jump diffusion processes and the term structure of interest rates the authors investigate the term structure of interest rates when the underlying state variables and production technologies follow the jump diffusion processes even in some cases where the traditional expectations theory about the term structure is consistent with general equilibrium under diffusion processes the traditional theory is not consistent under jump diffusion processes it is shown that bond prices are strictly higher under jump risks than otherwise and that consumers with logarithmic utility functions will develop hedge portfolios in the presence of jump diffusion a number of continuous time asset pricing models have been derived under stochastic diffusion processes with continuous sample paths see e g black and scholes 2 merton 21 breeden 3 and cox ingersoll and ross 8 however recent empirical studies see e g brown and dybvig 4 feinstone 10 and jarrow and rosenfeld 17 suggest that the underlying processes may follow

a comparison of average and discounted cost models for the dynamic lot size inventory problem abstract it is a common practice in the inventory literature to use average cost models as approximations to the theoretically correct discounted cost models an average cost model minimizes the average undiscounted cost per period while a discounted cost model minimizes the total discounted cost over the problem horizon this paper attempts to answer an important question how good are the results the total discounted costs for the average cost models compared to those for the discounted cost models this question has been conclusively answered for the simplest inventory model where the demand rate and other parameters are assumed to remain constant in time this paper addresses this issue for the first time for the case where demand rates are allowed to be nonstationary in time a discounted cost model has been developed in the paper to carry out this comparison it is shown that a simple dynamic programming algorithm can be used to find optimal order policies for the discounted cost model the effect of the varying interest rates and other parameters on the relative performance of the average cost model has been studied by developing an insightful analysis and also by doing a computational study the results show that while the average cost model can cost as much as about 26 more than the discounted cost model in extreme cases this increase is not significant for the parameter values in the range of the common interest

optimal lot sizing for an unreliable production system based on net present value approach abstract the paper considers the net present value npv approach to determine the economic manufacturing quantities for an unreliable production system over an infinite planning horizon the npv of the expected total cost is obtained under general failure time and general repair time distributions and its asymptotic characteristics are examined by perturbation of the instantaneous discount rate the criteria for the existence and uniqueness of the optimal production time lot size are derived under exponential failure and constant zero repair time the performance of the npv model is compared with the traditional long run average cost model in terms of the npv of the expected total cost based on the optimal decisions of the two models from numerical experiments it is observed that the decision based on the average cost can be 10 worse than the decision based on the npv depending upon the machine failure rate

an extended production recycling model with stationary demand and return rates abstract a production recycling system is investigated a constant demand can be satisfied with production and recycling the used items are bought back and then recycled the non recycled products are disposed of two types of models will be analyzed the first model examines the eoq related costs and minimizes the relevant costs the second model generalizes the first model with the introduction of the cost function with linear waste disposal recycling production and buyback costs it is asked whether the pure either production or recycling or mixed strategies are optimal and it will be shown that under these circumstances the mixed strategies are dominated by the pure strategies the paper generalizes a former model proposed by the authors for the case of one recycling and one production batch to the case of arbitrary batch numbers

optimal monopolist pricing under demand uncertainty in dynamic markets we examine pricing policy for a monopolist facing uncertain demand in a market characterized by dynamics on the demand side such as diffusion or saturation effects and or on the cost side experience curve effects our model explicitly incorporates the impact of demand uncertainty and thus allows us to analyze the implications of uncertainty on the optimal price path by contrasting the stochastic policy with the corresponding deterministic policy we begin with an analysis of the general model and then focus on several special cases based on well known demand specifications to gain more specific insights and to suggest directional guidelines for dynamic pricing decisions in an uncertain environment in general the interaction among uncertainty demand and or cost dynamics and firm s discount rate thus farsighted firms operating under dynamic market conditions with high demand uncertainty such as high tech companies with innovative products for consumer or industrial markets should attach partic

lp modeling for asset liability management a survey of choices and simplifications dynamic linear programming lp models for asset liability management alm are quite powerful and flexible but face two challenges 1 many modeling choices not all consistent with one another or with finance theory and 2 solution difficulties due to the large number of scenarios obtained from standard interest rate models we first survey these modeling choices with a view to help researchers make self consistent choices next we review how the dynamic lp model for alm and the representation of uncertainty therein have been simplified in the past to motivate new or hybrid models emphasizing tractability to this end we review existing static lp models as extreme modeling simplifications and aggregation as a simplification of uncertainty

the effects of inflation and time value of money on an economic order quantity model with a random product life cycle abstract for several decades the economic order quantity eoq model and its variations have received much attention from researchers recently there has been an investigation into an eoq model incorporating a random product life cycle and the concept of time value of money this paper extends the previous research in several areas first we investigate the impact of inflation on the choice of replenishment quantities second the unit cost which has been inadvertently omitted in the previous research is included in the objective function to properly model the problem third we consider the normal distribution as a product life cycle in addition to the exponential distribution fourth we develop a simulation model which can be used for any probability distribution

interest rate volatility and the term structure a two factor general equilibrium model we develop a two factor general equilibrium model of the term structure the factors are the short term interest rate and the volatility of the short term interest rate we derive closed form expressions for discount bonds and study the properties of the term structure implied by the model the dependence of yields on volatility allows the model to capture many observed properties of the term structure we also derive closed form expressions for discount bond options we use hansen s generalized method of moments framework to test the cross sectional restrictions imposed by the model the tests support the two factor model there are essentially two approaches to the modeling of the term structure of interest rates in continuous time the equilibrium approach pioneered by

a cross functional approach to evaluating multiple line extensions for assembled products assembled product manufacturers often introduce line extensions that share components with existing products or among themselves resulting in cost interactions among products because of shared costs and revenue interactions because of cannibalization we present a cross functional approach to evaluating multiple line extensions that simultaneously considers revenue implications of component sharing at the product level and cost implications at the component level we develop a source of volume model and a measurement procedure to decompose the life cycle sales volume from a line extension into sales from cannibalization competitive draw and demand expansion we develop an activity based costing procedure for estimating the life cycle costs of line extensions that share components we develop an optimization model that uses these revenue and cost estimates to identify a subset of line extensions that maximizes incremental profits we implement our approach at a quartz wristwatch manufacturer results suggest that our approach would have improved profits for the firm by over 5 while actually launching fewer line extensions we also find that the drivers of cannibalization are counterintuitive in simulation studies our approach outperforms three managerial heuristics we demonstrate that this approach is most valuable when cannibalization dominates competitive draw as a source of volume and discuss its relative merits under low and high parts sharing

china s official rates and bond yields abstract recent research shows that bond yields are influenced by monetary policy decisions to learn how this works in a bond market that differs significantly from those in the us and europe we model chinese bond yields using the one year deposit interest rate as a state variable we also include the spread between the one year market interest rate and the one year deposit interest rate as another factor the model is developed in an affine framework and closed form solutions are obtained we then test the model empirically with a markov chain monte carlo simulation procedure the results show that the new model that incorporates the official rate in china characterizes the changing shape of the yield curve well

long forward and zero coupon rates can never fall in frictionless markets having no arbitrage the asymptotic zero coupon rate never falls the same is true of the long forward rate the long par coupon rate can rise and fall due to forward rate movements at short maturities this article relates the three types of interest rates and formalizes and proves the impossibility results for falling asymptotic rates these results can be tested in a parametric term structure specification that is rich enough to identify a time series of long rates the results show that it is not possible to specify arbitrarily the long forward or zero coupon rate process copyright 1996 by university of chicago press

the economic lot size and relevant costs abstract in many accounting textbooks it is strongly argued that decisions should always be evaluated on relevant costs that is variable costs and opportunity costs surprisingly when it comes to economic order quantities or lot sizes some textbooks appear to be less straightforward the question whether described eoq models are in fact based upon variable costs and opportunity costs is generally not explicitly dealt with this paper will investigate relevant costs if lot sizes in a components manufacturing plant are changed the nature of opportunity costs is examined and several kinds of semi variable costs regarding the use of infrastructural capacity and material flow are discussed in this manner it is shown that in eoq models sunk costs are always included it also occurs that variable costs must be analyzed carefully this is also the case for more advanced models as described by for instance wagner and within or bertrand opportunity costs are in fact neglected which nevertheless is not always that dramatic as some authors suggest

on arbitrage free pricing of interest rate contingent claims unlike most interest rate claim models the ho lee model utilizes full information on the current term structure unfortunately the model has a major deficiency in that negative interest rates can occur this article modifies the model such that interest rates are well behaved

an equilibrium model of bond pricing and a test of market efficiency in two previous and related papers 3 4 the authors have reported the results of estimating a particular equilibrium model of bond pricing using quarterly data on canadian government bonds for the period 1964 to 1979 this paper reports the results of applying a similar model to the pricing of u s government bonds for the period 1958 1979 using data from the crsp government bond file the paper also extends the previous empirical analysis by evaluating the ability of the pricing model to detect underpriced and overpriced bonds the data reveal a strong relation between price prediction errors and subsequent bond returns

ford whitman harris and the economic order quantity model ford whitman harris first presented the familiar economic order quantity eoq model in a paper published in 1913 even though harris s original paper was disseminated widely it apparently was unnoticed for many years before its rediscovery in 1988 during this period much confusion developed over the origin of the eoq model this paper explores the early literature on this model and traces the evolution of the confusion it also sketches the remarkable life of harris who made contributions as an engineer inventor author and patent attorney even though he received no formal education beyond high school harris s original 1913 essay is reprinted following this paper

tail estimation and mean var portfolio selection in markets subject to financial instability abstract risk managers are increasingly required by international regulatory institutions to adopt accurate techniques for the measurement and control of portfolios financial risks the task requires first the identification of the different risk sources affecting the portfolio and the measurement of their impact then after the adoption of appropriate portfolio strategies aimed at neutralising these risks the comprehensive concept of value at risk var as a maximum tolerable loss with a given confidence interval has become in this regard the industry standard in risk management in the paper we focus on the implications of different risk measurement techniques and portfolio optimisation strategies in presence of markets subject to periods of severe instability resulting in significant deviations of financial returns from the normality assumption typically adopted in mainstream finance comparative results on 1 day var 99 estimation are presented over a range of bond and equity markets with different risk profiles the reference period of our analysis includes several market shocks and in particular the argentinean eurobond crisis of july 2001 the solution of an optimal portfolio problem over the crisis period is discussed within a mean variance var99 portfolio space emphasising the difficulty of the portfolio s relative return maximisation problem faced by fund managers

jump diffusion option valuation in discrete time we develop a simple discrete time model to value options when the underlying process follows a jump diffusion process multivariate jumps are superimposed on the binomial model of cox ross and rubinstein 1979 to obtain a model with a limiting jump diffusion process this model incorporates the early exercise feature of american options as well as arbitrary jump distributions it yields an efficient computational procedure that can be implemented in practice as an application of the model we illustrate some characteristics of the early exercise boundary of american options with certain types of jump distributions jump diffusion processes are popular in option valuation models these processes were incorporated by merton 1976 into the theory of option valuation and constitute an important alternative to the lognormal diffusion process assumed in the black and scholes 1973 model in this paper we develop a tractable discrete time model for valuing options with these processes many authors have suggested that incorporating jumps in option valuation models may explain some of the large empirical biases exhibited by the black scholes model 1 however in many cases closed form solutions for valuing options are not available for example this is true when there is a positive probability of early exercise when the jump distribution is neither lognormal nor discrete or when the option is based on the term structure of interest rates see ahn and thompson 1988 and jarrow and madan 1991 in these important cases the model developed in this paper can be used to value options another aim of this paper is to provide a model which relies on only simple mathematics to price options with jump diffusion processes it is hoped that the key economic relationships underlying jump diffusion models are transparent in this model we provide enough details to make the procedure readily accessible

a nonlinear general equilibrium model of the term structure of interest rates abstract we derive and test an alternative closed form general equilibrium model of the term structure within the cox ingersoll and ross theoretical framework in which yields are nonlinear functions of the risk free rate we show that equilibrium bond prices and the risk free rate are not always inversely related and that bond risk need not be strictly increasing in maturity using hansen s generalized method of moments to obtain parameter estimates this nonlinear model outperforms the cox ingersoll and ross square root model in describing actual treasury bill yields for the 1964 1986 period

continuous time methods in finance a review and an assessment i survey and assess the development of continuous time methods in finance during the last 30 years the subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing term structure theory asset pricing and optimal consumption and portfolio choices during the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance this latter subperiod has seen significant progress in econometric theory computational and estimation methods to test and implement continuous time models capital market frictions and bargaining issues are being increasingly incorporated in continuous time theory the roots of modern continuous time methods in finance can be traced back to the seminal contributions of merton 1969 1971 1973b in the late 1960s and early 1970s merton 1969 pioneered the use of continuous time modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting merton 1973b also showed how such a framework can be used to develop equilibrium asset pricing implications thereby significantly extending the asset pricing theory to richer dynamic settings and expanding the scope of applications of continuous time methods to study problems in financial economics 1 within a span of about 30 years from the publication of merton s inf luential papers continuous time methods have become an integral part of financial economics indeed in certain core areas in finance such as e g asset pricing derivatives valuation term structure theory and portfolio selection continuoustime methods have proved to be the most attractive way to conduct research and gain economic intuition the continuous time approach in these areas has produced models with a rich variety of testable implications the econometric theory for testing continuous time models has made rapid strides in the last decade and has thus kept pace with the impressive progress on the theoretical front one hopes that the actual empirical investigations and estimation using the new procedures will follow suit soon

the eoq models modified by introducing discount of purchase price or increase of setup cost abstract the eoq model of inventory problem can determine ordering cycle and quantity when the purchase unit price is constant ordering cycle and ordering quantity which minimize the one day s average inventory cost is not dependent on the purchase price but if purchase price may change the eoq model must be modified the purchase unit price is discounted as the ordering becomes larger the discount of purchase price is described with a decreasing function of ordering quantity this function is not always continuous with respect to the ordering quantity under this condition one day s average profit can be defined and we can determine ordering cycle and ordering quantity which maximize one day s average profit moreover we consider the situations under which the setup cost depends on the ordering quantity in this case the setup can be described with the increasing function of ordering quantity we show that the eoq model can be applied if it is modified by introducing the continuous setup cost function this function is not differentiable at some levels of ordering quantity

a joint economic lot size model with financial collaboration and uncertain investment opportunity establishing long term relationships among the members of a supply chain has become necessary to enhance the supply chain s competitiveness in a globalized environment besides coordinating operational decisions such as how much and when to produce or to order the members of a supply chain may also share financial resources or act jointly on the capital market this is important especially when companies have unequal access to capital for example because they are located in countries with different economic conditions and banking policies and or they have different credit ratings the joint financing of investments across the supply chain may thus ensure the stability of production and of the flow of products to the customers in addition it strengthens the established relationships among the supply chain members the paper at hand takes up these issues and presents a joint economic lot size model that allows investments financed cooperatively by the members of the supply chain in particular it considers a two stage single vendor single buyer supply chain and assumes that the vendor has the option to invest in increasing its production rate the outcome of these attempts to improve production capabilities however is uncertain and subject to an investment success probability due to different access to capital the vendor and the buyer may also share the investment and the outcome uncertainty which can be beneficial to both parties

an international study of tax effects on government bonds it is shown that coupon bonds alone are not sufficient to span time dated claims on ordinary income capital gains and non taxable wealth in an incomplete bond market where the pure dated claims are not spanned by existing bonds marginal rates of substitution between present consumption and pure dated claims on ordinary income capital gains income and non taxable wealth respectively can differ across bondholders however the relative pricing of coupon bonds in each of these countries is shown to be consistent with the tax status of the major non tax exempt holders of government debt

vrp revisited the impact of behavioural costs in balancing standardisation and variety abstract the objective of this paper is to bring a new element to the academic and industrial debate concerning the optimum level of variety in component design in mass production companies many authors have explored the trade off between functional and variety costs and this could be considered as a well acknowledged management issue at least from an engineering perspective nevertheless while defining the theoretically optimal level of component variety there are other elements more related to operators attitude or to operative conditions which may intervene and prevent effective exploitation of the existing variety these elements have been given scant attention in literature while they may play a relevant role in real organisations in this paper we will present a case study and an analytic model for these behavioural costs in manufacturing environments so as to show how the theoretically optimal amount of variety changes if one takes into account these aspects researchers and practitioners might leverage on this contribution in order to rejuvenate the variety reduction paradigm and to increase their awareness in designing and managing mass production manufacturing processes

unspanned stochastic volatility and fixed income derivatives pricing we propose a parsimonious unspanned stochastic volatility model of the term structure and study its implications for fixed income option prices the drift and quadratic variation of the short rate are affine in three state variables the short rate its long term mean and variance which follow a joint markov vector process yet bond prices are exponential affine functions of only two state variables independent of the current interest rate volatility level because this result holds for an arbitrary volatility process such a process can be calibrated to match fixed income derivative prices furthermore this model can be extended by relaxing the time homogeneity to fit any arbitrary term structure in its hjm form this model nests the analogous stochastic equity volatility model of heston 190 heston s l 1993 a closed form solution for options with stochastic volatility review of financial studies 6 327 343 in particular if the volatility process is specified to be affine closed form solutions for interest rate options obtain we propose an efficient algorithm to compute these prices an application using data on caps and floors shows that the model can capture very well the implied black spot volatility surface while simultaneously fitting the observed term structure c 2005 elsevier b v all rights reserved

implications of implicit credit spread volatilities on interest rate modelling abstract we test seven term structure models in the heath jarrow and morton 1992 class in order to find the best representation of the libor rate in interest rate markets after the credit crunch of 2007 the libor rate is considered as a risky rate subject to the credit risk of a generic counterparty whose credit quality is refreshed at each fixing date we study the volatilities of the credit spreads implicitly obtained from libor time series in order to understand how assumed volatility functions affect interest rate curve modelling and asset pricing we develop a model to estimate basis swap prices through the monte carlo simulations we compare obtained results and individuate systematic relations existing between the basis spread forecast error and both the accuracy in volatility modelling and the accuracy of the monte carlo estimates we analyse and document these relations by defining appropriate pricing error measures

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

revisiting foundations in lot sizing connections between harris crowther monahan and clark abstract while many review articles exist on deterministic lot sizing models used in the context of price and quantity discounts buyer vendor coordination supply chain management and joint economic lot sizing problems they do not convey the impact of important findings which date back to at least 2002 or in hindsight to 1984 as a result many recent articles still model the financial implications of lot sizing decisions without having the assurance that these models would help the firm s involved in maximising the net present value npv this paper therefore reviews these findings while adding also its own contributions as to convey the general importance to lot sizing theory we show that the underlying principles used in the four key articles that have led to a division in modelling approaches are in fact all in line with npv and argue that therefore there should not be these discrepancies that currently persist in the literature we establish the connections between these four strands of the literature using the solution to a simple variation of harris eoq model deriving thereby results from boyaci and gallego 2002 and beullens and janssens 2011 but showing their general applicability to any type of supply chain structure the breath of implications to deterministic lot sizing theory is illustrated using practical examples we present a stochastic version of the model of crowther 1964 which is arguably the least understood and applied model but on the other hand the most important one in realising how these modelling strands can be unified

a dynamic model for the forward curve this article develops and estimates a dynamic arbitrage free model of the current forward curve as the sum of i an unconditional component ii a maturity specific component and iii a date specific component the model combines features of the preferred habitat model the expectations hypothesis et and affine yield curve models it permits a class of low parameter multiple state variable dynamic models for the forward curve we show how to construct alternative parametric examples of the three components from a sum of exponential functions verify that the resulting forward curves satisfy the heath jarrow morton hjm conditions and derive the risk neutral dynamics for the purpose of pricing interest rate derivatives we select a model from alternative affine examples that are fitted to the fama bliss treasury data over an initial training period and use it to generate out of sample forecasts for forward rates and yields for forecast horizons of 6 months or longer the forecasts of this model significantly outperform those from common benchmark models jel c53 e43 e47 the structure of forward rates for fixed maturity loans to begin at various dates in the future can be inferred from the prices of treasury securities or directly observed from the extremely active eurodollar futures market the constellation of these rates or of the related yields plays a central role intheallocationofcapital therandombehaviorofthis yieldcurve or the relationship between the yields and the term to maturity is a subject of considerable theoretical and empirical study

discretized reality and spurious profits in stochastic programming models for asset liability management in the literature on stochastic programming models for practical portfolio investment problems relatively little attention has been devoted to the question how the necessarily approximate description of the asset price uncertainty in these models influences the optimal solution in this paper we will show that it is important that asset prices in such a description are arbitrage free descriptions which have been suggested in the literature are often inconsistent with observed market prices and or use sampling to obtain a set of scenarios about the future we will show that this effectively introduces arbitrage opportunities in the optimization model for an investor who cannot exploit arbitrage opportunities directly because of market imperfections and trading restrictions we will illustrate that the presence of such arbitrage opportunities may cause substantial biases in the optimal investment strategy

term structure movements and pricing interest rate contingent claims this paper derives an arbitrage free interest rate movements model ar model this model takes the complete term structure as given and derives the subsequent stochastic movement of the term structure such that the movement is arbitrage free we then show that the ar model can be used to price interest rate contingent claims relative to the observed complete term structure of interest rates this paper also studies the behavior and the economics of the model our approach can be used to price a broad range of interest rate contingent claims including bond options and callable bonds

broader product line a necessity to achieve success strategic product line breadth decisions evoke differential responses from the manufacturing and the marketing areas manufacturing prefers keeping process disruptions to a minimum and as a result discourages product proliferation however marketing in its attempt to match products to heterogeneous consumer needs and gain market share emphasizes a broader product line we systematically investigate the market benefits and cost disadvantages of broader product lines on a large sample of over 1 400 business units our results indicate significant market share benefits and increases in firms profitability with broader product lines moreover widely held beliefs of increases in production costs are not empirically supported american manufacturing firms may indeed be flexible enough to accommodate product variety without significant detrimental effects on costs

some international evidence on the stochastic behavior of interest rates abstract this paper examines the stochastic behavior of short term interest rates in eleven countries following chan et al 1992a we consider eight stochastic models of short term interest rates all of which are nested within a discretized approximation to a differential equation we use the generalized method of moments to estimate the model the empirical results show that no single model can satisfactorily describe the stochastic structure of interest rates for all countries on balance if we classify the sample countries according to the size of the elasticity of variance of short term interest rates france holland and the usa belong to the group of high elasticity in comparison australia belgium germany and japan belong to the group of medium elasticity while canada italy switzerland and the uk belong to the group of low elasticity

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

the discounted r q inventory model the shrewd accountant s heuristic abstract the discounted continuous review r q inventory model with continuous and stochastic demand is investigated new optimality conditions are derived clarifying the difference to the average cost case also graphically supported by depreciation theory applied to the value of a setup the results suggest an insightful and very precise approximation the shrewd accountant s heuristic based on a new average cost model it deepens and extends the work of hadley 1964 three examples are worked out in detail and the model is generalized to poisson demand and to stochastic lead times

eoq and inflation uncertainty abstract inflation uncertainty is introduced into a basic eoq model and its potential to make mischief is explored among other things it is shown that even when the expected rate of inflation is less than the marginal cost of capital the appropriate discount rate to use in computing a discounted expected total inventory cost will not necessarily be negative therefore the classic eoq square root formula may drastically underestimate the optimal lot size the results may be generalized to the more complex inventory models

the analysis and valuation of interest rate options abstract this paper provides a simple alternative model for the valuation of european style interest rate options the assumption that drives the hedging argument in the model is that the forward prices of bonds follow an arbitrary two state process later this assumption is made more specific by postulating that the discount on a zero coupon bond follows a multiplicative binomial process in contrast to the black scholes assumption applied to zero coupon bonds the limiting distribution of this process has the attractive features that the zero bond price has a natural barrier at unity thus precluding negative interest rates and that the bond price is negatively skewed the model is used to price interest rate options in general and interest rate caps and floors in particular the model is then generalized and applied to european style options on bonds a relationship is established between options on swaps and options on coupon bonds the generalized model then provides a computationally simple formula closely related to the black scholes formula for the valuation of european style options on swaps

on measuring credit risks of derivative instruments abstract this paper critically reviews current practices for measuring credit risks of derivative instruments it argues that there are two major problems with the standard measurement approach first it uses models of the stoachstic behavior of finanacial variables while ignoring both their inherent oversimplification and the uncertainty in their parameters second it ignores the correlations among exposures in derivative intruments and the probabilities of countrypartly default this paper deomonstrates that these practices can produce large errors in the estimation of distribution of both future credit exposures and future credit losses

inventory ordering policies of delayed deteriorating items under permissible delay in payments abstract the existing literature on inventory of deteriorating items considers deterioration to begin as soon as the items are stocked however there are several deteriorating items that do not start deteriorating immediately they are held in stock some farm produce like potatoes yams and even some fruits and vegetables have this property depletion of these items as soon as they are stocked will depend on demand and when deterioration begins it will depend on both demand and deterioration in this paper we develop a mathematical model on the inventory of deteriorating items that do not start deteriorating immediately they are stocked the model also takes into cognizance the fact that in business activities nowadays customers are given some allowed period within which to settle for the goods supplied to them they can use the accrued money from sales of the supplied goods to earn interest within the allowed period they are charged interest only when they fail to settle the amount they owe the supplier at the end of the allowed period

a century of evolution from harris s basic lot size model survey and research agenda abstract determining the economic lot size has always represented one of the most important issues in production planning this problem has long attracted the attention of researchers and several models have been developed to meet requirements at minimum cost in this paper we explore and discuss the evolution of these models during one hundred years of history starting from the basic model developed by harris in 1913 up to today following harris s work a number of researchers have devised extensions that incorporate additional considerations the evolution of eoq theory strongly reflects the development of industrial systems over the past century here we outline all the research areas faced in the past by conducting a holistic analysis of 219 selected journal papers and trying to give a comprehensive view of past work on the eoq problem finally a new research agenda is proposed and discussed

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

the effect of commonality on safety stock in a simple inventory model we examine the effects of component commonality on optimal safety stock levels in a two product two level inventory model the criterion is to minimize system safety stock subject to a service level constraint although our model is specialized its analysis provides insights not available in other multilevel inventory models

the economics of product variety a survey demand for variety may arise from a taste for diversity in individual consumption and or from diversity in tastes even when each consumer chooses a single variant the full degree of variety potentially demanded will not in general be supplied because scale economies even to a small degree mean that the potential welfare or revenue gain from greater variety must be balanced against the lower unit production costs with fewer variants the economics of product variety consists essentially in analysing the effect of this balance in different situations and comparing the degree of product variety for different market structures with each other and with the optimum the survey commences with the work on market structures with single product firms generalized monopolistic competition tracing modern developments in both the chamberlinian and hotelling traditions the latter has been particularly fruitful due to the expansion of the original locational ideas into virtual spaces in product characteristics the emphasis in recent work on product variety has been on multiproduct firms in both monopolistic and oligopolistic structures including strategic market preemption although most work has been in a full information context there have been advances in product variety under imperfect information either by consumers to properties of the firms products or firms as to consumers demands

one factor interest rate models and the valuation of interest rate derivative securities this paper compares different approaches to developing arbitrage free models of the term structure it presents a numerical procedure that can be used to construct a wide range of one factor models of the short rate that are both markov and consistent with the initial term structure of interest rates

the intersection of market and credit risk abstract economic theory tells us that market and credit risks are intrinsically related to each other and not separable we describe the two main approaches to pricing credit risky instruments the structural approach and the reduced form approach it is argued that the standard approaches to credit risk management creditmetrics creditrisk and kmv are of limited value when applied to portfolios of interest rate sensitive instruments and in measuring market and credit risk empirically returns on high yield bonds have a higher correlation with equity index returns and a lower correlation with treasury bond index returns than do low yield bonds also macro economic variables appear to influence the aggregate rate of business failures the creditmetrics creditrisk and kmv methodologies cannot reproduce these empirical observations given their constant interest rate assumption however we can incorporate these empirical observations into the reduced form of jarrow and turnbull 1995b drawing the analogy risk 5 63 70 model here default probabilities are correlated due to their dependence on common economic factors default risk and recovery rate uncertainty may not be the sole determinants of the credit spread we show how to incorporate a convenience yield as one of the determinants of the credit spread for credit risk management the time horizon is typically one year or longer this has two important implications since the standard approximations do not apply over a one year horizon first we must use pricing models for risk management some practitioners have taken a different approach than academics in the pricing of credit risky bonds in the event of default a bond holder is legally entitled to accrued interest plus principal we discuss the implications of this fact for pricing second it is necessary to keep track of two probability measures the martingale probability for pricing and the natural probability for value at risk we discuss the benefits of keeping track of these two measures

an empirical comparison of forward rate and spot rate models for valuing interest rate options our main goal is to investigate the question of which interest rate options valuation models are better suited to support the management of interest rate risk we use the german market to test seven spot and forward rate models with one and two factors for interest rate warrants for the period from 1990 to 1993 we identify a one factor forward rate model and two spot rate models with two factors that are not significantly outperformed by any of the other four models further rankings are possible if additional criteria are applied

lattice models for pricing american interest rate claims this article establishes efficient lattice algorithms for pricing american interest sensitive claims in the heath jarrow and morton paradigm under the assumption that the volatility structure of forward rates is restricted to a class that permits a markovian representation of the term structure the class of volatilities that permits this representation is quite large and imposes no severe restrictions on the structure for the spot rate volatility the algorithm exploits the markovian property of the term structure and permits the efficient computation of all types of interest rate claims specific examples are provided

pricing derivatives on financial securities subject to credit risk this article provides a new methodology for pricing and hedging derivative securities involving credit risk two types of credit risks are considered the first is where the asset underlying the derivative security may default the second is where the writer of the derivative security may default we apply the foreign currency analogy of jarrow and turnbull 1991 to decompose the dollar payoff from a risky security into a certain payoff and a spot exchange rate arbitrage free valuation techniques are then employed this methodology can be applied to corporate debt and over the counter derivatives such as swaps and caps the purpose of this article is to provide a new theory for pricing and hedging derivative securities involving credit risk two sources of credit risk are identified and analyzed the first is where the asset underlying the derivative security may default paying off less than promised this is the case for example with imbedded options on corporate debt the second is the credit risk introduced by the writer of the derivative security who may also default examples include over the counter writers of options on eurodollar futures swaps and swaptions for pricing derivative securities involving credit risk there are currently two approaches the first views these derivatives as contingent claims not on the financial securities themselves but as compound options on the assets underlying the financial securities this is the case for example with the pricing of imbedded options on corporate debt see merton 1974 1977 black and cox 1976 ho and singer 1982 chance 1990 and kim ramaswamy and sundaresan 1993 or the pricing of vulnerable options see johnson and stulz 1987 in practice however this valuation methodology is difficult to use first the assets underlying the financial security are often not tradeable and therefore their values are not observable this makes application of the theory and estimation of the relevant parameters problematic second as in the case of corporate debt all of the other liabilities of the firm senior to the corporate debt must first and simultaneously be valued this generates significant computational difficulties as a result this approach has not

risk management of non maturing liabilities abstract risk management of non maturing liabilities is a relatively unstudied issue of significant practical importance non maturing liabilities include most of the traditional deposit accounts like demand deposits savings accounts and short time deposits and form the basis of the funding of depository institutions therefore the asset and liability management of depository institutions depends crucially on an accurate understanding of the liquidity risk and interest rate risk profile of these deposits in this paper we propose a stochastic three factor model as general quantitative framework for liquidity risk and interest rate risk management for non maturing liabilities it consists of three building blocks market rates deposit rates and deposit volumes we give a detailed model specification and present algorithms for simulation and calibration our approach to liquidity risk management is based on the term structure of liquidity a concept which forecasts for a specified period and probability what amount of cash is available for investment for interest rate risk management we compute the value the risk profile and the replicating bond portfolio of non maturing liabilities using arbitrage free pricing under a variance minimizing measure the proposed methodology is demonstrated by means of a case study the risk management of savings accounts

currency option pricing with mean reversion and uncovered interest parity a revision of the garman kohlhagen model abstract we consider a model for the pricing of currency options where the logarithm of the exchange rate exhibits mean reversion i e follows the omstein uhlenbeck process we mention reasons why exchange rates could exhibit mean reversion the domestic and foreign short interest rates are related to the logarithm of the exchange rate through uncovered interest parity under these assumptions we derive formulas for the value of a european currency option from the point of view of both domestic and foreign investors we also derive formulas for options on forward and futures contracts we compare option values computed by means of the garman kohlhagen model with corresponding results from our model it appears that our model cannot explain all instances of mispricing of currency options by the garman kohlhagen model which have been reported by previous authors the main virtue of our paper however is that we derive a simple model which incorporates clear theoretical relationship between the exchange rate and the domestic and foreign interest rates

single factor heath jarrow morton term structure models based on markov spot interest rate dynamics this paper considers the class of heath jarrow morton term structure models where the spot interest rate is markov and the term structure at time t is a function of time maturity and the spot interest rate at time t a representation for this class of models is derived and i show that the functional forms of the forward rate volatility structure and the initial forward rate curve cannot be arbitrarily chosen i provide necessary and sufficient conditions indicating which combinations of these functional forms are allowable i also derive a partial differential equation representation of the term structure dynamics that does not require explicit modeling of both the market price of risk and the drift term for the spot interest rate process using the analysis presented in this paper a class of intertemporal term structure models is derived

dynamic models of the term structure in the past 25 years tremendous progress has been made in modeling the dynamics of the term structure of interest rates which play an instrumental role in determining prices and hedging portfolios of fixed income derivative securities this article reviews the theoretical development of the dynamic models of the default free term structure and their applications in pricing interest rate options classic models sometimes termed equilibrium models and their multifactor extensions are outlined these models provide clear economic intuitions connecting the term structure with economic fundamentals they also lay a foundation for the framework of the arbitrage models that price interest rate derivatives on the basis of the market prices of bonds this framework has been expanded and enriched by recent advances in directly modeling observable market rates through the market models and in incorporating an internally consistent correlation structure through the infinite dimensional models

a multifactor spot rate model for the pricing of interest rate derivatives we propose a multifactor model in which the spot rate libor follows a lognormal process with a stochastic conditional mean under the risk neutral measure in addition to the spot rate factor the second factor is related to the premium of the first futures rate over the spot libor similarly the third factor is related to the premium of the second futures rate over the first futures rate we calibrate the model to the initial term structure of futures rates and to the implied volatilities of interest rate caplets we then apply the model to price interest rate derivatives such as european and bermudan style swaptions and yieldspread options the model can be employed to price more complex interest rate derivatives such as path dependent derivatives or multi currency dependent derivatives because of its markovian property

adapting inventory models for handling various payment structures using net present value equivalence analysis beullens patrick univ southampton southampton so17 1bj hants england janssens gerrit k univ southampton southampton sch management southampton so17 1bj hants england janssens gerrit k hasselt univ res grp logist b 3590 diepenbeek belgium

bond pricing and the term structure of interest rates a discrete time approximation this paper studies the binomial approximation to the continuous trading term structure model of heath jarrow and morton 1987 the discrete time approximation makes the original methodology accessible to a wider audience and provides a computational proce dure necessary for calculating the contingent claim values derived in the continuous time paper this paper also extends and generalizes ho and lee s 1986 model to include multiple random shocks to the forward rate process and to include an analysis of continu ous time limits the generalization provides insights into the limitations of the existing empirical implementation of ho and lee s model

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

estimating value at risk under a heath jarrow morton framework with jump this article proposes a new methodology for measuring value at risk hereafter var using a model that incorporates both volatility and jumps heath jarrow morton hjm model has been used for the valuation of interest rate derivatives this study extends the use of hjm model to the estimation var this article specifically uses a two factor hjm jump diffusion model for the computation the study models the eurodollar futures prices using its derivatives in addition this article uses a new volatility specification of ze to 2002 to construct the hjm dynamics the result indicates that the var model using hjm jump diffusion framework performs well in capturing the nonnormality and in providing accurate var forecasts in the in sample and out sample tests

holding costs under push or pull conditions the impact of the anchor point holding costs are traditionally determined from the investment in physical stock during a cycle an alternative approach instead derives holding costs from net present value npv functions it is known that applying both frameworks to the same system can lead to different holding cost valuations but little explanation has been offered by introducing the anchor point in a model this paper shows for four different systems that traditional holding cost models implicitly assume pull conditions while current npv approaches model push conditions this explains in part the differences between the methods it is shown that the anchor point concept allows the construction of npv models under pull conditions giving results in better correspondence with traditional models the traditional framework is restricted to pull conditions and important considerations could be easily overlooked leading to wrong valuations of holding costs npv seems superior as such considerations are automatically incorporated the application to multi echelon inventory systems provides interesting insights on the roles of echelon stocks and lead times and offers potential for future research

a cyclical square root model for the term structure of interest rates this paper presents a cyclical square root model for the term structure of interest rates assuming that the spot rate converges to a certain time dependent long term level this model incorporates the fact that the interest rate volatility depends on the interest rate level and specifies the mean reversion level and the interest rate volatility using harmonic oscillators in this way we incorporate a good deal of flexibility and provide a high analytical tractability under these assumptions we compute closed form expressions for the values of different fixed income and interest rate derivatives finally we analyze the empirical performance of the cyclical model versus that proposed in cox et al 1985 and show that it outperforms this benchmark providing a better fitting to market data

pricing contingent claims under interest rate and asset price risk this paper presents a general framework for pricing contingent claims under interest rate and asset price uncertainty the framework extends ho and lee s 1986 valuation framework by allowing not only future interest rates but also future asset prices to depend on the current term structure of interest rates the approach is shown to provide risk neutral valuation relationships that are consistent with the initial term structure of interest rates and can be applied to valuation of a broad class of assets including stock options convertible bonds and junk bonds

on the cost of capital in inventory models with deterministic demand abstract in the operations management literature the financial risk in an inventory model is usually assumed to be captured by the constant weighted average cost of capital wacc of the firm this assumption is at best an approximation since this cost depends on the risk of the cash flows which in turn depends on the inventory policy we investigate what the right cost of capital should be in an inventory model with deterministic demand to do so we study an inventory model with a generic inventory cost function where risk depends on the inventory decision made additive and multiplicative financial noise functions are included to assess the impact of these on both the cost of capital of the firm and the optimal inventory policy we find that in contrast to previous models risk is not in general a monotone function of inventory also a rate close to the risk free rate which typically deviates significantly from the wacc should be used to value inventory related investments when the inventory cost function is dominated by holding cost for large order quantities even if investments are subject to other sources of financial variability

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

effects of discounting and demand rate variability on the eoq the economic order quantity eoq formula is probably the most well known formula in inventory theory it determines the optimal value of the ordering quantity by minimizing the average cost in an ordering cycle it is based on the assumptions that there is a fixed lead time and a constant demand rate these assumptions are usually not fulfilled in practice especially when dealing with slow moving items demand seems to fluctuate furthermore since the time between two successive orderings is often large for slow moving items discounted costs instead of average costs should be minimized in this paper we determine the optimal ordering quantity if demand is modelled by a poisson process and the expected discounted costs are minimized we also analyze the case where demand is uniform and or the average cost criterion is used we give graphical presentations of the optimal ordering quantities besides easily determining the optimal values these allow us to show what the effects of changing the objective function and of changing the demand distribution are we derive a simple discounted cost ordering quantity formula denoted by eoq d for slow moving items we show that for items with a small demand rate and high fixed ordering costs the eoq d is much closer to the optimal discounted cost ordering quantity than the traditional eoq formula c 1998 elsevier science b v all rights reserved

a direct discrete time approach to poisson gaussian bond option pricing in the heath jarrow morton model abstract term structure models employing poisson gaussian processes may be used to accommodate the observed skewness and kurtosis of interest rates this paper extends the discrete time pure gaussian version of the heath jarrow morton model to the pricing of american type bond options when the underlying term structure of interest rates follows a poisson gaussian process the poisson gaussian process is specified using a hexanomial tree six nodes emanating from each node and the tree is shown to be recombining the scheme is parsimonious and convergent this model extends the class of hjm models by i introducing a more generalized volatility specification than has been used so far and ii including jumps yet retaining lattice recombination thus making the model useful for practical applications

the implied jump risk of libor rates abstract this paper examines implied parameters from options on libor futures jump diffusion models are found to offer superior in sample and out of sample performance when compared to their pure diffusion counterpart the need to incorporate stochastic jump magnitudes into libor dynamics is also documented in addition empirical evidence reveals that the jump component in libor rates is important for pricing their derivatives furthermore variation in jump risk often coincides with federal open market committee fomc decisions and a small subset of macroeconomic announcements

discounting the distant future how much does model selection affect the certainty equivalent rate evaluating investment with long term consequences using discount rates that decline with the time horizon declining discount rates of ddrs means that future welfare changes are of greater consequence in present value terms recent work in this area has turned towards operationalising the theory and establishing a schedule of ddrs for use in cost benefit analysis using us data we make the following points concerning this transition i model selectionhas important implications for operationalising a theory of ddrs that depends upon uncertainty ii misspecification testing naturally leads to employing models that account for changes in the interest reat generating medanism lastly we provide an analysis of the policy implications of ddrs in the context of climate change for the us and show that the use of a state space model can increase valuations by 150 compared to conventional constant discounting

pricing interest rate options in a two factor cox ingersoll ross model of the term structure solutions are presented for prices on interest rate options in a two factor version of the cox ingersoll ross model of the term structure specific solutions are developed for caps on floating interest rates and for european options on discount bonds coupon bonds coupon bond futures and euro dollar futures the solutions for the options are expressed as multivariate integrals and we show how to reduce the calculations to univariate numerical integrations which can be calculated very quickly the two factor model provides more flexibility in fitting observed term structures and the fixed parameters of the model can be set to capture the variability of the term structure over time article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

discrete time valuation of american options with stochastic interest rates we develop an arbitrage free discrete time model to price american style claims for which domestic term structure risk foreign term structure risk and currency risk are important this model combines a discrete version of the heath jarrow and morton 1992 term structure model with the binomial model of cox ross and rubinstein 1979 it converges weakly to the continuous time models in amin and jarrow 1991 1992 the general model is path dependent and can be implemented with arbitrary volatility functions to value claims with maturity up to five years the model is illustrated with applications to long dated american currency warrants and a cross rate swap from the quanto class article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

pricing interest rate derivatives a general approach the relationship between affine stochastic processes and bond pricing equations in exponential term structure models has been well established we connect this result to the pricing of interest rate derivatives if the term structure model is exponential affine then there is a linkage between the bond pricing solution and the prices of many widely traded interest rate derivative securities our results apply to m factor processes with n diffusions and l jump processes the pricing solutions require at most a single numerical integral making the model easy to implement we discuss many options that yield solutions using the methods of the article

implied volatility functions in arbitrage free term structure models abstract we test six term structure models in the heath jarrow and morton 1992 class using eurodollar futures and options data from 1987 1992 we study the time series of implied interest rate volatilities from these models using one day lagged implied volatilities our one and two parameter models simultaneously price an average of 18 5 options each day with an average absolute error of one and a half to two basis points although the models fit well we document systematic strike price and time to maturity biases for all models we also implement simple trading strategies to test whether the models identify genuine biases

pricing of index options when interest rates are stochastic an empirical test abstract this paper tests amin and jarrow s amin and jarrow 1992 version of merton s merton 1973 stochastic interest rate option pricing formula for stock options in their model the interest rate dynamics are given by the heath et al 1992 term structure model the empirical results using data on european stock index options from the swedish option market show that the amin and jarrow model clearly outperforms the black and scholes 1973 model furthermore the time to maturity bias found in tests of the black and scholes model disappears when the options are priced with the amin and jarrow model

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

pricing interest rate derivative securities this article shows that the one state variableinterest rate models of vasicek 1977 and cox ingersoll and ross 1985b can be extended sothat they are consistent with both the current termstructure of interest rates and either the currentvolatilities of all spot interest rates or the currentvolatilities of all forward interest rates theextended vasicek model is shown to be very tracta ble analytically the article compares option pricesobtained using the extended vasicek model withthose obtained using a number of other models