pricing continuously resettled contingent claims abstract this paper is a study of continuously resettled contingent claims prices in a stochastic economy as special cases the relationship between futures and forward prices is analyzed and a preference free expression is derived for these prices as well as the price of a continuously resettled futures option whose formula differs from black s futures option pricing formula due to the effects of marking to market the changes in the futures option premium

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

the effect of annuity insurance and savings and inequality this paper examines the amount of precautionary savings and wealth inequality arising from life span uncertainty by comparing saving behavior under perfect insurance arrangements with that arising under imperfect arrangements namely when longevity risk can be pooled only with members of one s own family the central findings of the paper are 1 perfecting insurance arrangements can lower savings in intergenerationally altruistic and life cycle economies and 2 in altruistic economies perfecting annuity insurance can influence in equality indeed in the long run in the model switching from imperfect family insurance to perfect insurance can mean the difference between absolute inequality and absolute equality copyright 1986 by university of chicago press

a composite leading indicator of the inflation cycle for the euro area we evaluate the performance of composite leading indicators of turning points of inflation in the euro area constructed by combining the techniques of fourier analysis and kalman filters with the national bureau of economic research methodology in addition the study compares the empirical performance of euro simple sum and divisia monetary aggregates and provides a tentative answer to the issue of whether or not the uk should join the euro area our findings suggest that first the cyclical pattern of the different composite leading indicators very closely reflect that of the inflation cycle for the euro area second the empirical performance of the euro divisia is better than its simple sum counterpart and third the uk is better out of the euro area 2005 taylor francis group ltd

optimal hedging in a dynamic futures market with a nonnegativity constraint on wealth abstract this paper examines the issue of optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of lognormal rather than normal returns and of a constant absolute risk aversion utility function in this context the nonnegativity constraint on wealth is binding and the optimal hedging demands are not identical with those encountered in the bulk of the literature which has largely overlooked this problem negative results concerning the derivation of equilibrium in the futures markets and the computation of the open interests then follow

the numeraire portfolio abstract a portfolio formed from a given list of assets is defined as a numeraire portfolio for the list if a it is self financing b its value is always positive and c zero is always the best conditional forecast of the numeraire dominated rate of return of every asset on the list the numeraire portfolio exists if and only if there are no profit opportunities from trading assets on the list for a sample list of heterogeneous assets nyse size quintile portfolios corporate bonds and short term bills numeraire dominated returns are similar to market model forecast errors and as abnormal return measures clearly dominate market adjusted returns

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

futures markets and commodity options hedging and optimality in incomplete markets abstract this paper examines the allocational roles of futures markets and commodity options in multi good and multi period economies in a continuous time model with time additive utilities and homogeneous beliefs trading in unconditional futures contracts the market portfolio and a riskless asset gives any pareto optimal allocation individuals optimal holdings of futures contracts in the continuous time model are related to their consumption bundles and to their risk tolerances it is shown that both hedging and reverse hedging behavior are possible in the general model with discrete trading options on portfolios of commodity options are shown to permit any unconstrained pareto optimal allocation

money is what money does monetary aggregation and the equation of exchange this paper develops a method for distilling the transactions role of the array of monetary assets available to the public into a single aggregate measure of effective transactions balances the result is a monetary quantity index number designated mq which corresponds closely with the monetary aggregate contemplated in the equation of exchange mv pq in general mq and the conventional aggregate m 1 exhibit strikingly similar behavior however during episodes when the behavior of m1 is abnormal relative to income and interest rates mq behaves differently from m 1 during these periods anomalies in the behavior of mq are not detectable

on the optimal hedge of a nontraded cash position in this paper we focus on the optimal demand for futures contracts by an investor with a logarithmic utility function who attempts to hedge a nontraded cash position when the analysis is conducted in the cash commodity price space we show that the value function associated with the bernoulli investor program is not additively separable thus suggesting that this investor hedges against shifts in the opportunity set as represented by the commodity price by establishing the equivalence between the cash formulation of the problem and the wealth formulation we are able to analyze the problem in the wealth commodity price space in this space we show the additive separability of the value function when the futures settlement price process is perfectly locally correlated with the commodity price process the demand for futures in this instance is composed of a a mean variance term and b a minimum variance component that is a classic feature of models with nontraded assets since the first best nonmyopic optimum is attained however the deviation from a mean variance demand should not be interpreted as the expression of a nonmyopic behavior but rather as an attempt to restore a first best optimum on the other hand when the correlation between the futures price and the underlying commodity price is imperfect in general the value function does not separate additively the first best solution cannot be attained and the optimal futures trading strategy involves a hedging term against shifts in the opportunity set in the classic dynamic portfolio problem the investor selects a trading strategy in risky and riskless assets so as to maximize his or her expected lifetime utility in this environment where all assets can be freely traded the logarithmic investor behaves myopically to the extent that he or she ignores shifts in the opportunity set when making current choices samuelson 271 mossin 24 hakansson 16 merton 22 in particular in models with continuous trading it turns out that the value function corresponding to the investor s program is additively separable in wealth and state variables the implication is that his or her behavior will be myopic i e that his or her demand functions for assets will be of the pure meanvariance efficiency type and in particular will not include any dynamic hedging components that are characteristic of financial markets with shifting opportunities in this paper we investigate the structure of the bernoulli investor s demand functions in the situation where one asset cannot be freely traded in the market

investment and hedging under a stochastic yield curve abstract this paper examines portfolio decisions involving both fixed and non fixed income securities two state variables the short term and the long term interest rates fully determine the bonds prices and partly influence the other assets prices we propose first a methodology for determining optimal portfolios in such a context and then use that methodology to solve the portfolio problem of investors whose long term bond holdings are constrained which generates undesirable interest rate risk that are hedged with futures contracts the individual futures positions which involve several hedging components and the futures market equilibrium open interest are derived and analysed

bond pricing and the term structure of interest rates a new methodology for contingent claims valuation this paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates the methodology based on the equivalent martingale measure technique takes as given an initial forward rate curve and a family of potential stochastic processee for its subsequent movements a no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk examples are provided to illustrate the key results in relation to the term structure of interest rates arbitrage pricing theory has two purposes the first is to price all zero coupon default free bonds of varying maturities from a finite number of economic fundamentals called state variables the second is to price all interest rate sensitive contingent claims taking as given the prices of the zero coupon bonds this paper presents a general theory and a unifying framework for understanding arbitrage pricing theory in this context of which all existing arbitrage pricing models are special cases in particular vasicek 1977 brennan and schwartz 1979 langetieg 1980 ball and torous 1983 ho and lee 1986 schaefer and schwartz 1987 and artzner and delbaen 1988 the primary contribution of this paper however is a new methodology for solving the second problem i e the pricing of interest rate sensitive contingent claims given the prices of all zero coupon bonds the methodology is new because i it imposes its stochastic structure directly on the evolution of the forward rate curve ii it does not require an inversion of the term structure to eliminate the market prices of risk from contingent claim values and iii it has a stochastic spot rate process with multiple stochastic factors influencing the term structure the model can be used to consistently price and hedge all contingent claims american or european on the term structure and it is derived from necessary and more importantly sufficient conditions for the absence of arbitrage the arbitrage pricing models of vasicek 1977 brennan and schwartz 1979 langetieg 1980 and artzner and delbaen 1988 all require an iformerly titled bond pricing and the term structure of interest rates a new methodology

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

optimal hedging and equilibrium in a dynamic futures market abstract this paper considers an agent maximizing the expected utility of the sum of the terminal value of a fixed portfolio of spot market assets and the terminal value of a margin account on a futures trading position closed form solutions for the optimal hedging strategy are provided in several special cases

dynamic asset pricing theory with uncertain time horizon abstract this paper addresses the problem of pricing and hedging a random cash flow received at a random date in a general setup with a random time that is not a stopping time of the filtration generated by asset prices we first provide an explicit characterization of the set of equivalent martingale measures we also present price bounds consistent with perfect replication in the absence of arbitrage as is often the case such bounds are too wide to be of any practical use and we consider several choices for narrowing down to one the number of equivalent martingale measures

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

two illustrations of the quantity theory of money of two central implications of the quantity theory of money that a given change in the rate of change in the quantity of money induces i an equal change in the rate of price inflation and ii an equal change in nominal rates of interest the illustrations were obtained by comparing moving averages of the three variables in question using quarterly u s time series for the period 1953 77 readers may find the results of interest as additional confirmation of the quantity theory as an example of one way in which the quantity theoretic relationships can be uncovered via atheoretical methods from time series which are subject to a variety of other forces or as a measure of the extent to which the inflation and interest rate experience of the postwar period can be understood in terms of purely classical monetary forces the theoretical background of the study is reviewed very briefly as it is familiar material in the next section the data processing methods are described and rationalized in section ii the illustrations

on optimal portfolio choice under stochastic interest rates abstract in an economy where interest rates and stock price changes follow fairly general stochastic processes we analyze the portfolio problem of an investor endowed with a non traded cash bond position he can trade on stocks the riskless asset and a futures contract written on the bond so as to maximize the expected utility of his terminal wealth when the investment opportunity set is driven by an arbitrary number of state variables the optimal portfolio strategy is known to contain a pure preference free hedge component a speculative element and merton breeden hedging terms against the fluctuations of each and every state variable while the first two components are well identified and easy to work out the implementation of the last ones is problematic as the investor must identify all the relevant state variables and estimate their distribution characteristics using the martingale approach we show that the optimal strategy can be simplified to include in addition to the pure hedge and speculative components only two merton breeden type hedging elements however large is the number of state variables the first one is associated with interest rate risk and the second one with the risk brought about by the co movements of the spot interest rate and the market prices of risk the implementation of the optimal strategy is thus much easier as it involves estimating the characteristics of the yield curve and the market prices of risk only rather than those of numerous a priori unknown state variables moreover the investor s horizon is shown explicitly to play a crucial role in the optimal strategy design in sharp contrast with the traditional decomposition finally the role of interest rate risk in actual portfolio risk management is emphasized