In this paper, we characterize, interpret, and test the over-identifying restrictions imposed in affine models of the term-structure. "We begin by showing, using the classification scheme proposed by Dai, Liu, and Singleton [10] for general affine diffusions, that the family of N-factor models can be classified into N + 1 non-nested sub-families of models. For each subfamily, we derive a canonical model with the property that every admissible member of this family is equivalent to or a nested special case of our canonical model. Second, using our classification scheme and canonical models, we show that many of the three-factor models in the literature impose potentially strong over-identifying restrictions, and we completely characterize these restrictions. Finally, we compute simulated-method-of-moments estimates for several members of the sub-family of three-factor models that nest the "benchmark" model of Chen [8], and test the over-identifying restrictions on the joint distribution...

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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.

This article presents a technique for nonparametrically estimating continuous-time di#usion processes which are observed at discrete intervals. We illustrate the methodology by using daily three and six month Treasury Bill data, from January 1965 to July 1995, to estimate the drift and di#usion of the short rate, and the market price of interest rate risk. While the estimated di#usion is similar to that estimated by Chan, Karolyi, Longsta# and Sanders (1992), there is evidence of substantial nonlinearity in the drift. This is close to zero for low and medium interest rates, but mean reversion increases sharply at higher interest rates.

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...

We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollar-denominated bonds. We consider the determinants of the Russian yield spread, the yield differential across different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios. THIS PAPER DEVELOPS A MODEL of the termstructure of credit spreads on sovereign bonds that accommodates: (i) Default or repudiation: The sovereign announces that it will stop making payments on its debt; (ii) Restructuring or renegotiation: The sovereign and the lenders ‘‘agree’ ’ to reduce (or postpone) the remaining payments; and (iii) A‘‘regime switch,’’such as a change of government or the default of another sovereign bond that changes the perceived risk of future defaults.We build on the framework of Duffie and Singleton (1999), showing that

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 ...