Likelihood-based specification analysis of continuous-time models of the short-term interest rate

An extensive collection of continuous-time models of the short-term interest rate is evaluated over data sets that have appeared previously in the literature. The analysis, which uses the simulated maximum likelihood procedure proposed by Durham and Gallant (2002), provides new insights regarding several previously unresolved questions. For single factor models, I find that the volatility, not the drift, is the critical component in model specification. Allowing for additional flexibility beyond a constant term in the drift provides negligible benefit. While constant drift would appear to imply that the short rate is nonstationary, in fact, stationarity is volatility-induced. The simple constant elasticity of volatility model fits weekly observations of the three-month Treasury bill rate remarkably well but is easily rejected when compared with more flexible volatility specifications over daily data. The methodology of Durham and Gallant can also be used to estimate stochastic volatility models. While adding the latent volatility component provides a large improvement in the likelihood for the physical process, it does little to improve bond-pricing performance.     

Forecasting economic time series with unconditional time-varying variance

The classical forecasting theory of stationary time series exploits the second-order structure (variance, autocovariance, and spectral density) of an observed process in order to construct some prediction intervals. However, some economic time series show a time-varying unconditional second-order structure. This article focuses on a simple and meaningful model allowing this nonstationary behaviour. We show that this model satisfactorily explains the nonstationary behaviour of several economic data sets, among which are the U.S. stock returns and exchange rates. The question of how to forecast these processes is addressed and evaluated on the data sets.     

基于外汇期权方法的汇率预测研究

文章利用2004年芝加哥商品交易所的美元-欧元期货期权的信息,分析了其隐含偏度和隐含波动率在预测短期汇率中的效力。结果发现,隐含偏度、隐含波动率的偏度与每日汇率变化率有紧密的联系。     

Minnesota-type adaptive hierarchical priors for large Bayesian VARs

Large Bayesian VARs with stochastic volatility are increasingly used in empirical macroeconomics. The key to making these highly parameterized VARs useful is the use of shrinkage priors. We develop a family of priors that captures the best features of two prominent classes of shrinkage priors: adaptive hierarchical priors and Minnesota priors. Like adaptive hierarchical priors, these new priors ensure that only ‘small’ coefficients are strongly shrunk to zero, while ‘large’ coefficients remain intact. At the same time, these new priors can also incorporate many useful features of the Minnesota priors such as cross-variable shrinkage and shrinking coefficients on higher lags more aggressively. We introduce a fast posterior sampler to estimate BVARs with this family of priors—for a BVAR with 25 variables and 4 lags, obtaining 10,000 posterior draws takes about 3 min on a standard desktop computer. In a forecasting exercise, we show that these new priors outperform both adaptive hierarchical priors and Minnesota priors.     

基于高频数据的深圳基金市场日内周期性研究

本文利用深市基金指数高频数据,采用Anderson和Bollerslev(1997)提出的弹性傅立叶回归(FlexibleFourierFormregression,即FFF回归)方法首次对深市基金市场进行了日内周期性的研究。通过对高频收益的定性分析,发现基金市场具有同股票市场相似的周期性,并对这一周期性进行了初步的理论解释。通过FFF方法,将该周期因子进行滤波处理以后,基金指数高频绝对收益不再具有明显周期性。FFF回归能较好地确定日内周期因子。     

Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models

We examine and compare a large number of generalized autoregressive conditional heteroskedastic (GARCH) and stochastic volatility (SV) models using series of Bitcoin and Litecoin price returns to assess the model fit for dynamics of these cryptocurrency price returns series. The various models examined include the standard GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, t-distributed and moving average innovations. We report that the best model for Bitcoin is SV-t while it is GARCH-t for Litecoin. Overall, the t-class of models performs better than other classes for both cryptocurrencies. For Bitcoin, the SV models consistently outperform the GARCH models and the same holds true for Litecoin in most cases. Finally, the comparison of GARCH models with GARCH-GJR models reveals that the leverage effect is not significant for cryptocurrencies, suggesting that these do not behave like stock prices.     

Nonparametric estimation of stochastic volatility models

This letter introduces nonparametric estimators of the drift and diffusion coefficient of stochastic volatility models which exploit techniques for estimating integrated volatility with high-frequency data. The performance of the proposed estimators is assessed on simulations of two popular stochastic volatility models.     

On the forecastability of share prices on the Viennese stock exchange

In this paper the Viennese stock exchange data are analysed by using ARMA and GARCH technology. After using AIC and BIC for estimating the linear structure of the time series, to the resulting innovations a GARCH(1,1) model is fit. The resulting residuals are then tested for serial independence and constancy of its distribution to check whether the models are reasonable. Main result is that the residuals of this ARMA-GARCH(1,1)-model are reasonably iid (which is checked by BDS and classical independence tests) for index data and significantly less well-behaved for stock data. Second, there is considerable autocorrelation in the data (especially in the Viennese indices WBK and ATX) which can be exploited even with 1.25% transaction costs (which is checked by a posteriori analysis of a strategy which exploits an underlying time-varying AR(1) model), however, much higher profit can be made with 0.5% transaction costs. Furthermore, the same techniques are applied to US Standard & Poor 500 index and the results for both data sets are compared giving the result that the US-market looks much more mature than the Viennese one.Financial Support by the Institute for Advanced Studies, Vienna, and the Fonds zur Förderung der wissenschaftlichen Forschung, Vienna, Grant P 9176 is gratefully acknowledged. This paper is a slightly abbreviated version of the Research Report No. 135 by the same authors (see References), which contains many detailed plots of the results.     

Valuation of commodity derivatives in a new multi-factor model

This paper extends existing commodity valuation models to allow for stochastic volatility and simultaneous jumps in the spot price and spot volatility. Closed-form valuation formulas for forwards, futures, futures options, geometric Asian options and commodity-linked bonds are obtained using the Heston (1993) and Bakshi and Madan (2000) methodology. Stochastic volatility and jumps do not affect the futures price at a given point in time. However, numerical examples indicate that they play important roles in pricing options on futures. This revised version was published online in June 2006 with corrections to the Cover Date.     

Implied Volatility of Interest Rate Options: An Empirical Investigation of the Market Model

We analyze the empirical properties of the volatilityimplied in options on the 13-week US Treasury bill rate. These options havenot been studied previously. It is shown that a European style put optionon the interest rate is equivalent to a call option on a zero-coupon bond.We apply the LIBOR market model and conduct a battery of validity tests tocompare three different volatility specifications: contact, affine, and exponentialvolatility. It appears that the additional parameter in the affine and theexponential volatility function is not justified. Overall, the LIBOR marketmodel fares well in describing these options.