Journal of Financial Econometrics - Advance Access

Markov Chain Monte Carlo Methods for Parameter Estimation in Multidimensional Continuous Time Markov Switching Models

Hahn, M., Fruhwirth-Schnatter, S., Sass, J. — Tue, 17 Nov 2009 07:09:02 PST

We consider a multidimensional, continuous-time model where the observation process is a diffusion with drift and volatility coefficients being modeled as continuous-time, finite-state Markov chains with a common state process. For the econometric estimation of the states for drift and volatility and the rate matrix of the underlying Markov chain, we develop both an exact continuous time and an approximate discrete-time Markov chain Monte Carlo (MCMC) sampler and compare these approaches with maximum likelihood (ML) estimation. For simulated data, MCMC outperforms ML estimation for difficult cases like high rates. Finally, for daily stock index quotes from Argentina, Brazil, Mexico, and the USA we identify four states differing not only in the volatility of the various assets but also in their correlation.

Structural Conditional Correlation

Weber, E. — Sat, 14 Nov 2009 20:53:23 PST

A small strand of recent literature is occupied with identifying simultaneity in multiple equation systems through autoregressive conditional heteroscedasticity. Since this approach assumes that the structural innovations are uncorrelated, any contemporaneous connection of the endogenous variables needs to be exclusively explained by mutual spillover effects. In contrast, this paper allows for instantaneous covariances, which become identifiable by imposing the constraint of structural constant/dynamic conditional correlation (SCCC/SDCC). In this, common driving forces can be modeled in addition to simultaneous transmission effects. The methodology is applied to the Dow Jones and Nasdaq Composite indexes, illuminating scope and functioning of the new models.

Understanding Analysts' Earnings Expectations: Biases, Nonlinearities, and Predictability

Aiolfi, M., Rodriguez, M., Timmermann, A. — Sun, 08 Nov 2009 22:20:53 PST

This paper studies the asymmetric behavior of negative and positive values of analysts’ earnings revisions and links it to the conservatism principle of accounting. Using a new three-state mixture of lognormal models that accounts for differences in the magnitude and persistence of positive, negative, and zero revisions, we find evidence that revisions to analysts’ earnings expectations can be predicted using publicly available information such as lagged interest rates and past revisions. We also find that our forecasts of revisions to analysts’ earnings estimates help to predict the actual earnings figure beyond the information contained in analysts’ earnings expectations.

A Cohort Analysis of Equity Shares in Japanese Household Financial Assets

Fukuda, K. — Thu, 05 Nov 2009 08:09:53 PST

Aggregate data on equity shares in Japanese household financial assets, classified by period and age, are decomposed into age, period, and cohort effects by using two different identification methods: one assumes that each effect fluctuates smoothly and the other assumes that the period effect is orthogonal to a linear time trend. Both methods provide a very similar and striking empirical finding. The main factor in the life-cycle movement of equity shares is not the age effect but the cohort effect. Comprehensive robustness checks support this finding.

An ACD-ECOGARCH(1,1) Model

Czado, C., Haug, S. — Wed, 04 Nov 2009 02:01:55 PST

In this paper we introduce an ACD-ECOGARCH(1,1) model. An exponential autoregressive conditional duration model is used to describe the dependence structure in durations of ultra-high-frequency financial data. The innovation process of the ACD model then defines the interarrival times of a compound Poisson process. We use this compound Poisson process as the background driving Lévy process of an exponential continuous time GARCH(1,1) process. The dynamics of the random time transformed log-price process are then described by the latter process. To estimate its parameters we construct a quasi maximum likelihood estimator under the assumption that all jumps of the log-price process are observable. Finally, the model is fitted for illustrative purpose to General Motors tick-by-tick data of the New York Stock Exchange.

Does the Open Limit Order Book Matter in Explaining Informational Volatility?

Pascual, R., Veredas, D. — Mon, 12 Oct 2009 00:18:26 PDT

We evaluate the informational content of the open limit order book by studying its role in explaining the volatility of the efficient price. We separate transitory (liquidity-driven) volatility from informational (efficient price-related) volatility using a dynamic state-space co-integration model for ask and bid quotes. Consistently with Foucault, Moinas, and Theissen (2007, Review of Financial Studies), we show that for any given trade size, the higher the round-trip costs, the higher the ex post informational volatility. Other pieces of the LOB, such as quoted depth, both at and away from the best quotes, and the book imbalance, are also informative.

Price Discovery in Fragmented Markets

De Jong, F., Schotman, P. C. — Thu, 10 Sep 2009 14:31:49 PDT

This paper proposes a structural time-series model for the intraday price dynamics on fragmented financial markets. We generalize the structural model of Hasbrouck (1993) to a multivariate setting. We discuss identification issues and propose a new measure for the contribution of each market to price discovery related to the Hasbrouck (1995) information shares. We apply the model to two sets of Nasdaq dealer quotes.

Shifts in Individual Parameters of a GARCH Model

Galeano, P., Tsay, R. S. — Tue, 18 Aug 2009 09:26:03 PDT

Most asset return series, especially those in high frequency, show high excess kurtosis and persistence in volatility that cannot be adequately described by the generalized conditional heteroscedastic (GARCH) model, even with heavy-tailed innovations. Many researchers have argued that these characteristics are due to shifts in volatility that may be associated with significant economic events such as financial crises. Indeed, several authors have investigated the case of pure structural changes, in which all of the parameters in the GARCH model are assumed to change simultaneously. In this paper, we take an alternative approach by studying the case in which changes occur in individual parameters of a GARCH model. We investigate the impacts of such changes on the underlying return series and its volatility, and propose an iterative procedure to detect them. In all cases, the changes affect permanently the level of the volatility, but in some cases, the changes also alter the dynamic structure of the volatility series. Monte Carlo experiments are used to investigate the performance of the proposed procedure in finite samples, and real examples are used to demonstrate the impacts of detected volatility changes and the efficacy of the proposed procedure. Practical implications of the parameter changes in financial applications are also discussed.

Comparison of Volatility Measures: a Risk Management Perspective

Brownlees, C. T., Gallo, G. M. — Mon, 27 Jul 2009 09:29:47 PDT

In this paper we address the issue of forecasting Value–at–Risk (VaR) using different volatility measures: realized volatility, bipower realized volatility, two-scales realized volatility, realized kernel, as well as the daily range. We propose a dynamic model with a flexible trend specification bonded with a penalized maximum likelihood estimation strategy: the P-spline multiplicative error model. Exploiting ultra-high-frequency data (UHFD) volatility measures, VaR predictive ability is considerably improved upon relative to a baseline GARCH but not so relative to the range; there are gains from modeling volatility trends and from using realized kernels that are robust to dependent microstructure noise.

Stock Options and Credit Default Swaps: A Joint Framework for Valuation and Estimation

Carr, P., Wu, L. — Tue, 21 Jul 2009 11:39:33 PDT

We propose a dynamically consistent framework that allows joint valuation and estimation of stock options and credit default swaps written on the same reference company. We model default as controlled by a Cox process with a stochastic arrival rate. When default occurs, the stock price drops to zero. Prior to default, the stock price follows a jump-diffusion process with stochastic volatility. The instantaneous default rate and variance rate follow a bivariate continuous process, with its joint dynamics specified to capture the observed behavior of stock option prices and credit default swap spreads. Under this joint specification, we propose a tractable valuation methodology for stock options and credit default swaps. We estimate the joint risk dynamics using data from both markets for eight companies that span five sectors and six major credit rating classes from B to AAA. The estimation highlights the interaction between market risk (return variance) and credit risk (default arrival) in pricing stock options and credit default swaps.