rates are stochastic the significance of the cir effect may be hard to investigate using only data from the bill market because of the potentially complicating effects of taxes and transaction costs unique to this market by using data from the foreign exchange market we are able to eliminate the tax effect and reduce the impact of transaction costs the question we address is whether the discrepancies observed in the treasury bill market are also observed in the foreign exchange market if they are then we have evidence that the differences are due to a combination of the cir effect and the transaction costs common to both markets if they are not then either the magnitude of the cir effect is much less in the foreign exchange market or the treasury bill results are due to the unique tax treatment and transaction costs of that market this paper is organized as follows in section i the trading mechanics of the forward and futures markets in foreign exchange are discussed section ii reviews the explanations for the discrepancies between the forward and futures prices for treasury bills the institutional differences between the foreign exchange and bill markets are also summarized to show which of these explanations cannot apply to the foreign exchange market in section iii the data are decribed and the empirical results are presented the conclusions are summarized in the final section

incentives and commonality in a decentralized multiproduct assembly system in this paper we explore the impact of decentralized decision making on the behavior of multiproduct assembly systems specifically we consider a system where three components two product specific and one common are used to produce two end products to satisfy stochastic customer demands we study the system under both centralized and decentralized decision making in the decentralized system we prove that for any set of wholesale prices there exists a unique pareto optimal equilibrium in the suppliers capacity game we show that the assembler s optimal wholesale prices lie in one of two regions one leads to capacity imbalance and one does not we use these results to derive insights regarding the inefficiencies that decentralization can cause in such systems in particular several of our findings indicate that outsourcing the management of component supplies may inhibit the use of operational hedging approaches for managing uncertainty

stochastic processes for interest rates and equilibrium bond prices default free bonds represent in essence money sold forward the investor gives dollars say to the government now in exchange for a contract which promises to pay with probability one a given number of dollars at maturity and possibly a stream of intermediate coupon payments prior to maturity only recently have financial economists begun to examine the pricing of those bonds in a portfolio context in that framework nominal liquidity premiums or risk premiums on long term default free bonds are attributable to uncertainty about taste technological and price level changes which may occur prior to maturity of the bonds and prior to each coupon payment if any to the extent that the investor is unable to diversify away that uncertainty there is a systematic risk attached to the marginal utility which he or she can derive from the use in consumption or investment of the dollar payoffs on the bonds in some term structure models the instantaneous or short term rate of interest denoted here as a function of time t by r t in nominal terms and r t in real terms can be taken as a sufficient statistic1 for the source of systematic uncertainty about the marginal utility of the proceeds to be derived from defaultfree bonds maturing beyond the next instant e g merton 1974 vasicek 1977 cox ingersoll and ross 1977 specific assumptions about tastes technology and utility functions lead to specific equilibrium stochastic processes for the instantaneous short term riskless rate and longer term bond prices which are modelled as functionally dependent upon maturity and that short term riskless rate if a closed form solution exists for the long term bond price as a function of maturity and the short term interest rate it will be conditional inter alia on the parameters of the stochastic process for that short term rate marsh 1981 proposed that the closed form solutions could be tested in terms of the restrictions implied cross sectionally on the parameters of the time series process for the returns or prices of longer term bonds each with a given term to maturity for an analogy outside the term structure literature think of the closed form solution given by black and scholes 1972 for the price of an option on a nondividend paying stock with lognormal price dynamics given the model the cross section of time series for the changes in prices for each of the several options written on the same stock are not unrestricted their dispersion is functionally linked to the same volatility parameter for the stock price thus the option model including

pricing and operational recourse in coproduction systems coproduction systems in which multiple products are produced simultaneously in a single production run are prevalent in many industries such systems typically produce a random quantity of vertically differentiated products this product hierarchy enables the firm to fill demand for a lower quality product by converting a higher quality product in addition to the challenges presented by random yields and multiple products coproduction systems often serve multiple customer classes that differ in their product valuations furthermore the sizes of these classes are uncertain employing a utility maximizing customer model we investigate the production pricing downconversion and allocation decisions in a two class stochastic demand stochastic yield coproduction system for the single class case we establish that downconversion will not occur if prices are set optimally in contrast we show that downconversion can be optimal in the two class case even if prices are set optimally we consider the benefit of postponing certain operational decisions e g the pricing or allocation rule decisions until after uncertainties are resolved we use the term recourse to denote actions taken after uncertainties have been resolved we find that recourse pricing benefits the firm much more than either downconversion or recourse allocation do implying that recourse demand management is more valuable than recourse supply management special cases of our model include the single class and two class random yield newsvendor models

technology investment under flexible capacity strategy with demand uncertainty abstract this paper investigates technology investment under flexible capacity strategy with demand uncertainty technology investment enables a firm to reduce its total production cost while flexible capacity strategy aims to reduce a firm s production waste by postponing production until demand is known adopting a general technology investment cost we examine how technology investment cost structure affects a firm s technology investment decisions we derive the conditions under which the firm will benefit from technology investment we show that the firm can increase its expected profit through technology investment only when the unit technology investment cost that varies inversely with the basic technology level is below a threshold however even though the technology investment cost is zero the benefit from the increase in technology level is limited furthermore we analytically determine the optimal technology levels and establish their relationships under different technology investment cost structures our findings will help firms evaluate various technology investment options and choose the most proper one