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

incentive compatible regulation of foreign owned subsidiaries a tax simulation for the jamaican bauxite industry abstract in 1974 jamaica replaced the corporate income tax on multinationals in the bauxite sector with a production levy on bauxite in order to increase tax revenue the results were mixed tax revenue jumped initially but the multinationsl quickly started shifting production elsewhere we model jamaica s taxation problem assuming that it has incomplete information about the multinationals costs and derive the optimal incentive compatible tax mechanism we simulate and compare the effects on output and tax revenue of the actual and the incentive compatible tax regimes and conclude that there might be substantial benefits to implementing an incentive mechanism

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

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

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

learning from personal experience one rational guy and the justification of myopia abstract the paper examines a large population analog of fictitious play in which players learn from personal experience focusing on what happens when a single rational player is added to the population because the learning process naturally generates contagion dynamics the rational player at times has an incentive to act nonmyopically in 2 2 games the dynamics are asymmetric and favor risk dominant equilibria a variety of other examples are presented journal of economic literature classification number c7

rapid evolution under inertia abstract this paper demonstrates that inertia driven by switching costs leads to more rapid evolution in a class of games that includes m m pure coordination games under the best response dynamic and a fixed rate of mutation the expected waiting time to reach long run equilibrium is of lower order in the presence of switching costs due to the creation of new absorbing states that allow ellison s ellison g 2000 basins of attraction long run stochastic stability and the speed of step by step evolution rev econ stud 67 17 45 step by step evolution to occur

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

the performance of alternative interest rate risk measures and immunization strategies under a heath jarrow morton framework using a monte carlo simulation this study addresses the question of how traditional risk measures and immunization strategies perform when the term structure evolves in a heath jarrow morton 1992 manner the results suggest that for immunization purposes im munization strategies and portfolio formation strategies are more important than interest rate risk measures the performance of immunization strategies depends more on the transaction costs and the holding period than on the risk measures moreover the immu nization performance of bullet and barbell portfolios is not very sensitive to interest rate risk measures

using proxies for the short rate when are three months like an instant the dynamics of the unobservable short rate are frequently estimated directly using a proxy we examine the biases resulting from this practice the proxy problem analytic results show that the proxy problem is not economically significant for single factor affine models in the two factor affine model of longstaff and schwartz 1992 the proxy problem is only economically significant for pricing discount bonds with maturities of more than five years we also describe two different numerical procedures for assessing the magnitude of the proxy problem in a general interest rate model when applied to a nonlinear single factor model they suggest that the proxy problem can be economically significant article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

a markovian framework in multi factor heath jarrow morton models we consider the general n factor heath jarrow and morton model 1992 and provide a sufficient condition on the volatility structure for the spot rate process to be markovian with 2 n state variables the price of a discount bond is also markovian with the same state variables and hence claims against the term structure can be efficiently priced using standard simulation techniques our results extend earlier works such as ritchken and sankarasubramanian 1995 where the one factor model is treated and carverhill 1994 where the volatility structure is non random numerical experiments show that our model can explain the volatility smile observed in the interest rate options market and also overcome the biases noted by flesaker 1993

throwing away a billion dollars the cost of suboptimal exercise strategies in the swaptions market abstract this paper studies the costs of applying single factor exercise strategies to american swap options when the term structure is actually driven by multiple factors using a multifactor string market model of the term structure we find that even when single factor models are recalibrated to match the market at every exercise date the exercise strategies they imply can be suboptimal based on estimates of notional amounts outstanding the total present value costs of following single factor strategies could be several billion dollars these results illustrate the importance of using well specified term structure models

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

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

do bonds span the fixed income markets theory and evidence for unspanned stochastic volatility most term structure models assume bond markets are complete that is that all fixed income derivatives can be perfectly replicated using solely bonds however we find that in practice swap rates have limited explanatory power for returns on at the money straddles portfolios mainly exposed to volatility risk we term this empirical feature unspanned stochastic volatility usv while usv can be captured within an hjm framework we demonstrate that bivariate models cannot exhibit usv we determine necessary and sufficient conditions for trivariate markov affine systems to exhibit usv for such usv models bonds alone may not be sufficient to identify all parameters rather derivatives are needed

discrete choice with social interactions this paper provides an analysis of aggregate behavioural outcomes when individual utility exhibits social interaction effects we study generalized logistic models of individual choice which incorporate terms reflecting the desire of individuals to conform to the behaviour of others in an environment of noncooperative decisionmaking laws of large numbers are generated in such environments multiplicity of equilibria in these models which are equivalent to the existence of multiple self consistent means for average choice behaviour will exist when the social interactions exceed a particular threshold local stability of these multiple equilibria is also studied the properties of the noncooperative economy are contrasted with the properties of an economy in which a social planner determines the set of individual choices finally a likelihood function based on the theoretical model is given and conditions for the econometric identifiability of the model are established

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

a theory of the nominal term structure of interest rates a model of the nominal term structure of interest rates is developed that has a positive and stationary process for the interest rate and delivers closed form expressions for the prices of discount bonds and european options on bonds unlike the one state variable version of the cox ingersoll and ross 1985 model this model even in its one state variable version allows the term premium to change sign as a function of the state and the term to maturity and also allows for shapes of the yield curve that are observed in the u s data but that are disallowed in the cox ingersoll and ross model article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

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

corrections and additions to a nonlinear equilibrium model of the term structure of interest rates abstract longstaff 1989 introduces a new process for the short rate of interest he claims to derive the zero coupon bond pricing formula and state transition density for his model we demonstrate that longstaff s pricing formula is not the solution to the pricing problem which he poses the source of his error is a failure to properly account for a boundary condition we introduce a new model economy and derive a new endogenous interest rate process and find the green s function and the price of a zero coupon bond for our model economy

switching costs in frequently repeated games abstract we add small costs of changing actions and frequent repetition to finitely repeated games making some surprising commitments credible naturally switching costs make it credible not to change action however this can occur for small switching costs and gives a unique subgame perfect equilibrium in coordination games when pareto dominance and risk dominance coincide in the prisoners dilemma switching costs reduce the incentive to deviate from mutual cooperation but reduce the incentive to switch from cooperation to punish defection hence whether switching costs enable cooperation depends on which effect dominates switching costs can make complex threats credible enabling a player to earn more than his stackelberg payoff journal of economic literature classification numbers c7 c73

modelling the term structure of interest rates an efficient nonparametric approach abstract we propose a new approach for estimating the coefficients of the term structure equation by means of the volatility of the interest rates and the slope of the yield curve one advantage of this approach consists in the fact that the drift and the market price of risk are jointly estimated and need not be individually specified we then generate trajectories in a test problem to investigate the finite properties of this approach our simulation results show that this new approach outperforms the classic nonparametric models in the literature finally an application to usa treasury bill data is also illustrated

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

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

evolution in games with endogenous mistake probabilities abstract j bergin and b lipman econometrica 64 1996 943 956 show that the selection effect from the random mutations in the adaptive population dynamics in m kandori g mailath and r rob econometrica 61 1993 29 56 and p young econometrica 61 1993 57 84 is due to restrictions on how these mutation rates vary across population states we here model mutation rates as endogenously determined mistake probabilities by assuming that players with some effort can control the probability of implementing the intended strategy this is shown to corroborate the results in kandori mailath rob 1993 and under certain regularity conditions those in young 1993 journal of economic literature classification number c72

closed form solutions for term structure derivatives with log normal interest rates we derive a unified model that gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero coupon bonds the crucial assumption is that simple interest rates over a fixed finite period that matches the contract which we want to price are log normally distributed moreover this assumption is shown to be consistent with the heath jarrow morton model for a specific choice of volatility closed form solutions for interest rate derivatives in particular caps floors and bond options have been obtained by a number of authors for markovian term structure models with normally distributed interest rates or alternatively log normally distributed bond prices see for example jamshidian 1989 1991a heath jarrow and morton 1992 brace and musiela 1994 geman el karoui and rochet 1995 these models support black scholes type formulas most frequently used by practitioners for pricing bond options and swaptions unfortunately these models imply negative interest rates with positive probabilities and hence they are not arbitrage free in an economy with opportunities for riskless and costless storage of money briys crouhy and schobel 1991 apply the gaussian framework to derive closed form solutions for caps floors and european zero coupon bond options to exclude the influence of negative forward rates on the pricing of zero coupon bond options they introduce an additional boundary condition as shown by rady and sandmann 1994 these pricing formulas are only supported by a term structure model with an absorbing boundary for the forward rate at zero where the absorbing probability is not negligible which for a term structure model is a quite problematic assumption

recent advances in estimating term structure models in the past 10 years increasingly sophisticated statistical techniques have been applied to the estimation of increasingly complex models of the term structure of interest rates in reviewing this literature we highlight the facts that have been established and the key unresolved issues the data indicate that within a wide range of interest rates mean reversion in rates is at best weak whether mean reversion is stronger for very high or very low levels of rates is an unresolved issue the absolute volatility of rates increases as the level of rates increases but the strength of this effect and the role and nature of either stochastic volatility or regime switching components in rates are still unclear unfortunately these unresolved issues have important implications for fixed income option pricing and risk measurement including value at risk calculations

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

adaptive play by idiosyncratic agents abstract equilibrium selection in coordination games has generated a large literature kandori mailath and rob econometrica 61 1993 29 and young econometrica 61 1993 57 studied dynamic models of aggregate behaviour where agents best respond to observations of population play crucially infrequent mistakes mutations allow agents to take actions contrary to current trends and prevent initial configurations from determining long run play an alternative approach is offered here trembles are added to payoffs so that with some probability it is optimal to act against the flow of play the long run distribution of population behaviour is characterised modes correspond to stable bayesian nash equilibria allowing the variance of payoff trembles to vanish a purification process a single equilibrium is played almost always in the long run kandori mailath and rob and young show that the number of contrary actions required to escape an equilibrium determines selection here the likelihood that such actions are taken is equally important

efficient equilibrium selection in evolutionary games with random matching abstract this paper investigates the sensitivity of recent evolutionary models of learning to the specification of the matching mechanism we study a literally random matching mechanism combined with a process of strategy adjustment based on the realized average performance of each strategy in the key class of symmetric 2 2 coordination games the pareto efficient equilibrium per se is selected rather than the risk dominant equilibrium as the probability of experimentation or mutation goes to zero furthermore convergence to the equilibrium is relatively fast we extend these results for example to games of common interest journal of economic literature classification numbers c72 c73

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

shifting incidence and interstate exportation of production taxes on energy resources this paper analyzes the shifting incidence and interstate exportation of state and local government production taxes on four primary energy resources in the united states coal uranium oil and natural gas results of the analysis are then compared with those obtained from a standard partial equilibrium incidence model although a limited literature in this area does exist the discussion focuses more directly on the ways general incidence models must be modified to be appropriately applied to these natural resources from both a short run and a long run perspective 24 references

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