a note on competitive investment under uncertainty uncertainty over future output prices or input costs can affect investment by a riskneutral firm in two opposing ways first it can increase the value of the marginal unit of capital which leads to more investment this only requires that the stream of future profits generated by the marginal unit be a convex function of the stochastic variable by jensen s inequality the expected present value of that stream is increased this result was demonstrated by richard hartman 1972 and later extended by andrew abel 1983 and others in their models constant returns to scale and the substitutability of capital with other factors ensure that the marginal profitability of capital is convex in output price and input costs even with fixed proportions however this convexity can result from the ability of the firm to vary output so that the marginal unit of capital need not be utilized at times when the output price is low or input costs are high if investment is irreversible and can be postponed a second effect of uncertainty is to create an opportunity cost of investing now rather than waiting for new information to arrive before committing resources this increases the full cost of investing in a marginal unit of capital which reduces investment 2 hence the net effect of uncertainty on irreversible investment depends on the size of this opportunity cost relative to the increase in the value of the marginal unit of capital the sign of the net effect is significant because of its possible policy implications pindyck 1988 and giuseppe bertola 1989 developed models in which a firm faces a downward sloping demand curve and found the net effect to be negative ricardo caballero 1991 has recently studied investment by an individual firm facing a stochastically shifting demand curve he shows that as returns to scale become constant and the elasticity of demand faced by the firm rises this opportunity cost of investing now rather than waiting approaches zero thus in the limit of constant returns and an infinitely elastic demand curve an increase in uncertainty tends to raise rather than decrease current investment even if that investment is irreversible it is important to stress that caballero s limiting result treats the firm in isolation and describes the effect of a meanpreserving increase in price uncertainty and not an increase in industry wide demand uncertainty this note shows that in a competitive market the key interactions between irreversibility and uncertainty occur at the industry level and can only be understood by making price and industry output endogenous 3 doing so restores the positive opportunity cost associated with irreversible investment in addition caballero s result is based on a model with convex adjustment costs an innovative aspect of the model is that these costs can be asymmetric thereby allowing for partial or complete irreversibility complete irreversibility corresponds to a cost of massachusetts institute of technology cambridge ma 02139 this work was supported by the national science foundation under grant no ses 8618502 and by mit s center for energy policy research my thanks to julio rotemberg and especially ricardo caballero for very helpful comments and discussions 1then the marginal profit of capital at each time t in the future is max o pt ct where ct is variable cost thus a unit of capital represents a set of all options on future production which are worth more the greater the variance of pt or ct 2for a detailed discussion of this point and a survey of the recent literature on irreversibility and its implications for investment and market evolution see pindyck 1991 3studies that make price endogenous include steven lippman and richard rumelt 1985 avinash dixit 1989 1991 and john leahy 1990

debt in industry equilibrium this article shows 1 how entry and exit of firms in a competitive industry affect the valuation of securities and optimal capital structure and 2 how given a trade off between tax advantages and agency costs a firm will optimally adjust its leverage level after it is set up we derive simple pricing expressions for corporate debt in which the price elasticity of demand for industry output plays a crucial role when a firm optimally adjusts its leverage over time we show that total firm value comprises the value of discounted cash flows assuming fixed capital structure plus a continuum of options for marginal increases in debt article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

the valuation of floating rate instruments abstract a framework for valuing floating rate notes is developed to examine the effects of 1 lags in the coupon formula 2 special contractual features and 3 default risk evidence from a sample of floaters indicates they sold at significant discounts while lags in the coupon formulas and other contractual features make these notes more variable they do not account for the magnitude of the discounts we conclude that the fixed default premium in the coupon formula of a typical note is inadequate to compensate for time varying default premiums demanded by investors who treat other corporate short term paper as close substitutes

optimal dynamic trading with leverage constraints we solve for the optimal dynamic trading strategy of an investor who faces a leverage constraint i e a limitation on his ability to borrow for the purpose of investing in a risky asset we assume that the investor has constant relative risk aversion and that the value of the risky asset follows a geometric brownian motion in the absence of the leverage constraint the optimal strategy involves investing a fixed proportion of wealth in the risky asset we prove that in the presence of the leverage constraint the optimal investment also involves investing a fixed proportion of wealth in the risky asset when the leverage constraint is not binding however the two proportions are different reflecting the extent to which the investor alters his strategy even when the leverage constraint is not binding because of the possibility that the leverage constraint will become binding in the future

asymmetric information and options in an extension of the kyle 1985 model of continuous insider trading it is shown that asymmetric information can make it impossible to price options by arbitrage even when an option would appear to be redundant its introduction into the market can cause the volatility of the underlying asset to become stochastic this eliminates the potential for dynamically replicating the option the change in the price process of the asset reflects a change in the information transmitted by volume and prices when the option is traded article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

avoiding default the role of credit in the consumption collapse of 1930 high consumer indebtedness threatens future consumption spending if default is expensive consumer spending collapsed in 1930 turning a minor recession into the great depression households were shouldering an unprecedented burden of installment debt down payments were large contracts were short equity in durable goods was therefore acquired quickly missed installment payments triggered repossession reducing consumer wealth in 1930 because households lost all acquired equity cutting consumption was the only viable strategy in 1930 for avoiding default institutional changes lowered the cost of default by 1938 when recession began again indebted households chose to default rather than reduce consumption

a pricing method for options based on average asset values abstract in this paper we present a new strategy for pricing average value options i e options whose payoff depends on the average price of the underlying asset over a fixed period leading up to the maturity date such options are of particular interest and importance for thinly traded assets e g crude oil since price manipulation is inhibited and both the investor and issuer enjoy a welcome degree of protection from the vagaries of the market these options are often implicit in a bond contract although they also appear in a straightforward form our results suggest that the price of an average value option will always be lower than that of a standard european option our pricing strategy involves monte carlo simulation with variance reduction elements and offers an enhanced pricing method to both arbitragers and hedgers as well as to the issuers of such bonds

monte carlo methods for security pricing the monte carlo approach has proved to be a valuable and flexible computational tool in modern finance this paper discusses some of the recent applications of the monte carlo method to security pricing problems with emphasis on improvements in efficiency we first review some variance reduction methods that have proved useful in finance then we describe the use of deterministic low discrepancy sequences also known as quasi monte carlo methods for the valuation of complex derivative securities we summarize some recent applications of the monte carlo method to the estimation of partial derivatives or risk sensitivities and to the valuation of american options we conclude by mentioning other applications

the analytic valuation of american options no analytic solutions exists for the valuation of american options written on futures contracts and foreign currencies for which early exercise may be optimal this article formulates the american option valuation problem in economically and mathematically meaningful ways this enables us to derive valuation formulas for american options the properties associated with the optimal exercise boundary are examined and a numerical technique to implement the valuation formulas is presented article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

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

information revelation through option exercise in many real world situations agents must formulate option exercise strategies with imperfect information in such a setting agents may infer the private signals of other agents through their observed exercise strategies the building of an office building the drilling of an exploratory oil well and the commitment of a pharmaceutical company toward the research of a new drug all convey private information to other market participants this article develops an equilibrium framework for option exercise games with asymmetric private information many interesting aspects of the patterns of equilibrium exercise are analyzed in particular informational cascades where agents ignore their private information and jump on the exercise bandwagon may arise endogenously article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

leverage constraints and the optimal hedging of stock and bond options this paper considers the problem of a financial institution that needs to hedge a stream of state contingent cash flows while facing borrowing and short sales restrictions the study determines analytically the strategy that minimizes the initial cost of hedging the desired cash flow which is also the upper bound on its market price and shows that the impact of leverage constraints on the cost of hedging call and put options is significant and therefore the biases detected by tests of option pricing models may not represent arbitrage opportunities the paper also shows that with credit limits it is optimal to reduce the rate of trading thus these constraints need to be recognized when estimating the trading volume generated in replicating contingent payoffs such as portfolio insurance

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 first best sharing rule in the continuous time principal agent problem with exponential utility abstract the continuous time principal agent model with exponential utility developed by holmstrom and milgrom admits a simple closed form solution the second best sharing rule is a linear function of aggregated output here we show that the first best sharing rule is also linear in aggregated output the result follows immediately from the separability of the problem and the fact that principal and agent both have cara utility journal of economic literature classification numbers d82 j33

pricing american style securities using simulation abstract we develop a simulation algorithm for estimating the prices of american style securities i e securities with opportunities for early exercise our algorithm provides both point estimates and error bounds for the true security price it generates two estimates one biased high and one biased low both asymptotically unbiased and converging to the true price combining the two estimators yields a confidence interval for the true price the proposed algorithm is especially attractive compared with lattice and finite difference methods when there are multiple state variables and a small number of exercise opportunities preliminary computational evidence is given

a continuous time model to determine the intervention policy for pbgc abstract the pension benefit guaranty corporation pbgc which insures private defined benefit pension plans is facing mounting deficits the main cause of this predicament for pbgc can be traced down to the misuse of the insurance by a few companies we therefore propose an active intervention policy which would result in termination of severely underfunded plans for the pbgc a continuous time model is provided to help determine the point of intervention if necessary using option pricing techniques a clear exposition of the intervention doctrine is thus obtained via this model we also provide a numerical illustration of the working of the model on a hypothetical pension plan

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

the impact of default risk on the prices of options and other derivative securities abstract this paper presents a model for valuing derivative securities when there is default risk the holder of a security is assumed to recover a proportion of its no default value in the event of a default by the counterparty both the probability of default and the size of the proportional recovery are random the paper shows how data on bonds issued by the counterparty can be used to provide information about model parameters

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

equilibrium interest rates and multiperiod bonds in a partially observable economy this paper analyzes the market for financial assets in a production and exchange economy with several realized outputs and a single unobservable source of nondiversifiable risk the paper demonstrates that for a large class of diffusion outputs and preferences optimizing consumers first estimate the realizations of the unobservable factor and then use these estimates to determine portfolio and consumption rules moreover the explicit consideration of this unobservable productivity factor affects equilibrium demands and prices the equilibrium spot rate of interest emerges as the best estimate of the unobservable factor and multiperiod default free bonds arise as the optimal hedge for the unobservable changes of the stochastic investment opportunity set this paper analyzes the market for financial assets in a production and exchange economy with several realized outputs and a single unobservable source of nondiversifiable risk the paper poses and answers three questions 1 how do consumers determine equilibrium demands and prices when their investment opportunities are unobservable 2 in equilibrium what financial assets provide an optimal hedge for the

over rejections in rational expectations models abstract standard tests for rationality may not have the correct size if there is feedback from innovations to future values of the regressors it is shown that nonparametric tests reject at their nominal level and display good power in a variety of specifications of a model involving feedback

the empirical implications of the cox ingersoll ross theory of the term structure of interest rates the one factor version of the cox ingersoll and ross model of the term structure is estimated using monthly quotes on u s treasury issues trading from 1952 through 1983 using data from a single yield curve it is possible to estimate implied short and long term zero coupon rates and the implied variance of changes in short rates analysis of residuals points to a probable neglected tax effect the term structure of interest rates is important to economists because the relationship among the yields on default free securities that differ in their term to maturity reflects the information available to the market about the future course of events the expectations hypothesis the liquidity preference hypothesis hicks 10 and the market segmentation hypothesis culbertson 6 are theories of the term structure that predict little more than that the implied forward rate is either equal to or not equal to the expectation of future spot rates cox ingersoll and ross 5 cir model the term structure of interest rates in a competitive equilibrium context their model has elements in common with the earlier hypotheses of the term structure however the cir model has a rich class of empirical implications not only for the pricing of default free securities but also for the pricing of bond options callable bonds and other types of financial claims this paper examines the extent to which the model in its simplest one factor form is descriptive of the prices of u s treasury bills bonds and notes traded from 1952 to 1983 section i describes the model and the parsimonious representation of bond prices which it implies section ii describes the data and section iii outlines the preliminary results obtained by fitting the model to observed data the final section outlines directions for future research

on the fluctuations in consumption and market returns in the presence of labor and human capital an equilibrium analysis abstract we examine the effects of human capital on consumption stock market and other fluctuations in a general equilibrium continuous time model a representative consumer worker investor derives utility from consumption and leisure a representative firm demands labor as the sole input to a stochastic production technology driven by general possibly nonmultiplicative shocks for cobb douglas utility and multiplicative shocks labor is nonstochastic and consumption and stock market volatility are equated as under no human capital deviations from this are analyzed for logarithmic utility and constant elasticity of substitution production technology cases are identified where the presence of labor causes consumption to be smoother than the stock market

transactions costs and portfolio choice in a discrete continuous time setting abstract this paper makes the following observation concerning a new formulation of the consumption and portfolio choice model of merton 1971 with transaction costs suppose an investor observes his or her current wealth only when making a transaction that transactions are costly and that decisions to transact can be made at any time based on all current information if at each transaction the agent is charged a fixed fraction of current portfolio value an optimal policy exists and the optimal interval of time between transactions is fixed independent of time and current wealth

a one factor model of interest rates and its application to treasury bond options 1990 a one factor model of interest rates and its application to treasury bond options financial analysts journal vol 46 no 1 pp 33 39

options on the spot and options on futures this paper analyzes and compares the valuation of two types of options that relate to the same asset options on the asset itself and options on the futures on the asset the early exercise privilege plays a central role in explaining the differences between the values of the two options it is shown that in the case of a cash instrument that does not make interim payments such as gold the value of a call option on the spot is smaller than the call option on the futures contract the opposite is true for put options the early exercise boundaries which characterize when it pays to exercise are also compared and analyzed the financial markets have recently witnessed a proliferation of various types of listed options on commodities and on financial assets commencing with call options on individual common stocks recent innovations have included call and put options on treasury bonds metals foreign currencies and stock market

nontraded asset valuation with portfolio constraints a binomial approach we provide a simple binomial framework to value american style derivatives subject to trading restrictions the optimal investment of liquid wealth is solved simultaneously with the early exercise decision of the nontraded derivative noshort sales constraints on the underlying asset manifest themselves in the form of an implicit dividend yield in the risk neutralized process for the underlying asset one consequence is that american call options may be optimally exercised prior to maturity even when the underlying asset pays no dividends applications to executive stock options eso are presented it is shown that the value of an eso could be substantially lower than that computed using the black scholes model we also analyze nontraded payoffs based on a price that is imperfectly correlated with the price of a traded asset the economics of asset pricing when one or more of the assets in the opportunity set are either subject to trading restrictions or entirely nontraded is a matter of great interest viewed from a practical perspective we have several important examples of such assets that are subject to trading restrictions pensions which represent perhaps the most significant of assets held by individual households are subject to trading restrictions it is typically the case that assets in pensions are not available for immediate consumption borrowing against pension assets is subject to significant direct and indirect costs by way of taxes and early withdrawal penalties human capital is another example housing investment is also illiquid and subject to significant transaction costs together pensions human capital and housing constitute a substantial part of a typical household s assets the significance of such nontraded assets for risk premia has already been noted by bewley 1982 there are other circumstances where lack of unrestricted trading plays an important role executive compensation plans usually take the this article was presented at boston university we would like to thank the editor bernard dumas and two anonymous referees for very helpful comments we also thank nalin kulatilaka and seminar participants for useful suggestions ganlin chang fei guan and carlton osakwe provided valuable research assistance j detemple acknowledges support from the social sciences and humanities research

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

the consumption based capital asset pricing model the paper provides conditions on the primitives of a continuous time economy under which there exist equilibria obeying the consumption based capital asset pricing model ccapm the paper also extends the equilibrium characterization of interest rates of cox ingersoll and ross 1985 to multi agent economies we do not use a markovian state assumption this work provides sufficient conditions on agents primitives for the validity of the consumption based capital asset pricing model ccapm of breeden 1979 as a necessary condition breeden showed that in a continuous time equilibrium satisfying certain regularity conditions one can characterize returns on securities as follows the expected instantaneous rate of return on any security in excess of the riskless interest rate the security s expected excess rate of return is a multiple common to all securities of the instantaneous covariance of this excess return with aggregate consumption increments this common multiple is the arrow pratt measure of risk aversion of a representative agent rubinstein 1976 published a discrete time precursor of this result the exis tence of equilibria satisfying breeden s regularity conditions had been an open issue we also show that the validity of the ccapm does not depend on breeden s assumption of markov state information and present a general asset pricing model extending the results of cox ingersoll and ross 1985 as well as the discrete time results of rubinstein 1976 and lucas 1978 to a multi agent environment since the ccapm was first proposed much effort has been directed at finding sufficient conditions on the model primitives the given assets the agents preferences the agents consumption endowments and in a production econ omy the feasible production sets conditions sufficient for the existence of continuous time equilibria were shown in duffie 1986 but the equilibria demonstrated were not shown to satisfy the additional regularity required for the ccapm in particular breeden assumed that all agents choose pointwise interior consumption rates in order to characterize asset prices via the first order conditions of the bellman equation interiority was also assumed by huang 1987 in demonstrating a representative agent characterization of equilibrium an approach exploited here the use of dynamic programming and the bellman equation aside from the difficulty it imposes in verifying the existence of interior 1 financial support from the national science foundation is gratefully acknowledged we thank

optimal consumption and portfolio policies when asset prices follow a diffusion process abstract we consider a consumption portfolio problem in continuous time under uncertainty a martingale technique is employed to characterize optimal consumption portfolio policies when there exist nonnegativity constraints on consumption and on final wealth we also provide a way to compute and verify optimal policies our verification theorem for optimal policies involves a linear partial differential equation unlike the nonlinear partial differential equation of dynamic programming the relationship between our approach and dynamic programming is discussed we demonstrate our technique by explicitly computing optimal policies in a series of examples in particular we solve the optimal consumption portfolio problem for hyperbolic absolute risk aversion utility functions when the asset prices follow a geometric brownian motion the optimal policies in this case are no longer linear when nonnegativity constraints on consumption and on final wealth are included by these examples one can see that our approach is much easier than the dynamic programming approach

strategic analysis of contingent claims traditional contingent claims analysis provides an elegant and complete model of the financing of the dynamic firm but has difficulty fitting the observations in the market recent work in corporate finance suggests this is because of its failure to model financial distress realistically we survey recent efforts to address this issue by deriving valuation formulae from the analysis of non cooperative equilibria in extensive form games we illustrate how a simple static bankruptcy model can be incorporated in a dynamic game we then show how to find the continuous time equivalent of this game this we use to find closed form bond formulae in special cases and to exploit efficient numerical techniques generally

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

valuation optimal asset allocation and retirement incentives of pension plans we provide a framework in which we link the valuation and asset allocation policies of defined benefits plans with the lifetime marginal productivity schedule of the worker and the pension plan formula in turn we examine the retirement policies that are implied by the primitives of the model and the value of pension obligations our model provides an explicit valuation formula for a stylized defined benefits plan the optimal asset allocation policies consist of the replicating portfolio of the pension liabilities and the growth optimum portfolio independent of the pension liabilities we show that the worker will retire when the ratio of pension benefits to current wages reaches a critical value which depends on the parameters of the pension plan and the discount rate using numerical techniques we analyze the feedback effect of retirement policies on the valuation of plans and on the asset allocation decisions article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

exploiting the conditional density in estimating the term structure an application to the cox ingersoll and ross model we propose an empirical method that utilizes the conditional density of the state variables to estimate and test a term structure model with known price formulae using data on both discount and coupon bonds the method is applied to an extension of a two factor model due to cox ingersoll and ross 1985 cir our results show that estimates based on only bills imply unreasonably large price errors for longer maturities we reject the original cir model using a likelihood ratio test and conclude that the extended cir model also fails to provide a good description of the treasury market

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

equilibrium and options on real assets in aggregate options on real and financial assets can have very different properties typically the good or service produced by a real asset has a finite elasticity of demand and developers have finite capacities also the supply of options can be limited and developers can be less than perfectly competitive in a subgame perfect nash equilibrium with these properties the optimal exercise policy and resulting values of developed and undeveloped assets are calculated explicitly the novel comparative statics are discussed in detail article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

a test of the cox ingersoll and ross model of the term structure we test the theory of the term structure of indexed bond prices due to cox ingersoll and ross cir the econometric method uses hansen s generalized method of moments and exploits the probability distribution of the single state variable in cir s model thus avoiding the use of aggregate consumption data it enables us to estimate a continuous time model based on discretely sampled data the tests indicate that cir s model for index bonds performs reasonably well when confronted with short term treasury bill returns the estimates indicate that term premiums are positive and that yield curves can take several shapes however the fitted model does poorly in explaining the serial correlation in real treasury bill returns article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

an exact solution to a dynamic portfolio choice problem under transactions costs the presence of any friction in financial markets qualitatively changes the nature of the optimization problem faced by an investor it requires one to either act or do nothing an issue which of course does not arise in frictionless situations the investor considered here accumulates wealth without consuming until some terminal point in time when he consumes all his objective is to maximize the expected utility derived from that terminal consumption we postpone the terminal point far into the future to obtain a stationary portfolio rule the portfolio policy is in the form of two control barriers between which portfolio proportions are allowed to fluctuate we show how to calculate them

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

corruption cooperation and endogenous time discount rates virtually all uses of repeated games tostudy of cooperation assume that people stime discount rates are exogenous andfixed here we offer an evolutionary gameembedded in a multi period model ofinvestment and consumption in whichindividual time discounts are determined bytheir convergence to values determined byevolutionary stable strategies oursubstantive motivation though iscorruption and its relationship to economicgrowth to understand the observedrelationship between levels of corruptionand economic indicators of social welfare we argue that corruption is a form ofcooperation that requires closeinterpersonal monitoring if we assume moreover that when people discount thefuture greatly the only sustainable formsof cooperation are those that allow forclose monitoring then our analysis can beinterpreted as a dynamic model of therelationship between corruption andinvestment

bond and option pricing when short rates are lognormal this article describes a one factor model for bond and option pricing that is based on the short term interest rate and that allows the target rate mean reversion and local volatility to vary deterministically through time for any horizon the distribution of possible short rates is lognormal so the rate neither falls below zero nor reflects off a barrier at zero a model like this allows one to match the yield curve the volatility curve and the cap curve surprisingly adding to future local volatility lowers the volatility curve a conventional binary tree with probabilities of 0 5 but variable time spacing is used to value bonds and options when the inputs are constant the slope of the yield curve starts out positive and ends up negative while its curvature shifts from negative to positive even when mean reversion is zero the volatility curve has a negative slope the differential cap curve rises steeply through the effects of volatility and then falls steeply through the effects of discounting and a falling forward rate used as the strike price

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

investments in flexible production capacity abstract we examine the technology and capacity choice problem of a multi output firm facing stochastic demands in a continuous time framework the firm can install output specific capital or at greater cost flexible capital that can be used to produce different outputs investment is irreversible the firm must choose a technology and decide how much capital to install knowing it can add more later as demand evolves we formulate the capacity choice problem as a singular stochastic control problem show that the value of the firm equals the value of its installed capital plus the value of its options to add capacity in the future and derive an optimal investment rule that maximizes the firm s market value we also address the analogous problem for a multi input firm that faces stochastically evolving factor costs and can install input specific or flexible capital

irreversible investment with price ceilings a model of irreversible investment in a competitive industry under demand uncertainty is developed in the absence of restrictions investment by itself will keep the price from rising above a natural ceiling that exceeds the long run average cost by an option value factor when a lower ceiling is imposed investment is triggered only by the observation of an even higher shadow price as the imposed ceiling is reduced to the long run average cost this shadow price goes to infinity and investment ceases completely because investment is depressed a tighter price ceiling generally leads to a higher long run average price

a general equilibrium model of international portfolio choice we investigate in a two country general equilibrium model whether a bias in consumption towards domestic goods will necessarily lead to a preference for domestic securities we develop a model where investors are constrained to consume only from their domestic capital stock and where it is costly to transfer capital across countries in this model investors less risk averse than an investor with log utility bias their portfolios towards domestic assets investors more risk averse than log however prefer foreign assets thus this model suggests that it is unlikely that the portfolios observed empirically can be explained by the high proportion of domestic goods in total consumption we investigate in a two country general equilbrium model whether a bias in consumption toward domestic goods will necessarily lead to a preference for domestic assets in an investor s optimal portfolio we constrain investors to consume only from their domestic capital stock and introduce a proportional cost for transferring goods from one country this cost gives rise to endogenous deviations from the law of one price lop thus the home and foreign investors do not hold identical portfolios we show that an investor s optimal portfolio is biased towards domestic equity only if she is less risk averse than an investor with log utility investors with relative risk aversion greater than one exhibit a preference for the foreign asset this is because the exchange rate derived endogenously is negatively correlated with the return on the foreign asset and therefore the translated return on the foreign stock is less risky than that on the domestic stock thus the results of this model suggest that it is unlikely that the preference for domestic assets that is observed empirically can be explained by the high proportion of domestic goods in total consumption there exists a considerable body of literature documenting the gains from international diversification grubel 1968 was the first to propose that international diversification allows investors to attain lower return variances than those achievable by diversifying domestically this proposition relies on the correlation between stock indices across countries being significantly less

the relation between forward prices and futures prices abstract this paper consolidates the results of some recent work on the relation between forward prices and futures prices it develops a number of propositions characterizing the two prices these propositions contain several testable implications about the difference between forward and futures prices many of the propositions show that equilibrium forward and futures prices are equal to the values of particular assets even though they are not in themselves asset prices the paper then illustrates these results in the context of two valuation models and discusses the effects of taxes and other institutional factors

asset pricing in a production economy with incomplete information this paper analyzes an economy in which investors operate under partial information about technology relevant state variables it is shown that for gaussian information structures under incomplete observations the consumer s problem can be transformed into an equivalent program with a completely observed state the conditional expectation of the underlying unobservable state variables a consequence of this transformation is that classic results in finance remain valid under an appropriate reinterpretation of the state variables the static capital asset pricing model capm of sharpe 24 lintner 16 and mossin 20 states that the expected premium on any risky asset is proportional to the premium on the market as a whole this theoretical linear relationship however is subject to criticisms on two grounds first it does not seem to be supported by the empirical evidence second it is based on the premises of a constant opportunity set merton 19 subsequently relaxes this assumption and shows that when the opportunity set fluctuates over time due to changes in the state of the economy individual securities are also priced with respect to selected portfolios funds providing a hedge against unanticipated fluctuations 2 more recently breeden 3 has extended merton s results by emphasizing the role of aggregate consumption in pricing relationships in this paper we seek to further our understanding of asset pricing by relaxing the assumption that investors observe the state of the economy in the mertonbreeden framework observed state variables affect the means and variances of asset returns implying deformations of the opportunity set over time from a practical point of view it seems that this complete information assumption is violated investors in financial markets operate under partial knowledge of the microvariables which influence production and the returns on assets their decisions rely mostly on information through noisy channels such as newspapers technical reviews or weather reports in this paper we attempt to model such

linearity with project selection and controllable diffusion rate in continuous time principal agent problems i extend holmstrom and milgrom s model by allowing the agent to control privately or publicly the diffusion rate process and show that the optimal contract is still linear i discuss the conditions under which conflicts over the choice of diffusion rate do and do not arise as an application i examine project selection problems of a firm conflicts between the manager and investors arise because giving the manager too much incentive to work to increase the profit from ongoing operations can induce him to be too conservative in project selection possibly resulting in optimal contracts with low sensitivities

consumption and portfolio policies with incomplete markets and short sale constraints the infinite dimensional case abstract we employ a martingale approach to study a dynamic consumption portfolio problem in continuous time with incomplete markets and short sale constraints we introduce a notion of minimax local martingale and transform the dynamic problem into a static problem of maximizing expected utility over the consumption bundles that satisfy a single budget constraint formed using that measure we establish the existence of and characterize the minimax local measure provide sufficient conditions for the dynamic consumption portfolio problem to have a solution and relate the optimal policies to the solution of quasi linear partial differential equation

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

equilibrium positive interest rates a unified view this article develops precise connections among two general approaches to building interest rate models a general equilibrium approach using a pricing kernel and the heath jarrow and morton framework based on specifying forward rate volatilities and the market price of risk the connections exploit the observation that a pricing kernel is uniquely determined by its drift through these connections we provide for any arbitrage free term structure model a representative consumer real production economy supporting that term structure model in equilibrium we put particular emphasis on models in which interest rates remain positive by modeling the dynamics of the drift of the pricing kernel we construct a new family of markovian positive interest rate models article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

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

path dependent options the case of lookback options lookback options are path dependent contingent claims whose payoffs depend on the extrema of a given security s price over a certain period of time using probabilistic tools we derive explicit formulas for various european lookback options and provide some results about their american counterparts

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