a comparative analysis of approaches for determining optimal price and order quantity when a sale increases demand abstract both average cost or profit and present value of cost or profit methods have been used in developing inventory policies although the present value method represents the costs and revenues better both methods generate identical solutions for the classical eoq case this paper discusses the differences between the two methods and illustrates situations where these two methods generate drastically different policies specifically when a supplier reduces the price of a product temporarily a retailer might place a special order and offer a discount on these units to its customers to increase demand this paper uses an average profit method to develop profit functions for different combinations of supplier s sale period and retailer s replenishment time and presents methods for determining the optimal price and order quantity experiments are then conducted to compare the results of average profit and present value of profit approaches for solving the problem the results indicate that these models may generate drastically different policies for the problem and neither model will consistently generate a larger order quantity this paper suggests that the present value approach be used to determine optimal policies when there is a temporary change in price and demand

optimal pricing and lot sizing under conditions of perishability finite production and partial backordering and lost sale abstract perishable products constitute a sizable component of inventories common questions in a production and selling situation involving a perishable or a non perishable product are what should be the price and what should be the size of the replenishment when demand for the product is price sensitive pricing and lot sizing decisions are interdependent similarly when a product is highly perishable the demand may need to be backlogged to avoid costs due to deterioration i e perishability and backlogging are complementary conditions in this paper we consider the pricing and lot sizing problem for a perishable good under finite production exponential decay and partial backordering and lost sale the backlogging phenomenon in the literature is often modeled using backordering and lost sale costs these cost parameters however are not easy to estimate in practice in this paper we use a new approach to model backlogging of demand in this approach customers are viewed to be impatient the backlogging option gets used only when it is economic to do so we extend the analysis presented for a perishable product to the case in which the product is non perishable

effects of a hybrid price stock dependent demand on the optimal solutions of a deteriorating inventory system and trade credit policy on re manufactured product abstract this study contributes to formulate a deteriorating inventory model with a hybrid price stock dependent demand with credit for units in stock period in the presence of trade credit policy by using the discounted cash flow approach on re manufactured products in real life the demand function is not always constant or linear or nonlinear the demand rate of any items goes up and down in the real market due to the sum of two different types of demand this study observes that the demand is depending on price and stock of the product time value of money and trade credit policy the objective of this study is to find optimum cycle time optimum selling price and present profit of all future cash flows the model starts with mathematical formulating and thereafter studies the necessary and sufficient conditions for obtaining the unique optimal solution the theoretical solution procedure and case examples have studied for validation of this model moreover the sensitivity analysis is expressed out with respect to main parameters and managerial application is obtained this study uses the different demand functions of a simple pricing inventory system to find out the maximum profit on re manufactured products

optimal joint pricing and lot sizing with fixed and variable capacity this paper examines previously unexplored fixed and variable capacity problems of jointly determining an item s price and lot size for a profit maximizing firm facing constant but price dependent demands over a planning horizon we apply geometric programming to these constrained nonlinear maximization problems with nonconcave objective functions and obtain global optimal solutions using kuhn tucker condition marginal and sensitivity analyses we investigate model interactions provide managerial implications on the optimal capacity decisions and explore the postoptimal behavior of the price lot size and capacity expansion and reduction size some findings cast interesting insights different from previous just in time management studies without pricing consideration

structural change in an open economy we study the importance of international trade in structural change our framework has both productivity and trade cost shocks and allows for non unitary income and substitution elasticities we calibrate our model to investigate south korea s structural change between 1971 and 2005 we nd that the shock processes propagated through the model s two main transmission mechanisms non homothetic preferences and the open economy explain virtually all of the evolution of agriculture and services labor shares and the rising part of the hump shape in manufacturing counterfactual exercises show that the role of the open economy is quantitatively important for explaining south korea s structural change

comments on a comparative analysis for determining optimal price and order quantity when a sale increases demand although the net present value npv criterion is theoretically the correct approach to developing optimal inventory policies in the classical eoq case the average profit criterion generates solutions that are practically identical to those resulting from the npv criterion nevertheless a recent paper suggests that when the demand for a product is price elastic and a wholesaler offers a one time only price discount use of the average profit criterion may obtain policies that are drastically suboptimal compared to the policies obtained by using the npv criterion we show that this suggestion is based on inaccurate models and inconsistent comparisons although in cases of large one time only discounts there may be significant differences in the policies and consequences resulting from the two criteria such large discounts are unrealistic furthermore the larger the discount the less practicable are the optimal order quantities based on either one of these criteria thus in most real life situations the use of the average profit criterion does not result in serious suboptimization in these situations what may be important is not whether a retailer uses the npv criterion or the average profit criterion but whether the retailer can and does implement the optimal decisions resulting from the use of either criterion

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

treasury bill factors and common stock returns capital asset pricing theory gives a linear ex ante relationship between a security s return and one special portfolio return the return on all assets this linear equation is called the capital asset pricing model capital asset pricing theory alone provides no empirical hypotheses because it is derived and defined wholly with expectations tests of empirical hypotheses with historical data require an additional proposition that relates ex ante and ex post returns a model for this second proposition is called a return generating equation arbitrage pricing theory gives a more compact method for deriving a linear ex ante security return model in the arbitrage theory developed by ross 6 the return generating equation is the basis for the ex ante return relationship briefly an approximate linear expected return equation is derived directly from the return generating equation so two separate models are not required in addition the ex ante return equation is defined in terms of an arbitrary number of special factor portfolio returns rather than a single market portfolio return in this sense arbitrage pricing theory has richer implications and a simpler structure than capital asset pricing arbitrage pricing theory starts with a linear return generating equation for each security

pricing and rebate policies in the two echelon supply chain with asymmetric information under price dependent stochastic demand abstract this paper analyzes the manufacturers strategy of optimizing the direct rebate to the final customer and the wholesale price to a profit maximizing retailer with a price dependent stochastic demand the manufacturer possesses full information about the cost and the functional relationship among demand price and rebate but may or may not know about the nature of the underlying demand uncertainty faced by the retailer the conditions under which a retailer benefits from passing on such information are identified the main features of the model are illustrated analytically and numerically using linear or iso elastic demand functions with additive or multiplicative error structures several important implications have been derived especially those dealing with price and rebate pass throughs and with the cost to the manufacturer of asymmetric information

integrated pricing and lot sizing decision in a two echelon supply chain with a finite production rate abstract in this paper we consider a supply chain consisting of a supplier and a retailer selling the product manufactured by the supplier in a market in which the demand for the product is decreasing in the price set by the retailer previous research on coordinating the supply chain with price sensitive demand often assumes that either the supplier purchases the product or the supplier has an infinitely large production rate we consider explicitly the supplier s finite production rate in the pricing and lot sizing decision which causes the problem much more challenging we first investigate the optimization problem in the decentralized scenario to find the optimal order quantity and selling price for the retailer as well as the optimal wholesale price and lot size multiplier for the supplier we then solve the joint optimization problem in the centralized supply chain to find the optimal order quantity the selling price and the optimal lot size multiplier we provide two sequential algorithms to solve the joint optimization problem computational experiments show that the algorithms are effective all 448 tested problems are solved optimally and efficient it only takes a few iterations to converge for each tested problem the supply chain coordination mechanism is then designed through an all unit quantity discount policy and a franchise fee

discount pricing decisions in distribution channels with price sensitive demand abstract in this paper we evaluate the effectiveness of quantity discounts and volume discounts as coordination mechanisms in distribution channels with demand that is price sensitive we consider a single vendor single retailer distribution channel demand for the product arises only at the retailer the demand faced by the retailer is assumed to be deterministic but price elastic the retailer in turn buys the product from the vendor the vendor and the retailer act independently and rationally each maximizing their own respective profit the equilibrium point that specifies the vendor s and buyer s inventory and pricing policy is determined by the solution to a stackelberg game we consider the cases when quantity discount and volume discount respectively are offered we develop methods to determine the optimal discount policy for these cases we then consider the case where both volume and quantity discounts are offered simultaneously and develop a method to determine the optimal simultaneous discount offer the relative performance of the alternative discount schemes is then evaluated through a numerical study the results of the study demonstrate that the effectiveness of volume discount as a coordination mechanism is higher when the sensitivity of demand to price changes is higher the effectiveness of quantity discount on the other hand is higher with lower price sensitivity of demand finally the results also demonstrate that perfect coordination is achieved when volume and quantity discounts are offered simultaneously

pricing and hedging interest rate options evidence from cap floor markets we examine the pricing and hedging performance of interest rate option pricing models using dailydata on us dollar cap and floor prices across both strike rates and maturities our results show that fitting the skew of the underlying interest rate probability distribution provides accurate pricing results within a one factor framework however for hedging performance introducing a second stochastic factor is more important than fitting the skew of the underlying distribution this constitutes evidence against claims in the literature that correctly specified and calibrated one factor models could replace multi factor models for consistent pricing and hedging of interest rate contingent claims 2004 elsevier b v all rights reserved

pricing and rebate policies for the newsvendor problem in the presence of a stochastic redemption rate abstract this paper develops the pricing rebate ordering policies of a profit maximizing vendor faced with a stochastic rebate redemption rate and a price rebate dependent random demand all within the single period framework of the newsvendor problem the profitability of these policies directly relates to the redemption rate which in turn depends upon the rebate value by itself and relative to the sales price a random element accounts for the uncertainty in the estimation of such rate the decision variables are the sales price the rebate value and the order size a numerical example and various sensitivity analyses illustrate the main managerial insights of the model one of the key results is that the introduction of uncertainty in the redemption rate contrary to what happens when moving from a deterministic to a stochastic demand leads the rebate policy to dominate its price discount counterpart

a joint optimal pricing rebate value and lot sizing model delayed incentives in the form of mail in cash rebates are very popular among manufacturers and more recently among retailers one of the main advantages of rebates is that while they increase demand a small proportion of consumers redeem them in this paper we formulate and solve models for jointly determining the optimal price rebate face value and the optimal order quantity for a price and rebate sensitive deterministic demand the models show that under realistic conditions offering rebates can have significant pricing and inventory policy implications and can lead to a significant increase in profit

a model to evaluate acquisition price and quantity of used products for remanufacturing abstract in this paper an analytical model is proposed to evaluate optimal acquisition price and quantity policy based on the quality of returned used products that are subsequently used for remanufacturing the model is developed from the perspective of a consolidation center which facilitates the collection of used products in various collection centers by offering an acquisition price based on the quality of used products receive all of the collected used products and consolidate them with replacement parts before sending the consignment to the remanufacturer it is assumed that the consolidation center receives an order from the remanufacturer for a set quantity and an associated price for used products in a quality level the consolidation center then evaluates optimal acquisition price and quantity policy for used products based on the available information on stochastic return quantity and quality and the cost of predefined set of replacement parts the policy so obtained is offered to the collection centers to initiate the collection of used products in their respective area of operation the impact of the model is studied through a numerical study the authors believe that the model developed here is the first such pricing model in a reverse logistics setting

coordinating price reductions and coupon events abstract in this article the authors use an economic model to show that it may be optimal to lower the retail price during a coupon event when marginal consumers have moderate hassle costs of coupon redemption results from the model offer predictions on the relationships among coupon redemptions shelf price and coupon face value the authors test these predictions on a large data set of hundreds of coupon events across six packaged goods categories the data show that when a small coupon face value is offered the shelf price is likely to be reduced they also find that coupon efficiency increases when there is a lower retail price the results are of interest to managers planning a promotion calendar and deciding whether to coordinate price promotions with coupon events and they contribute to economic theory when a firm moves from uniform pricing e g no coupons to second degree price discrimination e g coupons all consumers may face a lower price this finding has public policy implication

the pricing of options on default free bonds recent developments in the finance literature dealing with the valuation of contingent claims have been triggered by black and scholes 2 with their valuation of european options on corporate stocks the type of valuation model derived by black and scholes is attractive because it is independent of preferences this independence is possible due to the fact that the contingent claims are usually assumed to be contingent on traded assets or traded state variables for example a european call option is a claim contingent on the value of the corresponding stock to maintain the independence of the claim from preferences however some variables have to be discarded and considered as constants for example the rate of interest which is not a traded state variable is considered a constant in most of the literature see black and scholes 2 merton 11 and ingersoll 9 though this approximation might not cause important discrepancies in the case of corporate liabilities and options on corporate liabilities the effect of such an approximation on the value of default free bonds and options on default free bonds is more important since these liabilities depend only on the rate of interest

evaluation of callable bonds finite difference methods stability and accuracy the purpose of this paper is to evaluate numerically the semi american callable bond by means of finite difference methods this study implies three results first the numerical error is greater for the callable bond price than for the straight bond price and too large for real applications secondly the numerical accuracy of the callable bond price computed for the relevant range of interest rates depends entirely on the finite difference scheme which is chosen for the boundary points thirdly the boundary scheme which yields the smallest numerical error with respect to the straight bond does not perform best with respect to the callable bond the callable bond is a straight coupon bond with the provision that allows the debtor to buy back or to call the bond for a specified amount the call price plus the accrued interest since the last coupon date at some time the call date s during the life of the bond three types of callable bonds can be observed in financial markets the american callable bond may be repurchased at any time on or before the final redemption day in contrast to the european or semi american counterparts which may only be called at one or several specific dates respectively in the case of semi american bonds the debtor gives the bondholder two months notice the callable bond can be viewed as a compound security which consists of an otherwise identical straight bond and of an embedded call option which is not traded and the price of which is therefore not observable the embedded call option which is written on the underlying straight bond can be viewed as being sold by the initial

bond price dynamics and options this paper provides a closed form preference free means of valuing a european call option written on a default free pure discount bond investors may not agree upon a theory of the term structure but they will necessarily agree on equilibrium option values further these equilibrium option values may be obtained without recourse to numerical approximation default free pure discount bond prices were posited to follow a non standardized transformed brownian bridge process this specification implicitly incorporates the terminal constraint that the price of a default free pure discount bond equal its face value at maturity contingent claim valuation necessarily involves consideration of terminal constraints on the value of financial securities the brownian bridge specification permits an appropriate means of incorporating a number of such constraints therefore while this paper has considered only the application of the brownian bridge process to the valuation of debt options the introduction of this process may provide for many further financial applications

time dependent variance and the pricing of bond options in this paper we develop a model for valuing debt options that takes into account the changing characteristics of the underlying bond by assuming that the standard deviation of return is proportional to the bond s duration the resulting model uses the bond price as the single state variable and thus preserves much of the simplicity and robustness of the black scholes approach the paper provides comparisons between option prices computed using this model and those using the black scholes and brennan and schwartz models the last decade has seen a dramatic increase in the volatility of bond markets leading to a growing interest in financial instruments that can be used to hedge this risk thus in the u s canada and the u k there has been a proliferation of new interest rate dependent securities such as bond futures options on bonds options on bond futures swap agreements and bonds with option features such as callability putability retractability and so forth with the development of these markets the problems of valuation and the derivation of the hedging strategies have become subjects of increasing importance to both practitioners and academics several valuation methods have been suggested in the literature but so far no consensus has emerged as to the best solution to these problems the simplest approach to the valuation of debt options and probably the most widely used in practice is the black scholes model 3 this method originally developed for the valuation of stock options assumes that the variance of the rate of return on the underlying security is constant while this assumption is plausible for common stocks it is clearly unreasonable for bonds with a finite maturity the distinctive feature of the problem of debt option valuation is that the characteristics of the underlying asset change over time because the price is constrained to converge to the face value of the bond at maturity a second drawback of the black scholes approach is that it assumes a constant short term interest rate an assumption that is clearly inconsistent with stochastic returns on bonds in spite of these problems the black scholes model has been frequently used in practice to value debt options because of its overwhelming simplicity in comparison with other available methods

exchange rate exposure abstract in this paper we examine the relationship between exchange rate movements and firm value we estimate the exchange rate exposure of publicly listed firms in a sample of eight non us industrialized and emerging markets we find that exchange rate movements do matter for a significant fraction of firms though which firms are affected and the direction of exposure depends on the specific exchange rate and varies over time suggesting that firms dynamically adjust their behavior in response to exchange rate risk exposure is correlated with firm size multinational status foreign sales international assets and competitiveness and trade at the industry level

stochastic volatility movements in short term interest rates and bond option values abstract two classes of models for pricing interest rate contingent claims are compared the first contains standard single factor models while the second includes stochastic volatility variants of these it is demonstrated that incorporating stochastic volatility significantly improves the ability of the models to fit movements in short term interest rates the fundamental reason for this is that standard univariate models do not generate enough conditional heteroskedasticity the models are also compared on the basis of bond option prices when each is constrained to fit a particular yield curve the results suggest that stochastic volatility models will typically produce lower option values than corresponding single factor models particularly for near the money to deep out of the money options this is because estimated historical volatilities are significantly lower under stochastic volatility when single factor models are constrained to the same level of volatility as implied by stochastic volatility models in most cases the pricing differences become minor

changes in sectoral composition associated with economic growth in this paper the author uses dynamic general equilibrium methods to examine the interrelationship between sectoral composition and growth she shows that growth is affected by sectoral composition and vice versa the model is basically a solow model of sustained growth with multiple consumption goods and nonhomothetic preferences each consumption good is produced using different factor intensities the rate of exogenous technological change is different in each sector nonhomotheticity of preferences drives the result that sectoral composition affects growth rates copyright 1997 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

consumer inattention and bill shock regulation for many goods and services such as electricity health care cellular phone service debit card transactions or those sold with loyalty discounts the price of the next unit of service depends on past usage as a result consumers who are inattentive to their past usage but are aware of contract terms may remain uncertain about the price of the next unit i develop a model of inattentive consumption derive equilibrium pricing when consumers are inattentive and evaluate bill shock regulation requiring firms to disclose information that substitutes for attention when inattentive consumers are sophisticated but heterogeneous in their expected demand bill shock regulation reduces social welfare in fairly competitive markets which may be the effect of the federal communication commission s recent bill shock agreement if some consumers are attentive while others naively fail to anticipate their own inattention however then bill shock regulation increases social welfare and can benefit consumers hence requiring zero balance alerts in addition to the federal reserve s new opt in rule for debit card overdraft protection may benefit consumers

inventory policies under various optimizing criteria and variable markup rates this paper extends the deterministic eoq model to reflect various optimizing criteria and alternative demand and price structures its primary purpose is to develop decision rules for the management of finished goods inventories especially in retailing where inventories are evaluated in the same way as any other investment namely on their ability to generate profits rather than on the traditional least cost basis to that effect the models developed here consider demand to be a function of price with price defined as a markup of unit cost the decision variables are the order quantity and the markup rate possible optimizing objectives include profits return on investment or residual income the three most widely used evaluators of short term investment performance optimal solutions for each case are obtained and the resulting inventory policies evaluated

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

on the determinants of the value of call options on default free bonds the fundamental determinants of the value of an option on a bond are the level and slope of the term structure and the level of interest rate uncertainty competing models that have been developed to price bond options produce similar estimates as long as those models are conditioned on similar values for the fundamental determinants this result is established for simple options with known closed form solutions and for more complex options that require numerical methods for evaluation the finding is confirmed for a wide range of economic conditions and it is shown to be robust with respect to the number and nature of factors that generate interest rate movements copyright 1990 by the university of chicago

the valuation of options on coupon bonds abstract we derive simple closed form expressions for european options on coupon bonds using the general equilibrium term structure framework of cox ingersoll and ross the properties of these options are very different from those implied by the black scholes model for example bond call and put values can move in the same direction as the value of the underlying bond changes this has important implications for hedging interest rate risk with bond options furthermore bond option values can be decreasing functions of interest rate volatility as well as their time to expiration we also examine the properties of american bond options

a reexamination of exchange rate exposure finance theory suggests that changes in exchange rates should have little influence on asset prices in a world with integrated capital markets indeed the existing literature examining the relationship between international stock prices and exchange rates finds little evidence of systematic exchange rate exposure we argue in this paper that the absence of evidence may be due to restrictions imposed on the sample of data and the empirical specifications used in previous studies we study a broad sample of firms in eight countries over an eighteen year period we find that firm level and industry level share values are significantly influenced by exchange rates further we do not find evidence that exchange rate exposure is falling or becoming less statistically significant over time our results suggest that significant firm industry and country specific differences remain even as financial markets become more and more integrated

a cointegration study of the efficiency of the us treasury strips market one theoretical implication of cointegration according to granger 1986 is that asset prices in an efficient market cannot be cointegrated using price data on us treasury strips with maturities from 2 15 1997 to 8 15 2015 it is found that a set of three strips series is often cointegrated in addition by setting up a costless hedge portfolio from three strips with three different maturities it is found that the hedge portfolio is often stationary and thus arbitrage opportunities are likely to occur that is because the hedge portfolio is costless and stationary cash in can be done when the value of the hedge portfolio is either positive or negative however when taking liquidity tax effects and transaction costs into consideration these arbitrage profits would be unlikely hence it is concluded that the us treasury strips market is efficient

services sector and economic growth in india this study examines the long run equilibrium and short run dynamic relationship between services sector and gross domestic product gdp and between services and nonservices sectors in india the model is estimated using the optimal single equation and the maximum likelihood system estimators all the estimators consistently suggest the cointegrating relationship between services sector and gdp as well as between services and nonservices sectors the estimates of long run elasticity parameters are statistically significant and dimensionally consistent across the estimators the conventional cumulative sum cusum and the new cusum and moving sum mosum tests suggest the stability of the equilibrium residuals and reinforce the cointegrating relationship between the model series the error correction model provides some support for unidirectional granger causality from services sector to gdp the impulse response and variance decomposition analyses instead suggest the bidirectional causality between servic

optimal pricing and lot sizing under conditions of perishability and partial backordering we formulate a generalized model of dynamic pricing and lot sizing by a reseller who sells a perishable good we assume that when it is economic to backlog demand the reseller can plan for periods of shortage during which demand can be partially backordered when the good is highly perishable the reseller may need to backlog demand in order to market the good at a reasonable price we present a simple solution procedure for solving the optimization problem the procedure entails solving first a single nonlinear equation and then if required two nonlinear equations

simultaneous and dynamic price production inventory and capacity decisions abstract this paper concerns a profit maximizing firm that derives the optimal price for its output level of output level of inventory and composition of productive capacity over time first it is assumed that capacity may be acquired to either increase or replace the firm s existing productive capacity second it is assumed that the acquisition of new capacity causes a reduction in the firm s production cost lastly it is assumed that demand which is expressed as a function of time and price must be met either from current production or from inventory clearly the level of production cannot exceed the productive capacity at any time the optimal control model formulated requires the solution of a two point boundary value problem so that a discrete approximation numerical procedure is presented numerical results indicate that due to anticipated technological improvement the acquisition of new capacity is postponed and occurs in greater magnitude later in the planning horizon in addition as a result of upgrading productive capacity through the acquisition of new technology numerical results show that a firm lowers its per unit production cost and thereby reduces the optimal price charged for output which increases demand furthermore since the level of capacity is increased due to the purchase of new technology less reliance on inventory is necessary to meet peak demand lastly it is shown that a larger firm optimally acquires a greater level of new capacity over the planning horizon to reduce its operating costs and thereby further its competitive advantage

valuing debt options empirical evidence abstract a two factor model using the instantaneous rate of interest and the return on a consol bond to describe the term structure of interest rates the brennan schwartz model is used to derive theoretical prices for american call and put options on us government bonds and treasury bills these model prices are then compared with market prices the theoretical model used to value the dept options also provides hedge ratios which may be used to construct zero investment portfolios which in theory are perfectly riskless several trading strategies based on these riskless portfolios are examined

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

the volatility of short term interest rates an empirical comparison of alternative models of the term structure of interest rates we estimate and compare a variety of continuous time models of the short term riskless rate using the generalised method of moments we find that the most successful models in capturing the dynamics of the short term interest rate are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rate a number of well known models perform poorly in the comparisons because of their implicit restrictions on term structure volatility we show that these results have important implications for the use of different term structure models in valuing interest rate contingent claims and in hedging interest rate risk

a joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive this paper considers the seller buyer channel in which the end demand is price sensitive and the seller may offer trade credit to the buyer the unit price seller charged by the seller and the length of the credit period offered by the seller to the buyer both influence the final demand for the product hence we consider both to be policy variables for the seller we use the case of no credit as a benchmark in our analysis the paper provides procedures for determiningthe seller s and the buyer s policies under non cooperative as well as cooperative relationships in the non cooperative case we determine for the seller the optimal unit price and the length of the credit period for the cooperative structure we provide a procedure for characterizingpareto efficient solutions r 2002 elsevier science b v all rights reserved

government bond returns measurement of interest rate risk and the arbitrage pricing theory empirical tests are reported for ross arbitrage pricing theory using monthly data for u s treasury securities during the 1960 1979 period we find that mean returns on bond portfolios are linearly related to at least two factor loadings multivariate test results however are not consistent with the apt our sample data in the u s treasury securities market are also not consistent with either version of the capm one monthahead forecasts of excess returns using factor generating models are compared with corresponding naive predictions or predictions using the market model with various

optimal prices and order quantities when temporary price discounts result in increase in demand abstract suppliers often offer temporary price discounts to retailers the discount motivates retailers to increase their order quantity and offer a discount to their customers to increase demand and profit in this paper the change in price and the resulting change in demand and their effect on inventory policy and total profit is analyzed simultaneously to determine retailer s optimal price and optimal ordering policies the simultaneous analysis considers the joint effect of marketing and inventory policies on profits and prohibits the suboptimality that is inherent in the customarily serial treatment of these policies this paper uses a general price demand relationship and develops general models for determining optimal price and order quantity any specific price demand relationship may be substituted in these models to determine the optimal price and optimal order quantity for specific cases