I find that the standard class of a#ne models produces poor forecasts of future changes in Treasury yields. Better forecasts are generated by assuming that yields follow random walks. The failure of these models is driven by one of their key features: The compensation that investors receive for facing risk is a multiple of the variance of the risk. This means that risk compensation cannot vary independently of interest rate volatility. I also describe and empirically estimate a class of models that is broader than the standard a#ne class. These "essentially a#ne" models retain the tractability of the usual models, but allow the compensation for interest rate risk to vary independently of interest rate volatility. This additional flexibility proves useful in forming accurate forecasts of future yields. Address correspondence to the University of California, Haas School of Business, 545 Student Services Building #1900, Berkeley, CA 94720. Phone: 510-642-1435. Email address: du#ee@haas.b...

This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of time-varying intensity. We find that any reasonably descriptive continuous-time model for equity-index returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equity-index returns and the stylized features of the corresponding options market prices. MUCH ASSET AND DERIVATIVE PRICING THEORY is based on diffusion models for primary securities. However, prescriptions for practical applications derived from these models typically produce disappointing results. A possible explanation could be that analytic formulas for pricing and hedging are available for only a limited set of continuous-time representations for asset returns

This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when only discrete observations are available. The estimation is carried out using a tuned MCMC method, in particular a blocked Metropolis-Hastings algorithm, by introducing auxiliary points and using the Euler-Maruyama discretisation scheme. Techniques for computing the likelihood function, the marginal likelihood and diagnostic measures (all based on the MCMC output) are presented. Examples using simulated and real data are presented and discussed in detail.

Efficient Method of Moments (EMM) is used to fit the standard stochastic volatility model and various extensions to several daily financial time series. EMM matches to the score of a model determined by data analysis called the score generator. Discrepancies reveal characteristics of data that stochastic volatility models cannot approximate. The two score generators employed here are "Semiparametric ARCH" and "Nonlinear Nonparametric". With the first, the standard model is rejected, although some extensions are accepted. With the second, all versions are rejected. The extensions required for an adequate fit are so elaborate that nonparametric specifications are probably more convenient. Corresponding author: George Tauchen, Duke University, Department of Economics, Social Science Building, Box 90097, Durham NC 27708-0097 USA, phone 1-919-660-1812, FAX 1-919-684-8974, e-mail get@tauchen.econ.duke.edu. 0 1 Introduction The stochastic volatility model has been proposed as a descripti...

This paper studies the empirical performance of jump-diffusion models that allow for stochastic volatility and correlated jumps affecting both prices and volatility. The results show that the models in question provide reasonable fit to both option prices and returns data in the in-sample estimation period. This contrasts previous findings where stochastic volatility paths are found to be too smooth relative to the option implied dynamics. While the models perform well during the high volatility estimation period, they tend to overprice long dated contracts out-of-sample. This evidence points towards a too simplistic specification of the mean dynamics of volatility.

This paper proposes a new method for estimation of parameters in diffusion processes from

The purpose of this paper is to bridge two strands of the literature, one pertaining to the objectiveorphysical measure used to model the underlying asset and the other pertaining to the risk-neutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundamental price S t and a set of option contracts ### I it # i=1;m # where m # 1 and # I it is the Black-Scholes implied volatility.We use Heston's #1993# model as an example and appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the S&P 500 index contract, show that the univariate approach only involving options by and large dominates. Aby-product of this #nding is that we uncover a remarkably simple volatility extraction #lter based on a polynomial lag structure of implied volatilities. The bivariate approachinvolving both the fundamental and an option appears useful when the information from the cash market ...

This paper theoretically explores the characteristics underpinning quadratic term structure models (QTSMs), which designate the yield on a bond as a quadratic function of underlying state variables. We develop a comprehensive QTSM, which is maximally exible and thus encompasses the features of several diverse models including the double square-root model of Longsta (1989), the univariate quadratic model of Beaglehole and Tenney (1992), and the Squared-Autoregressive-Independent-Variable Nominal Term Structure (SAINTS) model of Constantinides (1992). We document a complete classication of admissibility and empirical identication for the QTSM, and demonstrate that the QTSM can overcome limitations inherent in ane term structure models (ATSMs). Using the Ecient Method of Moments of Gallant and Tauchen (1996), we test the empirical performance of the model in determining bond prices and compare the performance to the ATSMs. The results of the goodness-of-t tests suggest that the QTSMs...

Stochastic differential equations often provide a convenient way to describe the dynamics of economic and financial data, and a great deal of effort has been expended searching for efficient ways to estimate models based on them. Maximum likelihood is typically the estimator of choice; however, since the transition density is generally unknown, one is forced to approximate it. The simulation-based approach suggested by Pedersen (1995) has great theoretical appeal, but previously available implementations have been computationally costly. We examine a variety of numerical techniques designed to improve the performance of this approach. Synthetic data generated by a CIR model with parameters calibrated to match monthly observations of the U.S. short-term interest rate are used as a test case. Since the likelihood function of this process is known, the quality of the approximations can be easily evaluated. On data sets with 1000 observations, we are able to approximate the maximum likelihood estimator with negligible error in well under one minute. This represents something on the order of a 10,000-fold reduction in computational effort as compared to implementations without these enhancements. With other parameter settings designed to stress the methodology, performance remains strong. These ideas are easily generalized to multivariate settings and (with some additional work) to latent variable models. To illustrate, we estimate a simple stochastic volatility model of the U.S. short-term interest rate.

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