an equilibrium debt option pricing model in discrete time abstract in this paper we develop a discrete time binomial model for pricing options on default free debt securities the model is a single factor or spot rate model in which an arbitrage free term structure is developed and used to price any interest rate contingent claim the model differs from other work in this area in that the model is straightforward to program and use and is not bound by a restrictive equilibrium concept such as the expectations hypothesis the paper demonstrates various properties of the model and demonstrates how information from the existing term structure can be used to parameterize the model

advance notice and job search the value of an early start recent studies of the effect of advance notice on jobless duration following displacement misspecify the relationship between these two variables by treating advance notice as a dummy regressor in conventional survival time models job search theory however suggests that the major impact of advance notice is not to alter the efficiency of search after job loss but rather to allow workers to begin search before job loss the authors develop a sequential regimes job search model which allows search prior to displacement for workers with advance knowledge of layoff with different search intensities before and after layoff maximum likelihood estimates of the model are then computed using a pooled data set from the 1984 and 1986 displaced worker surveys advance knowledge is found to significantly shorten jobless duration for most labor force groups using these estimates the authors simulate the effect of various levels of advance knowledge on jobless duration their results indicate that relatively modest advance notice substantially benefits many displaced workers

partners or rivals strategies for the iterated prisoner s dilemma within the class of memory one strategies for the iterated prisoner s dilemma we characterize partner strategies competitive strategies and zero determinant strategies if a player uses a partner strategy both players can fairly share the social optimum but a co player preferring an unfair solution will be penalized by obtaining a reduced payoff a player using a competitive strategy never obtains less than the co player a player using a zero determinant strategy unilaterally enforces a linear relation between the two players payoffs these properties hold for every strategy used by the co player whether memory one or not

unemployment insurance and the rate of re employment of displaced workers the rate of transition from unemployment to re employment for a sample of displaced workers is estimated using a semiparametric specification which allows the effects of unemployment insurance benefits to vary over time three results which would be missed by more restrictive specifications demonstrate the value of this approach 1 the effects of ui benefits decline and eventually disappear as the date of expiration approaches 2 expiration of ui benefits are an inadequate explanation of the spikes commonly observed in nonparametric sample hazard rates for re employment 3 ui benefits do not significantly affect the rate at which a displaced worker becomes re employed in his or her previous industry but reduce the rate for transitions to other industries copyright 1991 by mit press

reading pibor futures options smiles the 1997 snap election abstract in this paper we compare various methods that extract a risk neutral density rnd out of pibor interest rate futures options and we investigate how traders react to a political event our benchmark model derives from a brace d gatarek m musiela mathematical finance 7 1997 127 155 we also consider a mixture of log normals as in w r melik c p thomas journal of financial and quantitative analysis 32 1997 91 116 an hermite expansion as in p abken d b madan s ramamurtie estimation of risk neutral and statistical densities by hermite polynomial approximation with an application to eurodollar futures options federal reserve bank of atlanta 1996 and a method based on maximum entropy according to p buchen m kelly journal of financial and quantitative analysis 31 1996 143 159 we take care of the early exercise feature and we show how to approximate rnds for a fixed time to maturity the various methods generate similar rnds a daily panel of options running from february 1997 to july 1997 reveals that operators expected the snap election a few days before the official announcement was made and that a substantial amount of political uncertainty subsisted even a month after the elections uncertainty evolved with polls forecasts of the future government

prepayment and the valuation of mortgage backed securities this paper puts forward a valuation framework for mortgage backed securities rather than imposing an optimal value minimizing call condition we assume that at each point in time there exists a probability of prepaying this conditional probability depends upon the prevailing state of the economy to implement our valuation procedure we use maximum likelihood techniques to estimate a prepayment function in light of recent aggregate gnma prepayment experience by integrating this empirical prepayment function into our valuation framework we provide a complete model to value mortgagebacked securities given an optimal value minimizing call policy a mortgage should never be called when its market value is less than its call price similarly a mortgage should be called if it is worth more than its call price however mortgagors often call their loans when the prevailing refinancing rate exceeds the contract rate on the loan dunn and mcconnell 1981 in addition some mortgagors do not call their loans when the loan s contract rate exceeds the prevailing refinancing rate the purpose of this paper is to put forward a valuation framework for mortgagebacked securities consistent with these stylized facts associated with mortgage prepayments the mortgagor s prepayment decision is integral to our valuation framework however we do not impose an optimal value minimizing call condition to price these securities rather we assume that at each point in time there exists a probability of prepaying this conditional probability depending upon the prevailing state of the economy by integrating this prepayment function into our valuation framework we provide a complete model to value mortgage backed securities to implement our valuation procedures we estimate a prepayment function given recent gnma prepayment experience we follow green and shoven 1986 by using a proportional hazards model to estimate the influence of various explanatory variables or covariates on the mortgagor s prepayment decision distinct from green and shoven we explicitly model the effects of seasoning as well as investigating the influence of interest cost savings from refinancing in addition we also consider the effects of lagged refinancing rates heterogeneity

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

generalising interest rate duration with directional derivatives direction x and applications conventional or fisher weil duration is an ordinary derivative that measures the response of portfolio value to marginal parallel shifts in the term structure while other proposed measures are generally specific to particular interest rate processes in this paper we show that portfolio responses to arbitrary shifts in the term structure may be handled by the use of frechet or directional derivatives presenting a simple algorithm for the directional derivative of a fixed interest portfolio viewed as a set of cash flows for a given portfolio one can locate the most sensitive areas along the term structure by computing a function or profile direction x that gives the term structure movement to which the portfolio is most exposed immunisation techniques can be based on choosing ancillary assets that ensure that the portfolio directional derivative is zero or as close to zero as possible this generalises approaches based on factor models of the term structure the analysis is applied to both continuous and discrete time

differential taxation and the equilibrium structure of interest rates equilibrium coupon bond pricing relationships given differential taxation are derived under uncertainty assuming that both corporate and municipal bonds were originally issued at par but are currently selling at a discount the impact of differential taxation upon the term structure and coupon structure of interest rates is investigated while the tax structure of interest rates is uniquely characterized differential taxation substantially alters the prevailing equilibrium structure of interest rates

the impact of the potential duration of unemployment benefits on the duration of unemployment abstract this paper examines the impact of the potential duration of unemployment insurance ui benefits on unemployment in the united states first we use a large sample of household heads to examine differences in the unemployment spell distributions of ui recipients and nonrecipients sharp increases in the escape rate from unemployment both through recalls and new job acceptances are apparent for ui recipients around the time of benefits exhaustion such increases are not apparent at similar points of spell duration for nonrecipients second our analysis of accurate administrative data from 12 states indicates that a one week increase in potential benefit duration increases the average duration of the unemployment spells of ui recipients by 0 16 to 0 20 weeks

dynamic strategies for fixed income investment the last 30 years have witnessed an enormous growth in fixed income markets how long term fixed income strategies should be implemented for the welfare of investors has become a major concern of bond managers this study makes use of stochastic optimal control to formulate a multi period portfolio selection model and implements it using backward recursion algorithm to find numerically the optimal allocation of wealth between long and short term bonds for an investor with power utility and an investment horizon of 10 years by way of a technical manipulation this study uses the fact that the long rate and the spread difference between long rate and short rate are uncorrelated to simplify model formulation and parameter estimation the results show that an investor would increase his her holding of short term bond if his her investment horizon becomes shorter or if he she is more risk averse or both

parameter estimation in stochastic scenario generation systems abstract scenario analysis offers an effective tool for addressing the stochastic elements in multi period financial planning models critical to any scenario generation process is the estimation of the input parameters of the underlying stochastic model for economic factors in this paper we propose a new approach for estimation known as the integrated parameter estimation ipe this approach combines the significant features of other well known estimation techniques within a non convex multiple objective optimization framework with the objective weights controlling the relative importance of the features we solve the non convex optimization problem using adaptive memory programming a variation of tabu search based on a short interest rate model using uk treasury rates from 1980 to 1995 the integrated approach compares favorably with maximum likelihood and the generalized method of moments we also evaluate performance with towers perrin s cap link scenario generation system

the default risk of swaps we characterize the exchange of financial claims from risky swaps these transfers are among three groups shareholders debtholders and the swap counterparty from this analysis we derive equilibrium swap rates and relate them to debt market spreads we then show that equilibrium swaps in perfect markets transfer wealth from shareholders to debtholders in a simplified case we obtain closed form solutions for the value of the default risk in the swap for interest rate swaps we obtain numerical solutions for the equilibrium swap rate including default risk we compare these with equilibrium debt market default risk spreads swaps have been one of the most explosive and important innovations in international capital markets in the last 10 years in its simplest form a swap consists of an agreement hetween two entities called counterparties to exchange in the future two streams of cash flows in a currency swap these streams of cash flows consist of a stream of interest and principal payments in one cvtrrency exchanged for a stream of interest and principal payments of the same maturity in another currency in an interest rate swap they consist of streams of interest payments of one type fixed or floating exchanged for streams of interest payments of the other type in the same currency the two types of swap are shown in appendix 1 the economic importance of swap transactions is the fact that they can he comhined with deht issues to change the nature of the liahility for the borrower the sum of a hond issue and a currency swap gives a net liability stream which is equivalent to transforming the bond liability into a different currency a floating rate note combined with an interest rate swap results in a liability equivalent to fixed rate debt two issues have dominated the academic literature on swaps the first concerns the reasons for their use arbitrage of imperfections in capital markets was the original cause of their appearance price and henderson 1984 turnbull 1987 shows that lowering borrowing costs by a synthetic transaction involving a swap is not possible in a complete integrated capital market subsequent authors wall and pringle 1988 arak estrella groodman and silver 1988 smith smithson and wakeman 1987 observe

interest rate dynamics and the term structure a note abstract the brennan and schwartz two factor model of the term structure is re examined using constant duration long term yields in place of the fluctuating duration consol yields and additional stability is achieved in the empirical estimations the model is then reformulated to examine more closely the relationship between changes in long and short rates of interest it is found that movements in the short rate of interest are related to movements in the long rate the spread between the long and short rates and the prior movement in the long rate the model is then tested for its out of sample predictive ability and found to possess a modest amount of predictive power

discrimination and the unemployment durations of white and black males in this study we develop a model to decompose the longer unemployment duration of blacks into discriminatory and non discriminatory components by extending becker s theory of discrimination to job search theory the discriminatory component is seen to be the result of two separate effects first a white treatment advantage shortens the unemployment duration of whites because they receive more frequent and higher wage offers than would prevail in the absence of discrimination for working alongside blacks second a black treatment disadvantage lengthens the jobless spell of blacks because blacks receive lower wage offers than would prevail without discrimination as discriminating employers extract quasi rents from their labour we estimate our model using date from the cps displaced workers survey the results show that 3 81 of the 4 58 weeks longer unemployment spell for blacks is due to discrimination with 3 11 weeks resulting from the white treatment advantage and 0 7 weeks emanating from the black

bargaining in dynamic markets abstract we study non stationary markets in which traders are randomly matched to bargain over the price of a heterogeneous good or the terms of a partnership the economy consists of a continuum of players drawn from a finite set of types players exogenously enter the market over time and exit upon trading at every date matching probabilities for each pair of types are determined by the endogenous distribution of trader types in the market the balance of bargaining power at any stage depends on variations in potential gains from trade the inflows of new traders the structure of agreements at future dates and the induced frequency of trading opportunities we establish that an equilibrium always exists moreover all equilibria that lead to the same evolution of the economy are payoff equivalent however we show that multiple self fulfilling expectations about the trajectory of the economy generating distinct equilibrium dynamics and payoffs may coexist

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

stochastic volatility option pricing this paper examines alternative methods for pricing options when the underlying security volatility is stochastic we show that when there is no correlation between innovations in security price and volatility the characteristic function of the average variance of the price process plays a pivotal role it may be used to simplify fourier option pricing techniques and to implement simple power series methods we compare these methods for the alternative mean reverting stochastic volatility models introduced by stein and stein 1991 and heston 1993 we also examine the biases in the black scholes model that are eliminated by allowing for stochastic volatility and we correct some errors in the stein and stein 1991 analysis of this issue empirical evidence on underlying asset prices and on their derivatives strongly suggests that asset price volatility is stochastic the pricing of options under this condition is therefore an important problem in this paper we study alternative option pricing methods that account for stochastic volatility we are particularly concerned with power series methods which we show to be quite accurate and easy to implement for alternative volatility specifications we point out their relation with recently proposed exact methods this permits a precise assessment of the approximation involved in the simple power series approach and of the impact of stochastic volatility on option prices following garman 1976 stochastic volatility option prices must satisfy a bivariate fundamental partial differential equation pde in the two state variables security price and volatility since volatility is not spanned by assets in the econ omy the volatility risk may not be eliminated by arbitrage methods therefore its market price explicitly enters into the pde the associated risk premium is owen graduate school of management vanderbilt university nashville tn 37203 and universita di siena facolta di scienza economiche e bancarie 53100 siena italy respectively part of this research was supported from a grant from the dean s fund and the financial markets research center at the owen school of management vanderbilt university some of this research was completed while roma was visiting the anderson graduate school of management ofthe university of california at los angeles we thank participants of the finance accounting and economics workshop at the owen school of management vanderbilt university for useful comments we appreciate the suggestions of roger huang craig lewis ron masulis and walter torous we thank joanne ball for editorial

financial asset pricing theory and stochastic programming models for asset liability management a synthesis practical portfolio investment problems under uncertainty can be modeled well as multiperiod stochastic programs however the numerical optimization methods that need to be used to solve such models seriously limit the level of detail in the uncertainty about future asset rices and returns that can be incorporated somewhat surprisingly the question how this necessarily approximate description of the uncertainty should be constructed has received relatively little attention in the stochastic programming literature moreover many of the descriptions that have been used are not arbitrage free and therefore inconsistent with modern financial asset pricing theory in this paper we will present aggregation methods that can be used in combination with financial asset pricing models to obtain a description of the uncertainty that is arbitrage free consistent with observed market prices as well as concise enough for a stochastic programming model furthermore we will discuss how these aggregation methods can form the basis of an iterative solution approach

valuation and analysis of collateralized mortgage obligations this study develops a model for the valuation of collateralized mortgage obligations cmos the model is based on a two factor model of the term structure of interest rates and embeds an empirically estimated mortgage prepayment function the model is used to analyze various cmo tranches including standard sequential pay fixed rate tranches planned amortization class pac tranches targeted amortization class tac tranches floating rate tranches interest only io and principal only po tranches z bonds and residuals the results of this analysis illustrate the sensitivity of the various tranches to differences in cmo structure changes in interest rates the characteristics of the underlying collateral and mortgage prepayments

the credibility revolution in empirical economics how better research design is taking the con out of econometrics since edward leamer s memorable 1983 paper let s take the con out of econometrics empirical microeconomics has experienced a credibility revolution while leamer s suggested remedy sensitivity analysis has played a role in this we argue that the primary engine driving improvement has been a focus on the quality of empirical research designs the advantages of a good research design are perhaps most easily apparent in research using random assignment we begin with an overview of leamer s 1983 critique and his proposed remedies we then turn to the key factors we see contributing to improved empirical work including the availability of more and better data along with advances in theoretical econometric understanding but especially the fact that research design has moved front and center in much of empirical micro we offer a brief digression into macroeconomics and industrial organization where progress by our lights is less dramatic although there is work in both fields that we find encouraging finally we discuss the view that the design pendulum has swung too far critics of design driven studies argue that in pursuit of clean and credible research designs researchers seek good answers instead of good questions we briefly respond to this concern which worries us little

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

the folk theorem with imperfect public information the authors study repeated games in which players observe a public outcome that imperfectly signals the actions played they provide conditions guaranteeing that any feasible individually rational payoff vector of the stage game can arise as a perfect equilibrium of the repeated game with sufficiently little discounting the central condition requires that there exist action profiles with the property that for any two players no two deviations one by either player give rise to the same probability distribution over public outcomes the results apply to principal agent partnership oligopoly and mechanism design models and to one shot games with transferable utilities copyright 1994 by the econometric society

the information content in bond model residuals an empirical study on the belgian bond market abstract we estimate daily vasicek cir and spline models on belgian data and compare the trading profits that can be made on the basis of their residuals abnormal returns measured using three different benchmarks are negatively related to once and twice lagged mispricing buying underpriced bonds and especially selling overpriced bonds yields significant abnormal returns even when the trade is delayed by up to five days after observing the mispricing the traditional spline model overfits the data and is least able to detect mispricing large model residuals are more likely to be the result of model misspecification or estimation than are small or medium sized residuals

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

generalized methods of moments we provide a brief overview of applications of generalized method of moments in finance the models examined in the empirical finance literature especially in the asset pricing area often imply moment conditions that can be used in a straight forward way to estimate the model parameters without making strong assumptions regarding the stochastic properties of variables observed by the econometrician typically the number of moment conditions available to the econometrician would exceed the number of model parameters this gives rise to overidentifying restrictions that can be used to test the validity of the model specifications these advantages have led to the widespread use of the generalized method of moments in the empirical finance literature

cooperation but no reciprocity individual strategies in the repeated prisoner s dilemma a recent advance in our understanding of repeated pds is the detection of a threshold d at which laboratory subjects start to cooperate predictively this threshold is substantially above the classic threshold existence of grim equilibrium and has been characterized axiomatically by blonski ockenfels and spagnolo 2011 bos in this paper i derive its behavioral foundations first i show that the threshold is equivalent to existence of a semi grim equilibrium s cc s cd s dc s dd it is cooperative s cc 0 5 non reciprocal s cd s dc and robust to imperfect monitoring belief free next i show that the no reciprocity condition s cd s dc also follows from robustness to random utility perturbations logit equilibrium finally i re analyze strategies in four recent experiments and find that the majority of subjects indeed plays semi grim when it is an equilibrium strategy which explains d s predictive success

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 delivery option on forward contracts a comment livingston contends that short futures long cash traders can eliminate the potential costs of the quality option through use of a dynamic trading strategy it is proposed here that if this is possible then futures prices will never reach a stable equilibrium alternatively if livingston s argument is flawed then no risk free arbitrage opportunities are likely to be available to either short cash long futures or long cash short futures traders under such conditions futures prices will reach an equilibrium when the expected return and risk of each type position are equally attractive

are mortgage lenders guilty of the housing bubble a uk perspective existing theoretical models of house prices and credit rely on continuous rationality of consumers an assumption that has been frequently questioned in recent years meanwhile empirical investigations of the relationship between prices and credit are often based on national level data which is then tested for structural breaks and asymmetric responses usually with subsamples meen 1999 argues that local markets are structurally different from one another and so the coefficients of any estimated housing market model should vary from region to region we investigate differences in the price credit relationship for 12 regions of the uk markov switching is introduced to capture asymmetric market behaviours and turning points results show that credit abundance had a large impact on house prices in greater london and nearby regions alongside a strong positive feedback effect from past house price movements this impact is even larger in greater london and the south east of england when house prices are falling which are the only instances where the credit effect is more prominent than the positive feedback effect a strong positive feedback effect from past lending activity is also present in the loan dynamics furthermore bubble probabilities extracted using a discrete kalman filter neatly capture market turning points

the stochastic properties of term structure movements abstract the aim of this paper is to identify a stationary statistical model for treasury bill discount changes we find that the sample variance of discount changes are non stationary over short differencing intervals but stabilize as the intervals increase to quarterly or semi annual periods this result has important implications for pricing options and for analyzing the predictive properties of forward rates we show that the stochastic process structure leads to a downward revision in estimates of forward rate predictive power

the money and bond markets in france abstract when rates of return on bonds are computed over extremely short holding periods the ex post cross sectional relationship between realized return and risk is linear it is therefore possible at any time to extrapolate the cross sectional relationship to a zero risk level and thus to determine the implied instantaneous riskless rate of interest we apply this technique to french bond price data using a rather unique data set in which prices are sampled daily we are able to compare the overnight rate implied in bond price data to the actual overnight money market rate we conclude that the two rates are significantly different which is evidence of segmentation between the two markets the institutional set up prevailing in france during the sample period explains the segmentation result

a comparative evaluation of alternative models of the term structure of interest rates abstract in the paper alternative models of the term structure of interest rates are classified in two different approaches the no arbitrage and the general equilibrium approach it is maintained that the general equilibrium approach is superior on a theoretical ground for two main reasons first relevant variables such as the spot interest rate and the interest risk premium are endogenous second the relationship between the real and the financial side of the economy becomes a clear and important element in the understanding of the term structure as regards the applications however the advantages of the general equilibrium over the no arbitrage approach are not so clear the major role in the empiricil performance of alternative models is played by their ability to capture volatility at the current state of the literature there is no model that outperforms others in particular on the empirical side

the graph of prisoners dilemma supergame payoffs as a function of the discount factor abstract the set of subgame perfect correlated equilibrium of the infinitely repeated discounted prisoners dilemma depends on the discount factor the graph of the correspondence of these equilibrium payoffs versus the discount factor is derived and presented these results are especially applicable to situations in which there is a random chance of the supergame ending or an exogenous probability of cooperative breakdown

evaluation of callable bonds finite difference methods stability and accuracy the purpose of this paper is to evaluate numerically the semi american callable bond by means of finite difference methods this study implies three results first the numerical error is greater for the callable bond price than for the straight bond price and too large for real applications secondly the numerical accuracy of the callable bond price computed for the relevant range of interest rates depends entirely on the finite difference scheme which is chosen for the boundary points thirdly the boundary scheme which yields the smallest numerical error with respect to the straight bond does not perform best with respect to the callable bond the callable bond is a straight coupon bond with the provision that allows the debtor to buy back or to call the bond for a specified amount the call price plus the accrued interest since the last coupon date at some time the call date s during the life of the bond three types of callable bonds can be observed in financial markets the american callable bond may be repurchased at any time on or before the final redemption day in contrast to the european or semi american counterparts which may only be called at one or several specific dates respectively in the case of semi american bonds the debtor gives the bondholder two months notice the callable bond can be viewed as a compound security which consists of an otherwise identical straight bond and of an embedded call option which is not traded and the price of which is therefore not observable the embedded call option which is written on the underlying straight bond can be viewed as being sold by the initial

rational prepayments and the valuation of collateralized mortgage obligations absteract this article presents a procedure for evaluating collateralized mortgage obligation cmo tranches the solution procedure is in the spirit of a dynamic programming problem in which an individual mortgagor s decision to prepay is the feedback control variable the mortgagor seeks to minimize the value of the mortgage subject to refinancing costs we employ a two step procedure to solve this dynamic programming problem the first step uses an implicit finite difference backward solution procedure to determine the optimal prepayment boundary for a class of mortgagors each of whom confronts the same proportional refinancing cost this step is repeated for several different classes of mortgagors that differ in the level of refinancing costs that they confront the outcome of this first step is a series of prepayment boundaries one set of boundaries for each level of refinancing costs i e one set of boundaries for each refinancing cost category of mortgagors in the second step the prepayment boundaries determined in the first step are used in conjunction with monte carlo simulation to value the cmo tranches the essence of the second step is that when the simulated interest rate hits the boundary for a particular class it triggers a prepayment scenario for that class of mortgagors we conduct extensive sensitivity analysis to determine the robustness of this approach and our solution procedure to alternative single factor models of the term structure of interest rates and to alternative specifications of the distribution of refinancing cost levels confronted by mortgagors the sensitivity analysis indicates that cmo tranche valuation is not particularly sensitive to alternative models of the term structure so long as the models are consistent with the current yield curve but even when alternative specifications of the refinancing cost categories generate nearly identical values for the collateral underlying the cmo i e the generic mortgage backed securities the resulting tranche values can differ widely between the two specifications the results point out the importance of accurate estimation of the distribution of refinancing costs when the rational valuation model is used for the analysis of cmo tranches

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

bond price dynamics and options this paper provides a closed form preference free means of valuing a european call option written on a default free pure discount bond investors may not agree upon a theory of the term structure but they will necessarily agree on equilibrium option values further these equilibrium option values may be obtained without recourse to numerical approximation default free pure discount bond prices were posited to follow a non standardized transformed brownian bridge process this specification implicitly incorporates the terminal constraint that the price of a default free pure discount bond equal its face value at maturity contingent claim valuation necessarily involves consideration of terminal constraints on the value of financial securities the brownian bridge specification permits an appropriate means of incorporating a number of such constraints therefore while this paper has considered only the application of the brownian bridge process to the valuation of debt options the introduction of this process may provide for many further financial applications

time dependent variance and the pricing of bond options in this paper we develop a model for valuing debt options that takes into account the changing characteristics of the underlying bond by assuming that the standard deviation of return is proportional to the bond s duration the resulting model uses the bond price as the single state variable and thus preserves much of the simplicity and robustness of the black scholes approach the paper provides comparisons between option prices computed using this model and those using the black scholes and brennan and schwartz models the last decade has seen a dramatic increase in the volatility of bond markets leading to a growing interest in financial instruments that can be used to hedge this risk thus in the u s canada and the u k there has been a proliferation of new interest rate dependent securities such as bond futures options on bonds options on bond futures swap agreements and bonds with option features such as callability putability retractability and so forth with the development of these markets the problems of valuation and the derivation of the hedging strategies have become subjects of increasing importance to both practitioners and academics several valuation methods have been suggested in the literature but so far no consensus has emerged as to the best solution to these problems the simplest approach to the valuation of debt options and probably the most widely used in practice is the black scholes model 3 this method originally developed for the valuation of stock options assumes that the variance of the rate of return on the underlying security is constant while this assumption is plausible for common stocks it is clearly unreasonable for bonds with a finite maturity the distinctive feature of the problem of debt option valuation is that the characteristics of the underlying asset change over time because the price is constrained to converge to the face value of the bond at maturity a second drawback of the black scholes approach is that it assumes a constant short term interest rate an assumption that is clearly inconsistent with stochastic returns on bonds in spite of these problems the black scholes model has been frequently used in practice to value debt options because of its overwhelming simplicity in comparison with other available methods

work incentive effects of taxing unemployment benefits before 1979 unemployment insurance ui benefits were not treated as taxable income in the united states several economists criticized this policy on the ground that not taxing ui benefits while taxing earned income allegedly encourages unemployed persons to conduct longer than socially optimal job searches since 1979 however ui benefits received by persons in higher income families have been subject to income tax this paper investigates whether the introduction of benefit taxation has had the predicted effect of reducing unemployment duration the study uses data on a sample of persons that filed for ui in 1978 or 1979 to examine whether high income claimants collected benefits for shorter periods after the tax change than they did before benefits became taxable as part of the empirical analysis the paper develops a generalization of the weibull distribution and applies a limited dependentvariable technique for this distribution similar to the tobit technique for the normal distribution despite some variation in the results from different model specifications the analysis presents persuasive evidence of a tax effect on unemployment duration the 1979 policy change is estimated to have reduced average compensated unemployment duration among the sampled high income claimants by about one week

time varying term premia on u s treasury bills and bonds abstract we use instrumental variables estimation to document variation in ex ante term premia on u s treasury bills and bonds of maturities ranging from two months to twenty years for the april 1959 to december 1989 sample period ex ante term premia are found to be positively related to the ex ante variability in the nominal one month risk free rate of interest significant shifts in the stochastic process generating term premia are documented subsequent to the october 1979 and october 1982 shifts in monetary policy subperiod results document variation in ex ante tenn premia in each of the three monetary regimes

the pricing of default free interest rate cap floor and collar agreements the paper focuses on the valuation of caps floors and collars in a contingent claim framework under continuous time these instruments are interpreted as options on traded zero coupon bonds the bond prices themselves are used as the underlying stochastic variables this has the advantage that we end up with closed form solutions which are easy to compute special attention is devoted to the choice of the stochastic process appropriate for the price dynamics of the underlying zero coupon bonds the increased volatility of interest rates and the introduction of numerous variable rate instruments have led to a more intensive use of highly sophisticated risk hedging tools among them interest rate caps floors and collars have recently gained a growing popularity an interest rate cap is an agreement between the provider of the cap and a borrower to limit the borrower s floating interest rate to a specific level for a given period of time to be more precise the borrower selects a reference rate to hedge e g libor a period of time to hedge e g 5 years and the level of protection desired e g a ceiling of 200 basis points above the current level of the libor if the market rate exceeds the ceiling rate the cap provider will make payments to the buyer sufficient to bring his rate back to the ceiling when the market rate is below the ceiling no payment is made

modeling the stochastic behavior of short term interest rates pricing implications for discount bonds abstract this paper models the stochastic behavior of short term interest rates and determines the correct specification of the drift and diffusion functions of the spot rate process a wide variety of one factor diffusion and two factor stochastic volatility models is compared in terms of their ability to capture the dynamics of interest rate volatility the empirical evidence on the one three and six month eurodollar deposit rates indicates that a new class of models with stochastic volatility is better than the single factor diffusion models in forecasting the future volatility of interest rate changes the paper extends the one factor bdt term structure model to a two factor setting and presents the pricing implications for discount bonds monte carlo simulation results for the implied yields of three and six month zero coupon bonds imply that incorporating the so called level and garch effects in volatility improves the pricing performance of the interest rate models

stochastic volatility movements in short term interest rates and bond option values abstract two classes of models for pricing interest rate contingent claims are compared the first contains standard single factor models while the second includes stochastic volatility variants of these it is demonstrated that incorporating stochastic volatility significantly improves the ability of the models to fit movements in short term interest rates the fundamental reason for this is that standard univariate models do not generate enough conditional heteroskedasticity the models are also compared on the basis of bond option prices when each is constrained to fit a particular yield curve the results suggest that stochastic volatility models will typically produce lower option values than corresponding single factor models particularly for near the money to deep out of the money options this is because estimated historical volatilities are significantly lower under stochastic volatility when single factor models are constrained to the same level of volatility as implied by stochastic volatility models in most cases the pricing differences become minor

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

the volatility of short term interest rates an empirical comparison of alternative models of the term structure of interest rates we estimate and compare a variety of continuous time models of the short term riskless rate using the generalised method of moments we find that the most successful models in capturing the dynamics of the short term interest rate are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rate a number of well known models perform poorly in the comparisons because of their implicit restrictions on term structure volatility we show that these results have important implications for the use of different term structure models in valuing interest rate contingent claims and in hedging interest rate risk

business cycles unemployment insurance and the calibration of matching models this paper theoretically and empirically documents a puzzle that arises when an rbc economy with a job matching function is used to model unemployment the standard model can generate sufficiently large cyclical fluctuations in unemployment or a sufficiently small response of unemployment to labor market policies but it cannot do both variable search and separation finite ui benefit duration efficiency wages and capital all fail to resolve this puzzle however either sticky wages or match specific productivity shocks can improve the model s performance by making the firm s flow of surplus more procyclical which makes hiring more procyclical too

shifting endpoints in the term structure of interest rates abstract this paper links the term structure to perceptions of monetary policy long horizon forecasts of short rates required by no arbitrage term structure models are heavily influenced by the endpoints or limiting conditional forecasts of the short rate process common assumptions that the short rate is mean reverting or contains a unit root are shown to generate unrealistic yield predictions failures occur because these assumptions inadequately account for historical shifts in market perceptions of the policy target for inflation this paper links endpoint shifts to agent learning about shifts in long term policy goals shifting endpoints in short rate processes significantly improve yield predictions

the redistributive roles of unemployment insurance and the dynamics of voting abstract public unemployment insurance is analyzed as the majority voting equilibrium policy of a dynamic stochastic economy abstracting from incentive effects we focus on redistribution some results are because of the distribution of heterogeneous employment opportunities public insurance may be democratically chosen even if complete private markets exist and because of the dynamics even when agents are intrinsically homogeneous the equilibrium benefit level or duration benefit schedule deviates from what has been described as optimal in the literature the effects of differences in the average frequency or duration of unemployment on equilibrium taxes and benefits are investigated with some unanticipated results

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

quality option profits switching option profits and variation margin costs an evaluation of their size and impact on treasury bond futures prices this paper provides empirical evidenee that the quality option in f bond futures is much less valuable than previously indicated in addition a dynamic trading strategy involving multiple switches of the cash bonds held in a long cash versus short futures position is shown to produce substantially greater profits than the single exercise of the quality op tion these findings suggest that the optimal management of long cash short futures positions is likely to involve dynamic trading strategies while passive strategies appear more appropriate for short cash long futures positions it is also shown that required variation margin payments are frequently large and may impact the profitability and risk of such positions to a greater extent than either of these options further evidenee is given indicating that observed t bond futures prices reflect an imputed value for the options and risks inherent in such positions

some estimates of the effects of unemployment insurance on re employment duration abstract this paper examines how re employment spell durations are affected by the potential unemployment benefit period an ex ante notion and benefit exhaustion an ex post notion the extent to which benefit duration affects re employment duration is found to depend on the nature of the separation

the evolution of cooperation in infinitely repeated games experimental evidence 1 for example in infinitely repeated prisoner s dilemma games with patient agents both cooperate and defect may be played in equilibrium even though the theory of infinitely repeated games has been used to explain cooperation in a variety of environments no definitive solution has been provided to the problem of equilibrium selection when both cooperation and defection are possible equilibrium outcomes which one should we expect to prevail previous experimental evidence has shown that subjects often fail to coordinate on a specific equilibrium when they play a small number of infinitely repeated games some subjects attempt to establish cooperative agreements while others defect but how would behavior evolve as subjects learn from previous repeated games would cooperation prevail when it can be supported in equilibrium or will subjects learn

valuing debt options empirical evidence abstract a two factor model using the instantaneous rate of interest and the return on a consol bond to describe the term structure of interest rates the brennan schwartz model is used to derive theoretical prices for american call and put options on us government bonds and treasury bills these model prices are then compared with market prices the theoretical model used to value the dept options also provides hedge ratios which may be used to construct zero investment portfolios which in theory are perfectly riskless several trading strategies based on these riskless portfolios are examined

long and short term interest rates in a risky world abstract the paper develops and tests a general equilibrium model in which variability or risk affects the choice of portfolios our measures of variability include only the variability of unanticipated growth in monetary and non monetary aggregates and our tests use data ending with the change in federal reserve procedures in october 1979 we find that increased variability of unanticipated money growth raises demands for debt and money and reduces the demand for real capital interest rates on both short and long term debt rise by a risk premium we estimate the size of the risk premium before and after the october 1979 change and we show that the change in federal reserve procedures moved the economy to a less efficient point

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

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

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