nonlinear mean reversion in the short term interest rate using a new bayesian method for the analysis of diffusion processes this article finds that the nonlinear drift in interest rates found in a number of previous studies can be confirmed only under prior distributions that are best described as informative the assumption of stationarity which is common in the literature represents a nontrivial prior belief about the shape of the drift function this belief and the use of flat priors contribute strongly to the finding of nonlinear mean reversion implementation of an approximate jeffreys prior results in virtually no evidence for mean reversion in interest rates unless stationarity is assumed finally the article documents that nonlinear drift is primarily a feature of daily rather than monthly data and that these data contain a transitory element that is not reflected in the volatility of longermaturity yields the drift of the short term interest rate is an important determinant of a wide variety of asset prices both inside and outside the boundaries of what is often called fixed income while volatilities may be estimated relatively accurately using high frequency observations of the short rate the short rate s extreme persistence makes identifying the true shape of the drift function a particularly elusive goal if our goal is merely to fit prices then the difficulty in estimating a drift function can be avoided by backing out implied drifts using a no arbitrage approach such as hull and white 1990 or heath jarrow and morton 1992 these methods bypass the true distribution entirely focusing on solving for the risk neutral drift function that is consistent with the cross section of bond prices if our goal however is to learn from prices and to be able to assess theories such as the expectations hypothesis that link short and long rates then estimating the drift function under the true measure is unavoidable in several recent articles a variety of sophisticated econometric techniques have been brought to bear on the problem in particular

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

time varying risk and long term reversals a re examination of the international evidence long term reversals ltrs have been extensively documented as existing in international markets the predictability of returns opens the question whether investors should continue to diversify across international markets such predictability also has implications for the corporate decision of where and when to raise capital this paper re examines the international evidence for long term contrarian profits using a longer time horizon than all previous studies 81 years of data from 1925 to 2005 and finds that the long term contrarian anomaly disappears when time varying conditional alphas are considered this is true even without transaction costs for the marginal trader conservative transaction costs subsume ltr profits whether returns are risk adjusted or not this suggests that benefits from actual trades on ltrs do not negate a strategy based on diversification although time varying beta has been extensively documented as ineffective in describing ltrs this paper demonstrates that it is important to control for time variation in alpha a full conditional capital asset pricing model captures the ltr premium this suggests that macroeconomic factors are important for understanding ltrs and their associated risk

domestic foreign interest rate differentials near unit roots and symmetric threshold models this paper investigates the near unit root behavior of interest rate differentials across countries using a symmetric band tar model that allows for a heteroscedastic error process we find that the time series properties of monthly short term interest differentials over the period 1974 2005 between the united states and canada france germany japan and the united kingdom can be characterized by a symmetric band tar process which can explain its near unit root behavior reported in the extant literature results significantly reject a linear model in favor of the alternative hypothesis of a two regime symmetric threshold model that exhibits significantly greater persistence within the threshold bands than when outside the threshold bands

further international evidence on asset pricing the case of the spanish capital market abstract a multivariate framework is used in order to study the price formation of risky assets in the spanish capital market issues regarding the efficiency of the spanish value weighted stock market index the validity of equilibrium considerations the size effect and the nature of the return generating process during january are analyzed

short term reaction of stock markets in stressful circumstances abstract in this paper we document the short term stock price behaviour following a period of stock market stress we focus on price behaviour using daily market indexes from 39 stock exchanges over the period 1989 1998 our results are not consistent with the overreaction hypothesis we find positive negative abnormal price performance in the short term window up to 10 days following positive negative price shocks our analysis also highlights differences between developed and emerging markets we show that the post shock abnormal performances are significantly larger for emerging markets but that this momentum behaviour is markedly less in the late 1990s we find the size of the after shock tremors to be related to market liquidity with larger post shock price changes in less liquid markets

what s causing overreaction an experimental investigation of recency and the hot hand effect a substantial body of empirical literature provides evidence of overreaction in markets past losers outperform past winners in stock markets as well as in sports markets two hypotheses are consistent with this observation the recency hypothesis states that traders overweight recent information they are too optimistic about winners and too pessimistic about losers according to the hot hand hypothesis traders try to discover trends in the past record of a firm or a team and thereby overestimate the autocorrelation in the series an experimental design allows us to distinguish between these hypotheses the evidence is consistent with the hot hand hypothesis

the intrinsic limits of modern economic theory the emperor has no clothes assumptions of the uniqueness and stability of general equilibrium in a walrasian framework have no theoretical justification this paper argues that the key reason for this is that the walrasian model treats people as acting independently of one another especially in their demand behavior this independence plays an essential role in constructing economies with arbitrary excess demand functions thus making individual behavior dependent or similar may open the way to obtaining meaningful restrictions on aggregate excess demand functions copyright 1989 by royal economic society

short term interest rates as subordinated diffusions in this article we cbaracterize and estimate the process for short term interest rates using federal funds interest rate data we presume that we are observing a discrete time sample of a stationary scalar diffusion we concentrate on a class of models in whicb the local volatility elasticity is constant and the drift has aflexible specufication to accommodate missing observations and to break the link between economic time and calendar time we model the sampling scheme as an increasing process that is not directly observed we propose and implement two new methods for estimation we find evidence for a volatility elasticity between one and onehalf and two when interest rates are high local mean reversion is smaul and the mechanism for inducing stationarity is the increased volatility of the diffusion process

day of the week and intraday effects in stock returns abstract this study examines day of the week effects using hourly values of the dow jones industrial average we find that over the 1963 1983 period the weekend effect has sifted from characterizing active trading on monday to characterizing the non trading weekend over the early part of our sample period negative returns characterize each hour of trading on monday while the return from friday close to monday open is positive in the most recent subperiod monday average hourly returns after noon are all positive and the weekend effect is due to negative average returns from friday close to monday open

overreaction in the spanish equity market abstract this paper examines the overreaction hypothesis within the spanish capital market the hypothesis is clearly accepted even after correcting for size when estimating excess returns twelve months after portfolio formation losers win 24 5 more than winners there is also a correspondence between excess returns and changes in the earnings pattern of losers and winners firms

the pricing of options on default free bonds recent developments in the finance literature dealing with the valuation of contingent claims have been triggered by black and scholes 2 with their valuation of european options on corporate stocks the type of valuation model derived by black and scholes is attractive because it is independent of preferences this independence is possible due to the fact that the contingent claims are usually assumed to be contingent on traded assets or traded state variables for example a european call option is a claim contingent on the value of the corresponding stock to maintain the independence of the claim from preferences however some variables have to be discarded and considered as constants for example the rate of interest which is not a traded state variable is considered a constant in most of the literature see black and scholes 2 merton 11 and ingersoll 9 though this approximation might not cause important discrepancies in the case of corporate liabilities and options on corporate liabilities the effect of such an approximation on the value of default free bonds and options on default free bonds is more important since these liabilities depend only on the rate of interest

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

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

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

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

a parametric nonlinear model of term structure dynamics recent nonparametric estimation studies pioneered by ait sahalia document that the diffusion of the short rate is similar to the parametric function r superscript 1 5 estimated by chan et al whereas the drift is substantially nonlinear in the short rate these empirical properties call into question the efficacy of the existing affine term structure models and beg for alternative models which admit the observed behavior this article presents such a model our model delivers closed form solutions for bond prices and a concave relationship between the interest rate and the yields we show that in empirical analyses our model outperforms the one factor affine models in both time series as well as cross sectional tests article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

a tale of three schools insights on autocorrelations of short horizon stock returns this article reexamines the autocorrelation patterns of short horizon stock returns we document empirical results which imply that these autocorrelations have been overstated in the existing literature based on several new insights we provide support for a market efficiency based explanation of the evidence our analysis suggests that institutional factors are the most likely source of the autocorrelation patterns

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

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

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

on the computation of returns in tests of the stock market overreaction hypothesis abstract a number of recent studies have attempted to find out whether investors overreact we argue that in many of these studies the method used to compute cumulative returns the arithmetic method is flawed and we show that estimates of portfolio performance can be affected our findings are relevant not only to tests of the overreaction hypothesis but to other areas in finance where the arithmetic method and event study approach are used