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

the term structure of euromarket interest rates an empirical investigation abstract this paper is an empirical investigation of the predictability and co movement of risk premia in the term structure of euromarket interest rates we present regression results which suggest that risk premia in three euromarket term structures and on uncovered foreign asset positions move together we test formally the hypothesis that these risk premia move in proportion to a single latent variable we are unable to reject this hypothesis the single latent variable model can be interpreted as in hansen and hodrick 1983 and hodrick and srivastava 1984 as a specialization of the icapm in which assets have constant betas on a single unobservable benchmark portfolio

money and asset prices in a continuous time lucas and stokey cash in advance economy abstract this paper develops a continuous time version of the lucas and stokey 1987 money and interest in a cash in advance economy econometrica 55 491 513 cash in advance economy the continuous time setting allows for an exact characterization of equilibrium expected excess returns real and nominal interest rates the price level and the inflation risk premium for general preferences and stochastic processes explicit general equilibrium solutions are obtained for separable logarithmic preferences and serially correlated processes for output and money growth a characteristic feature of the economy is that even when preferences are separable in cash and credit goods money supply still affects asset prices

general equilibrium pricing of cpi derivatives we examine the issue of pricing forward futures and option contracts written on the consumer price index cpi the change of which is a measure of inflation affecting the economy traditional approaches postulate an exogenous process for the price level and then derive cpi derivatives prices by standard arbitrage arguments by contrast we build the general equilibrium of a continuous time monetary economy that is affected by both real and nominal shocks the price level and thus the inflation rate are found endogenously and solutions for the prices of cpi derivatives are obtained which are in closed form in a specialized version of the economy

robust stochastic discount factors when the market is incomplete a new non redundant derivative security cannot be priced by no arbitrage arguments alone moreover there will be a multiplicity of stochastic discount factors and each of them may give a different price for the new derivative security this paper develops an approach to the selection of a stochastic discount factor for pricing a new derivative security the approach is based on the idea that the price of a derivative security should not vary too much when the payoff of the primitive security is slightly perturbed i e the price of the derivative should be robust to model misspecification the paper develops two metrics of robustness the first is based on robustness in expectation the second is based on robustness in probability and draws on tools from the theory of large deviations we show that in a stochastic volatility model the two metrics yield analytically tractable bounds for the derivative price as the underlying stochastic volatility model is perturbed the bounds can be readily used for numerical examination of the sensitivity of the price of the derivative to model misspecification

option pricing when the variance changes randomly theory estimation and an application in this paper we examine the pricing of european call options on stocks that have vari ance rates that change randomly we study continuous time diffusion processes for the stock return and the standard deviation parameter and we find that one must use the stock and two options to form a riskless hedge the riskless hedge does not lead to a unique option pricing function because the random standard deviation is not a traded security one must appeal to an equilibrium asset pricing model to derive a unique option pricing function in general the option price depends on the risk premium associated with the random standard deviation we find that the problem can be simplified by assuming that volatility risk can be diversified away and that changes in volatility are uncorrelated with the stock return the resulting solution is an integral ofthe black scholes formula and the distribution function for the variance of the stock price we show that accurate option prices can be computed via monte carlo simulations and we apply the model to a set of actual prices

technical note intertemporal price discrimination via reference price effects we consider the dynamic pricing problem a monopolistic seller faces when customers arrive in heterogeneous time periods and their purchase decisions are affected by reference prices formed from their past observations of prices we illustrate that a new form of price discrimination opportunity exists in such situations where the seller s optimal pricing strategy is a cyclic one even when the customers are loss neutral and their demand functions are identical this result differs from those of prior studies where the optimal price paths are shown to be asymptotically constant and thus is unique due to the interaction between the heterogeneous arrivals and the reference price effects we also provide the cycle length of the optimal pricing policy when the demand function is linear and when customers are loss neutral in this era when customer information is easier accessible our results suggest the sellers consider this new dimension of price discrimination in conjunction with the old ones to take advan

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

dynamic pricing in the presence of social learning and strategic consumers when a product of uncertain quality is first introduced consumers may choose to strategically delay their purchasing decisions in anticipation of the product reviews of their peers this paper investigates how the presence of social learning affects the strategic interaction between a dynamic pricing monopolist and a forward looking consumer population within a simple two period model our analysis yields three main insights first we find that the presence of social learning has significant structural implications for optimal pricing policies in the absence of social learning decreasing price plans are always preferred by the firm by contrast in the presence of social learning we find that i if the firm commits to a price path ex ante preannounced pricing an increasing price plan is typically announced whereas ii if the firm adjusts price dynamically responsive pricing prices are initially low and may either rise or decline over time second we establish that under both preannounced an

the timing and magnitude of retail store markdowns evidence from weekends and holidays we examine daily prices of eight goods at seventeen retail stores collected in ann arbor michigan over a four month period from november 1 to february 28 we focus on weekly and seasonal price patterns and on the frequency of price markdowns or sales there were frequent markdowns in the intensive shopping period prior to christmas and a tendency for such sales to occur on weekends we interpret these findings as evidence that a significant number of markdowns are timed to occur when shopping intensity is exogenously high we complement the imperfect information based motives for sales in the literature by contributing an additional element based on the role of bulk shopping and increasing returns in the shopping technology

durable goods monopoly with varying demand this paper solves for the proflt maximising strategy of a durable goods monopolist when incoming demand varies over time each period additional consumers enter the market these consumers can then choose whether and when to purchase we flrst characterise the consumer s utility maximisation problem and under a monotonicity condition show the proflt maximising allocation can be solved through a myopic algorithm which has an intuitive marginal revenue interpretation consumers ability to delay creates an asymmetry in the optimal price path which exhibits fast increases and slow declines this asymmetry pushes the price level above that charged by a flrm facing the average level of demand applications of this framework include deterministic demand cycles one ofi shocks and iid demand draws the optimal policy outperforms renting and can be implemented by a time consistent best price provision

interest rates and currency prices in a two country world abstract this paper is a theoretical study of the determination of prices interest rates and currency exchange rates set in an infinitely lived two country world which is subject both to stochastic endowment shocks and to monetary instability formulas are obtained for pricing all equity claims nominally denominated bonds and currencies and these formulas are related to earlier closely related results in the theories of money finance international trade

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

a dynamic programming approach for pricing options embedded in bonds abstract we propose a dynamic programming dp approach for pricing options embedded in bonds the focus being on call and put options with advance notice an efficient procedure is developed for the cases where the interest rate process follows the vasicek cox ingersoll ross cir or generalized vasicek models our dp methodology uses the exact joint distribution of the interest rate and integrated interest rate at a future date conditional on the current value of the interest rate we provide numerical illustrations for the vasicek and cir models comparing our dp method with finite difference methods our procedure compares quite favorably in terms of both efficiency and accuracy an important advantage of the our dp approach is that it can be applied to more general models calibrated to capture the term structure of interest rates e g the generalized vasicek model

the value of corporate risk management we model and estimate the value of corporate risk management we show how risk management can add value when revenues and costs are nonlinearly related to prices and estimate the model by regressing quarterly firm sales and costs on the second and higher moments of output and input prices for a sample of 34 oil refiners we find that hedging concave revenues and leaving concave costs exposed each represent between 2 and 3 of firm value we validate our approach by regressing tobin s q on the estimated value and level of risk management and find results consistent with the model

valuing managerial flexibility an application of real option theory to mining investments abstract the value of managerial flexibility is assessed using data on prices costs grades reserves ore extraction and metal output for a panel of canadian copper mines a real option model is estimated and solved for project and option values most empirical researchers i consider the initial investment decision but neglect flexible operation thereafter ii assume that price is stochastic but ignore cost and reserve uncertainty and iii model price as a nonstationary stochastic process the evolution of three state variables price cost and reserves is assessed here differences in assumptions compared to others are found to lead to large differences in estimated project and option values

systematic jump risks in a small open economy simultaneous equilibrium valuation of options on the market portfolio and the exchange rate abstract the valuation of stock options and currency options has witnessed an explosion of new development in the past 20 years these models set up either in a partial equilibrium or a general equilibrium framework have certainly enriched our understanding of option valuation in one way or the other however the main drawback of these models is that stock options and currency options are analyzed in separate contexts the co movement of the stock market and the currency market is absent from the option valuation analysis such co movement is extremely important and is best illustrated by the southeast asian financial crisis to overcome this drawback this paper uses an equilibrium model to investigate the joint dynamics of the exchange rate and the market portfolio in a small open monetary economy with jump diffusion money supplies and aggregate dividends it is shown that the exchange rate and the market portfolio are strongly correlated since both are driven by the same economic fundamentals furthermore options on the exchange rate and the market portfolio are evaluated in the same equilibrium context the analysis shows that parameters describing the same economic fundamentals have very different effects on currency and stock options

the pension costs from a defined benefit to individual pension accounts do they cost more in the case of taiwan this article develops a market based liability valuation model to price individual pension costs of a defined benefit db pension plan the purpose is to compare them with the new labour pension plan individual pension accounts ipas in the case of taiwan the results based on the numerical approach show that the new ipas cost a company more than the old db plan except if the average wage growth relative to the risk free interest rate is high enough

cyclic pricing by a durable goods monopolist in the model of this paper a monopoly seller of a durable good holds periodic sales as a means of price discrimination a new cohort of consumers enters the market in each period interested in purchasing the good either immediately or after a delay within each cohort consumers vary in their tastes for the good under broad conditions the seller will vary the price over time in most periods he will charge a price just low enough to sell immediately to consumers with a high willingness to pay periodically however he will drop the price far enough to sell to an accumulated group of consumers with a low willingness to pay

intertemporal price discrimination with two products we study the two product monopoly profit maximization problem for a seller who can commit to a dynamic pricing strategy we show that if consumers valuations are not strongly ordered then optimality for the seller can require intertemporal price discrimination the seller offers a choice between supplying a complete bundle now or delaying the supply of a component of that bundle until a later date for general valuations we establish a sufficient condition for such dynamic pricing to be more profitable than mixed bundling so we show that the established no discrimination across time result does not extend to two product sellers under standard taste distributions

the effect of transaction size on off the run treasury prices this paper examines intra day trading data from the inter dealer broker market for u s treasury securities and measures the degree of price pressure in the off the run treasury market as is well known securities that would appear to be very close substitutes i e on the run and off the run treasury bonds behave as if there is some degree of market segmentation this is the first systematic study of the off the run treasury note and bond market focused entirely on a price pressure effect using intra day data the paper analyzes price pressure through matched pairs of securities that differ only in liquidity

currency prices terms of trade and interest rates a general equilibrium asset pricing cash in advance approach currency prices terms of trade and interest rates a general equilibrium asset pricing cash in advance approach

an alternative valuation model for contingent claims abstract this paper studies contingent claim valuation in a lucas type exchange economy the derived fundamental valuation equation differs from its cox ingersoll ross production economy counterpart in that it is expressed in terms of the direct utility function and an exogenous output process thus offering superior tractability we apply our approach to derive closed form solutions for bond bond option individual stock and stock option prices under a more general setting than allowable in the cox ingersoll ross framework the resulting interest rate and stock price dynamics are empirically plausible moreover our stock option pricing formula with stochastic volatility and interest rates can reconcile certain puzzling empirical regularities including the volatility smile

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

commodity trade and the carry trade a tale of two countries persistent interest rate differentials account for much of the currency carry trade profitability commodity currencies offer high interest rates on average while countries that export finished goods tend to have low interest rates we develop a general equilibrium model of international trade and currency pricing where countries have an advantage in producing either basic inputs or final goods in the model domestic production insulates commodity producing countries from global productivity shocks forcing final good producers to absorb them commodity currency exchange rates and risk premia increase with productivity differentials and trade frictions these predictions are strongly supported in the data this article is protected by copyright all rights reserved

intertemporal pricing and consumer stockpiling we study a dynamic pricing problem for a class of products with stable consumption patterns e g household items staple foods consumers may stock up the product at current prices for future consumption but they incur inventory holding costs we model this situation as a dynamic game over an infinite time horizon in each period the seller sets a price and each consumer chooses how many units to buy we develop a solution methodology based on rational expectations by endowing each player with beliefs we decouple the dynamic game into individual dynamic programs for each player we solve for the rational expectations equilibrium where all players make optimal dynamic decisions given correct beliefs about others behavior in equilibrium the seller may either charge a constant fixed price or offer periodic price promotions at predictable time intervals we show that promotions are useful when frequent shoppers are willing to pay more for the product than are occasional shoppers we also develop several model extensions to study the impact of consumer stockpiling on the seller s inventory production and rationing strategies

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

stock price distributions with stochastic volatility an analytic approach we study the stock price distributions that arise when prices follow a diffusion process with a stochastically varying volatility parameter we use analytic techniques to derive an explicit closed form solution for the case where volatility is driven by an arithmetic ornstein ublenbeck or ar1 process we then apply our results to two related problems in the finance literature 1 options pricing in a world of stochastic volatility and 2 the relationship between stochastic volatility and the nature of fat tailes in stock price distributions article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

affine models of the joint dynamics of exchange rates and interest rates this paper extends the affine class of term structure models to describe the joint dynamics of exchange rates and interest rates in particular the issue of how to reconcile the low volatility of interest rates with the high volatility of exchange rates is addressed the in complete market approach of introducing exchange rate volatility that is orthogonal to both interest rates and the pricing kernels is shown to be infeasible in the affine setting models in which excess exchange rate volatility is orthogonal to interest rates but not orthogonal to the pricing kernels are proposed and validated via kalman filter estimation of maximal 5 factor models for 6 country pairs

an intertemporal general equilibrium model of asset prices this paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices in this model asset prices and their stochastic properties are determined endogenously one principal result is a partial differential equation which asset prices must satisfy the solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy in this paper we develop a general equilibrium asset pricing model for use in applied research an important feature of the model is its integration of real and financial markets among other things the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables the model is fully consistent with rational expectations and maximizing behavior on the part of all agents our framework is general enough to include many of the fundamental forces affecting asset markets yet it is tractable enough to be specialized easily to produce specific testable results furthermore the model can be extended in a number of straightforward ways consequently it is well suited to a wide variety of applications for example in a companion paper cox ingersoll and ross 7 we use the model to develop a theory of the term structure of interest rates many studies have been concerned with various aspects of asset pricing under uncertainty the most relevant to our work are the important papers on intertemporal asset pricing by merton 19 and lucas 16 working in a continuous time framework merton derives a relationship among the equilibrium expected rates of return on assets he shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes the random output of these processes is exogenously determined and perishable assets are defined as claims to all or a part of the output of a process and the equilibrium determines the asset prices our theory draws on some elements of both of these papers like merton we formulate our model in continuous time and make full use of the analytical tractability that this affords the economic structure of our model is somewhat similar to that of lucas however we include both endogenous production and

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 pricing of stock index options in a general equilibrium model this paper analyzes the pricing of stock index options in a simple general equilibrium model in this model the volatility of the stock index and the spot rate of interest are functions of a stochastic variable the paper investigates the biases that arise when using the black scholes model with the assumed volatility and interest rate dynamics it is shown that the model can in principle explain the biases observed in empirical work on stock index options

modeling time series information into option prices an empirical evaluation of statistical projection and garch option pricing model abstract this paper compares the empirical performances of statistical projection models with those of the black scholes adapted to account for skew and the garch option pricing models empirical analysis on s p500 index options shows that the out of sample pricing and projected trading performances of the semi parametric and nonparametric projection models are substantially better than more traditional models results further indicate that econometric models based on nonlinear projections of observable inputs perform better than models based on ols projections consistent with the notion that the true unobservable option pricing model is inherently a nonlinear function of its inputs the econometric option models presented in this paper should prove useful and complement mainstream mathematical modeling methods in both research and practice

a continuous time equilibrium model of forward prices and futures prices in a multigood economy abstract this paper is a theoretical investigation of equilibrium forward and futures prices we construct a rational expectations model in continuous time of a multigood identical consumer economy with constant stochastic returns to scale production using this model we find three main results first we find formulas for equilibrium forward futures discount bond commodity bond and commodity option prices second we show that a futures price is actually a forward price for the delivery of a random number of units of a good the random number is the return earned from continuous reinvestment in instantaneously riskless bonds until maturity of the futures contract third we find and interpret conditions under which normal backwardation or contango is found in forward or futures prices these conditions reflect the usefulness of forward and futures contracts as consumption hedges

asset prices and exchange rates in this paper we study the implications of introducing demand shocks and trade in goods into an otherwise standard international asset pricing model trade in goods gives rise to an additional channel of international propagation through the terms of trade absent in traditional single good asset pricing models the inclusion of demand shocks helps overturn many unrealistic implications of existing international flnance models in which productivity shocks are the sole source of uncertainty our model generates a rich set of implications on how stock bond and foreign exchange markets co move we solve the model in closed form which yields a system of equations that can be readily estimated empirically our estimation validates the main predictions of the theory

intertemporal price discrimination structure and computation of optimal policies we study a firm s optimal pricing policy under commitment the firm s objective is to maximize its long term average revenue given a steady arrival of strategic customers in particular customers arrive over time are strategic in timing their purchases and are heterogeneous along two dimensions their valuation for the firm s product and their willingness to wait before purchasing or leaving the customers patience and valuation may be correlated in an arbitrary fashion for this general formulation we prove that the firm may restrict attention to cyclic pricing policies which have length at most twice the maximum willingness to wait of the customer population to efficiently compute optimal policies we develop a dynamic programming approach that uses a novel state space that is general capable of handling arbitrary problem primitives and that generalizes to finite horizon problems with nonstationary parameters we analyze the class of monotone pricing policies and establish their suboptimality in general optimal policies are in a typical scenario characterized by nested sales where the firm offers partial discounts throughout each cycle offers a significant discount halfway through the cycle and holds its largest discount at the end of the cycle we further establish a form of equivalence between the problem of pricing for a stream of heterogeneous strategic customers and pricing for a pool of heterogeneous customers who may stockpile units of the product this paper was accepted by yossi aviv operations management

on real interest rate dynamics and regime switching abstract we find evidence of regime switching dynamics in the usa and the uk real interest rates over the period 1881 2003 for the uk there is a regime in which the real interest rate displays a relatively stronger mean reversion and a regime in which it displays a relatively weaker mean reversion the former regime is characterized by a relatively larger error in the estimation of the reversion parameter and higher volatility for the usa the two regimes differ in volatility the probability of transition from one regime to another is found to be significantly related to the inflation rate regime and to the political regime the results highlight the importance of regime switching in the dynamics of the real interest rate as well as the role of inflation and political regimes in explaining this switching

currency option pricing with stochastic domestic and foreign interest rates this study develops a currency option pricing model under stochastic interest rates when interest rate parity holds and it is assumed that domestic and foreign bond prices have local variances that depend only on time we demonstrate how existing currency option models are simply derived from one framework empirical tests employing transactions option data reveal that a particularly simple form of the stochastic rate model is uniformly more accurate than a constant rate model for all boundaries and maturities tested

an equilibrium model of exchange rate determination and asset pricing with nontraded goods and imperfect information this paper presents a two country model with maximizing households stochastic production stochastic money growth and perfect capital mobility because of the presence of nontraded goods households in different countries consume different goods analytic solutions are presented for the nominal exchange rate the real exchange rate nominal interest rates and real interest rates it is shown that the model is compatible with some important features of the real world behavior of exchange rates when households are imperfectly informed about the distribution of money growth the exchange rate exhibits patterns of overshooting and is more volatile than the ratio of the money stocks copyright 1987 by university of chicago press

high price or low price an experimental study on a markdown pricing policy abstract this study examines whether strategic customers behavioral patterns remain consistent in different pricing scenarios under a markdown pricing policy these customers decision patterns have been widely discussed because they significantly influence the expected monetary output contrary to rational assumptions the behavioral research literature indicates that customers behavioral biases manifest in their reference dependency risk and loss attitudes and fill rate misperceptions however the relationship between behavioral biases and various pricing scenarios has not been carefully examined accordingly we conducted laboratory experiments to observe customers behavioral performance in a series of pricing scenarios to provide pricing suggestions for sellers our experimental results demonstrate that behavioral factors reflecting risk and loss attitudes as well as reference dependency can clearly describe customers behavioral biases meanwhile our estimation shows that the degrees of risk and loss attitude are not constant but depend on price settings the lower the full price in the initial period the higher the degrees of aversion to both risk and loss given such behavioral patterns we suggest that sellers should set their full prices lower than the normative value when the fill rate in period two is low and set them higher than the normative value when the fill rate in period two is high

securities markets diffusion state processes and arbitrage free shadow prices this paper develops the parametric restrictions imposed on diffusion state processes by the requirement of arbitrage free asset pricing using the equivalent martingale measure as a starting point the diffusion property is exploited to specify the shadow pricing func tion which takes conditional state variable probabilities under the reference measure into arbitrage free contingent claim prices the main results of the paper provide differential equations associated with the shadow price function that are used to identify restrictions on the parameters of assumed diffusion processes the paper concludes with an application to the cir model where the state variable the instantaneous interest rate is assumed to follow a square root process calculations are also provided for the parametric restrictions imposed on the brownian bridge and ou state variable processes

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

spreading currency forwards why and how abstract in this paper we have adopted a continuous time framework in which a hedger has a currency risk sensitive non traded cash position the hedger has the opportunity to hedge against risk by using two currency forward contracts that differ only in their maturities the hedger is able to reach a perfect hedge of his non traded position by using only two currency forward contracts with different maturities even though four sources of uncertainty drive the international economy this perfect hedge is reached by spreading forward contracts where the hedger is short in the nearby contract and long in the deferred contract this strategy is easy to implement since no parameter has to be estimated empirically when the hedger is a price taker finally the analysis has been extended to currency futures contracts we show in explicit terms how the marking to market of futures positions affects the spreading strategy

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

time horizon and the discount rate abstract we consider an economy a la lucas 1978 econometrica46 1429 1446 with a risk averse representative agent the exogenous growth rate of the economy follows a random walk we characterize the set of utility functions for which it is efficient to discount more distant cash flows at a lower rate the benchmark result is that when the growth rate is almost surely nonnegative the yield curve is decreasing if and only if relative risk aversion is decreasing with wealth relaxing the assumption on the absence of recession requires more restrictions on preferences such as increasing relative prudence journal of economic literature classification numbers d81 d91 q25 q28

a simple nonnegative process for equilibrium models abstract this paper presents a general specification for dynamic equilibrium models where nonnegative variables follow the autoregressive gamma process in jasiak and gourieroux 2006 the model solution implies linear dynamics for endogenous variables and provides conditional and unconditional moments in closed form finding the solution is computationally inexpensive requiring only to solve linear and quadratic equations the specification can be applied to a wide variety of models in finance and economics two applications are presented first a time varying volatility premium in a long run risks asset pricing model second time varying volatility in policy shocks in a simple new keynesian model accuracy in these models solutions is high and not significantly affected by time varying volatility

pricing weather derivatives this article presents a general method for pricing weather derivatives specification tests find that a temperature series for fresno ca follows a mean reverting brownian motion process with discrete jumps and autoregressive conditional heteroscedastic errors based on this process we define an equilibrium pricing model for cooling degree day weather options comparing option prices estimated with three methods a traditional burn rate approach a black scholes merton approximation and an equilibrium monte carlo simulation reveals significant differences equilibrium prices are preferred on theoretical grounds so are used to demonstrate the usefulness of weather derivatives as risk management tools for california specialty crop growers

nominal contracts in a bimetallic standard as its central feature a bimetallic standard grants nominal debtors an option to deliver either of two metals with results from the option pricing literature construction of a formula to evaluate the bimetallic option in debt instruments is straightforward with this formula one can compute the option value in a wide range of nineteenth century u s treasury securities posession of the option values permits an adjustment of the yields on u s securities to make them comparable to yields on nonmetallic european securities evaluating the option allows the estimation of transfers from debtors to creditors copyright 1986 by american economic association

international interest rates exchange rates and the stochastic structure of supply in a dual currency flexible exchange rate model both nominal and real foreign exchange premia depend on investor risk attitudes consumption parameters and the stochastic structure of currency and commodity supplies when supplies are random their joint correlation structure determines the sign of the premia if the money supplies are identically distributed then all foreign exchange premia regardless of the currency of denomination are zero a positive correlation between the value of a country s currency and its nominal interest rate need not indicate real interest rate movements relative bond prices can be negatively correlated with the terms of trade recently there has been a great deal of interest in the construction and use of general equilibrium models of an international economy subject to random disturbances 1 however with the exceptions of stulz 1984 domowitz and hakkio 1985 hodrick and srivastava 1986 and stockman and svensson 1987 little effort has been devoted to expressing the relationships examined in these models in terms of parameters describing the underlying stochastic processes of the exogenous variables 2 stockman and svensson incorporated international capital flows into the model of svensson 1985 and calculated covariances between investment the current account the exchange rate and the terms of trade in terms of exogenous money and commodity supplies focusing more on financial market issues domowitz and hakkio and hodrick and srivastava simplified the case in advance model of lucas 1982 by assuming that the exogenous variables are independently lognormal and that investors have loglinear utility functions a procedure which allowed them to relate the premium required on forward exchange contracts to money supply variances stulz obtained similar results in a continuous time model where real money balances enter the utility function this paper employs a model similar to that developed by domowitz and hakkio 1985 and hodrick and srivastava 1986 but its emphasis and objectives are quite different those authors were concerned only with demonstrating that a time varying risk premium is a theoretical possibility prior to conducting a series of empirical tests only loosely related to the model itself consequently they did

on jump processes in the foreign exchange and stock markets exchange rates exhibit systematic discontinuities even after allowingfor conditional heteroskedasticity in the diffusion process the results are much more significant in theforeign exchange market than in the stock market which suggests differences in the structure of these markets finally this jump component is shown to explain some of the empirically observed mispricings in the currency options market the objective of this article is to analyze and compare the empirical distribution of returns in the stock market and in the foreign exchange market there are a number of reasons why a better understanding of the stochastic processes driving prices in these markets would be useful many financial models rely heavily on the assumption of a particular stochastic process while relatively little attention is paid to the empirical fit of the postulated distribution as a result models like option pricing models are applied indiscriminately to various markets such as the stock market and the foreign exchange market when the underlying processes may be fundamentally different the foreign exchange market for instance is characterized by active exchange rate man

an intertemporal general equilibrium asset pricing model the case of diffusion information this paper provides sufficient conditions for the equilibrium price system and a vector of exogenously specified state variable processes to form a diffusion process in a pure exchange economy the conditions involve smoothness of agents utility functions and certain nice properties of the aggregate endowment process and the dividend processes of traded assets in place of the dynamic programming a martingale representation technique is utilized to characterize equilibrium portfolio policies this technique is useful even when there does not exist a finite dimensional markov structure in the economy and thus the markovian stochastic dynamic programming is not applicable a gents are shown to hold certain hedging mutual funds and the riskless asset in contrast to earlier results the market portfolio does not have a special role in hedging since the markets are dynamically complete when there exists a finite dimensional markov system in the economy the dimension of the hedging demand identified through the markovian dynamic programming may be much larger than that identified by the martingale method copyright 1987 by the econometric society

the exchange rate and purchasing power parity extending the theory and tests abstract this paper analyzes the exchange rate in a no arbitrage or real business cycle equilibrium model and provides empirical evidence for this model vis a vis ppp our contribution is to show based on a generalization of the equilibrium model of exchange rates that i the test equation linking the exchange rate to fundamentals should allow for international heterogeneity in time preferences and risk attitudes as well as noise that is the model should not be tested as an exact relation ii empirical work should use levels of variables rather than first differences and iii tests on the existence of long run relations should be complemented by test on the signs of the coefficients our empirical work shows that as a long run relation the generalized model outperforms ppp moreover under the generalized model quarterly deviations from the estimated long term relation have a half life of only four to five quarters

exchange rates pass through and canadian export competitiveness an analysis using vector autoregressions the degree of the pass through of exchange rate changes to lower export prices measured in foreign currency is assessed for the case of canadian industries exporting to the united states contrary to earlier studies full pass through was 70 and 67 for the fabricated and end products sectors respectively these results correlate well with available elasticity estimates and exports as a percentage of world exports to evaluate international competitiveness exports prices were relatively unresponsive to changes in us competitors prices except for the crude materials sector where the increase in canadian export prices overshot the us increase before settling back to a parity increase these results suggest that canada s export industries are more competitive than previously thought cusumsq tests suggest that these new results were due to structural breaks in the export price equations towards the end of the 1970s perhaps reflecting the general reduction in tariff and non tariff barriers since then

a simple test of exogeneity for recursively structured var models the restriction of exogeneity of certain variables in structural var models is rarely tested for consistency with the actual data the reason is obvious such a test requires estimates of the structural parameters this paper proposes a solution for models that assume long run or contemporaneous recursive structures in identification we show that in such cases the exogeneity restriction can be assessed statistically using the well known granger non causality test which is conveniently performed in the reduced form var model two empirical examples are offered to demonstrate the usefulness of this result

dynamic and targeted bundle pricing of two independently valued products abstract bundling is when two or more products are offered as a single unit and at a price lower than the sum of the individual prices of the products we study a multi segment market in which a retailer aims to clear the inventory of an item by bundling it with a second product which is independently valued we investigate the question of how dynamic and segment specific bundle pricing impacts retailer s revenue we develop a revenue model that integrates the dynamic and segment specific aspects of the pricing decisions and present a computational study to analyze their revenue impact relative to a price promotion for the individual item only the computational results indicate that the bundle offers are most effective when the initial inventory of the item under consideration is high the results also demonstrate that dynamic pricing is beneficial when the initial inventory of the item is low an additional revenue improvement is observed when the price of the bundle is dynamically optimized in the computational study segment specific pricing is observed to have no direct impact on revenue when prices are static segment specific and dynamic pricing however can bring about substantial revenue improvements that are an increasing function of the initial inventory level of the item we consider the correlation in consumers valuations of the bundled products and show that dynamically priced and segment specific bundle offers yield a robust revenue performance mitigating the potentially revenue diminishing impact of positive correlation in consumers valuations of the products

liquidation fire sales and acquirers private information abstract we develop a dynamic model in which a distressed firm optimizes an exit choice between sell out and default as well as its timing we assume that the distressed firm is not informed about the acquirer s asset valuation we show that the firm delays liquidation to decrease the acquirer s information rent notably the firm can change the exit choice from sell out to default when the screening cost is high in this case shareholders declare default regardless of the acquirer s valuation which provides the acquirer the maximum information rent together with the deadweight costs of bankruptcy the maximal information rent which causes a wealth transfer from debt holders of the bankrupt firm to the acquirer lowers the sales price and debt recovery this mechanism can explain many empirical findings about fire sales and acquirers excess gains higher volatility leverage and asymmetric information increase the likelihood of a fire sale but higher bankruptcy costs could play a positive role in preventing a fire sale with asymmetric information the firm can reduce debt issuance to avoid the risk of a fire sale

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

long run price effects of exchange rate changes in finnish pulp and paper exports this paper presents long run exchange rate elasticities of finnish newsprint and pulp export prices in the united kingdom uk and germany over the period 1980 94 the elasticities were estimated for a markup pricing model using johansen s cointegration method the magnitudes of the elasticity estimates obtained by imposing price homogeneity indicate that pass through of exchange rate changes to export prices has been incomplete in both markets for newsprint the pass through elasticity was 0 60 in the uk and 0 46 in germany which means that about one half of the changes in the exchange rates is reflected in prices as expressed in the destination countries currencies and about a half in prices measured in finnish markka instead in pulp exports the pass through elasticities differed from each other between the two destination countries more clearly than in newsprint exports indicating a different pricing behaviour of finnish pulp exporters in the uk and germany when exchange rate changes pass throug

technical note dynamic pricing with gain seeking reference price effects we study a dynamic pricing problem of a firm facing reference price effects at an aggregate demand level where demand is more sensitive to gains than losses we find that even the myopic pricing strategy belongs to one type of discontinuous maps which can exhibit complex dynamics over time our numerical examples show that in general the optimal pricing strategies may not admit any simple characterizations and the resulting reference price price dynamics can be very complicated we then show for a special case that a cyclic skimming pricing strategy is optimal and we provide conditions to guarantee the optimality of high low pricing strategies

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

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

currency risk hedging futures vs forward abstract the objective of this paper is to address the issue of choosing between currency forward and currency futures contracts when hedging against currency risk within a stochastic interest rates environment we compare between the hedging effectiveness of the two derivative assets both within a narrow sense i e volatility minimization and within a wide sense i e risk return trade off when judging hedging effectiveness in the narrow sense forward and futures contracts give identical results even if they do not have identical prices when judging hedging effectiveness in the wide sense the choice between the two contracts is determined by the correlation between the domestic and the foreign term structures dynamics

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

exchange rates and interest rates can term structure models explain currency movements abstract we construct an international term structure model that has excellent empirical performance in tracking movements of exchange rates and currency returns the forward premium puzzle is accounted for yet the model does not have the undesirable properties found in backus et al j finance 56 2001 279 examination of the estimated factor structure indicates that local factors are not important in the us uk and german markets moreover we find that term structure factors alone cannot satisfactorily explain exchange rate movements in other words exchange rates are also affected by other factors that are not in the interest rate dynamics

optimal price skimming by a monopolist facing rational consumers this paper considers the intertemporal pricing problem for a monopolist marketing a new product the key feature differentiating this paper from the extant management science literature on intertemporal pricing is the assumption that consumers are intertemporal utility maximizers a subgame perfect nash equilibrium pricing policy is characterized and shown to involve intertemporal price discrimination we compare this policy to the optimal policy for a monopolist facing myopic consumers and find that for any given state prices are always lower with rational consumers than with myopic consumers for plausible parameter values the assumption of consumer rationality can be shown to lead to large differences in optimal prices moreover if a monopolist facing rational consumers implements the optimal myopic consumer pricing policy profits can be significantly less than if the monopolist follows the equilibrium pricing policy for rational consumers

durable goods monopoly with entry of new consumers this paper analyzes a model of a dynamic monopolist who produces at constant unit cost each period a new cohort of consumers enters the market each entering cohort is identical consumers within a cohort have different tastes for the good my main results are if players are sufficiently patient any positive average profit less than the maximum feasible level can be attained in a subgame perfect equilibrium in the subset of subgame perfect equilibria in which players use stationary strategies the seller cannot make sales at prices significantly greater than the lowest willingness to pay when period length goes to zero and the seller attains the maximum profit when commitment is feasible by charging the same static monopoly price in every period this paper analyzes a model of a dynamic monopolist who operates in a market in which there is a regular flow of new consumers the seller produces a durable good at constant unit cost each period a new cohort of consumers enters the market consumers wish to buy exactly one unit of the item but are willing to wait resales are not allowed each entering cohort is identical

on the theory of international currency portfolios abstract the paper develops a general equilibrium theory of the optimal currency composition of international bond portfolios like the partial equilibrium portfolio balance literature of the 1980s the theory emphasizes the critical roles of government debt and government balance sheet operations in the determination of portfolios prices and allocations consistent with empirical findings optimal foreign currency positions are found to be small with their size decreasing with exchange rate volatility while optimal domestic currency positions are large and increasing with domestic interest rates a large open market purchase of domestic currency bonds from private households lowers domestic interest rates

pricing and manufacturing decisions when demand is a function of prices in multiple periods in most deterministic manufacturing decision models demand is either known or induced by pricing decisions in the period that the demand is experienced however in more realistic market scenarios consumers make purchase decisions with respect to price not only in the current period but also in past and future periods we model a joint manufacturing pricing decision problem accounting for that portion of demand realized in each period that is induced by the interaction of pricing decisions in the current period and in previous periods we formulate a mathematical programming model and develop solution techniques we identify structural properties of our models and develop closed form solutions and effective heuristics for various special cases of our models finally we conduct extensive computational experiments to quantify the effectiveness of our heuristics and to develop managerial insights

moment based estimation of stochastic volatility abstract this paper makes use of the distributional information contained in high frequency data to test for the specification of the functional form of the volatility process within the class of stochastic volatility models it s calculus is implemented in order to obtain the first and second conditional moment of the driving stochastic differential equation for the volatility process these analytical expressions are augmented by their lag and lag squared and are used to form the corresponding gmm estimator the base case stochastic volatility model is extended to allow for the leverage effect and jumps in returns empirical estimation confirms the presence of fast mean reversion in volatility and jumps in returns for the 5 min s p 500 stock market index further estimation results also seem to indicate the presence of jumps in the volatility process that are correlated to the jumps in returns

stochastic risk premiums stochastic skewness in currency options and stochastic discount factors in international economies abstract we develop models of stochastic discount factors in international economies that produce stochastic risk premiums and stochastic skewness in currency options we estimate the models using time series returns and option prices on three currency pairs that form a triangular relation estimation shows that the average risk premium in japan is larger than that in the us or the uk the global risk premium is more persistent and volatile than the country specific risk premiums and investors respond differently to different shocks we also identify high frequency jumps in each economy but find that only downside jumps are priced finally our analysis shows that the risk premiums are economically compatible with movements in stock and bond market fundamentals

optimal dynamic mechanism design with deadlines a seller maximizes revenue from selling an object in a dynamic environment with buyers that differ in their patience each buyer has a privately known deadline for buying and a privately known valuation first we derive the optimal mechanism neglecting the incentive constraint for the deadline the deadline of the winner determines the time of the allocation and therefore also the amount of information available to the seller when he decides whether to allocate to a buyer depending on the shape of the markup that the seller uses this can lead to a violation of the neglected incentive constraint we give sufficient conditions on the type distribution under which the neglected constraint is fulfilled or violated second for the case that the constraint cannot be neglected we consider a model with two periods and two buyers here the optimal mechanism is implemented by a fixed price in period one and an asymmetric auction in period two the asymmetry which is introduced to prevent the patient type of the first buyer from buying in period one leads to pooling of deadlines at the top of the type space

dealing temporary price cuts by seller as a buyer discrimination mechanism this paper is concerned with temporary price cuts deals sales and specials as a mechanism for the seller to price discriminate between buyers with different intensities of demand we analyze why a seller offers such price cuts which buyers take advantage of them and what the parameters are that determine the amount and frequency of the discount offered in the remainder of this section we briefly review the literature on price deals 1 in section ii simple models of buyer and seller behavior are developed and we show why and how a seller adopts a dealing strategy section iii summarizes the key implications of the model and indicates how the price discrimination hypothesis could be tested in practice section iv suggests possible extensions of the model finally section v gives our conclusions in the marketing literature the issue of who is deal prone has been extensively researched an explanation for temporary price cuts usually called deals sales or specials is provided we hypothesize that they are a mechanism that discriminates between more intense and less intense demanders we further hypothesize a positive relationship between demand elasticity and holding costs buyers with more intense demand with high holding costs are those who will be buying the product at its regular price the low holdingcost buyers take advantage of deals by forward buying the model is applicable to three relationships 1 manufacturer reseller where the reseller may be a wholesaler or a retailer 2 resellerreseller for example wholesaler retailer and 3 retailer consumer we are grateful to michael mussa and albert madansky for their comments we also benefited from comments made by the marketing faculty of the wharton school at a seminar where an earlier version of this paper was presented neil beckwith in particular is acknowledged 1 for a more detailed review of deals and similar pricecutting mechanisms e g mail in rebates cents off labels coupons etc see narsimhan 1982 chan 2 journal of business 1985 vol 58 no 3 1985 by the university of chicago all rights reserved 0021 9398185 5803 0004 01 50

optimizing product launches in the presence of strategic consumers a technology firm launches newer generations of a given product over time at any moment the firm decides whether to release a new version of the product that captures the current technology level at the expense of a fixed launch cost consumers are forward looking and purchase newer models only when it maximizes their own future discounted surpluses we start by assuming that consumers have a common valuation for the product and consider two product launch settings in the first setting the firm does not announce future release technologies and the equilibrium of the game is to release new versions cyclically with a constant level of technology improvement that is optimal for the firm in the second setting the firm is able to precommit to a schedule of technology releases and the optimal policy generally consists of alternating minor and major technology launch cycles we verify that the difference in profits between the commitment and no commitment scenarios can be significant varying from 4 to 12

comparative dynamics of an equilibrium intertemporal asset pricing model this paper uses recursive competitive theory to develop a general equilibrium asset pricing model in this framework all prices and rates of return are endogenously determined thus enabling us to analyze the effects of changes in preferences technological uncertainty and expectations on the structure of security prices in particular we focus on how the market risk premium varies with changes in the underlying economic environment an issue which other asset pricing models have chosen not to address

hedging derivative securities and incomplete markets an e arbitrage approach given a european derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based we solve the optimal replication problem find a self financing dynamic portfolio strategy involving only the underlying securities that most closely approximates the payoff function at maturity by applying stochastic dynamic programming to the minimization of a mean squared error loss function under markov state dynamics we derive recursive expressions for the optimal replication strategy that are readily implemented in practice the approximation error or e of the optimal replication strategy is also given recursively and may be used to quantify the degree of market incompleteness to investigate the practical significance of these e arbitrage strategies we consider several numerical examples including path dependent options and options on assets with stochastic volatility and jumps