Modifying a simple agent-based model to disentangle the microstructure of Chinese and US stock markets

We modify a simple agent-based model (ABM) proposed by Franke and Westerhoff [J. Econ. Dyn. Control, 2012, 36(8), 1193–1211] through considering the price limits and the motion of the fundamental value. The method of simulated moments is applied to calibrate both initial and modified ABMs with CSI 300 and S&P 500 respectively, and the goodness-of-fit of each ABMs is tested. The calibration results indicate that the modified model performs better than initial one. Then, we utilize the GSL-div, proposed by Lamperti [Econometrics Stat, 2018, 5, 83–106.], to verify the explanatory power of ABMs. In this procedure, 13 ARCH family models are introduced as benchmarks. The result shows that the explanatory power of modified ABM exceeds ARCH models in both markets, while initial ABM may be defeated by some of the ARCH family models in explaining the microstructure of CSI 300. Finally, a heuristic algorithm is designed to disentangle the insights of Chinese and US stock markets to the observed time horizon through calibrating the initial fundamental value, and Kupiec test is used to check the robustness of the calibration. The result indicates that the explanation of modified model is robust in both markets, while initial model lost its robustness when explaining S&P 500.     

Power ARCH modelling of commodity futures data on the London Metal Exchange

A recent addition to the ARCH family of econometric models was introduced by Ding and co-workers wherein the power term by which the data is transformed was estimated within the model rather than being imposed by the researcher. This paper considers the ability of the Power GARCH class of models to capture the stylized features of volatility in a range of commodity futures prices traded on the London Metals Exchange (LME). The results of this procedure suggest that asymmetric effects are not generally present in the LME futures data. Further, unlike stock market data which is well described by the model, futures data is not as well described by the APGARCH model. Nested within the APGARCH model are several other models from the ARCH family. This paper uses the standard log likelihood procedure to conduct pairwise comparisons of the relative merits of each and the results suggest that it is the Taylor GARCH model which performs best.     

Volatility forecasts and at-the-money implied volatility: a multi-component ARCH approach and its relation to market models

This article explores the relationships between several forecasts for the volatility built from multi-scale linear ARCH processes, and linear market models for the forward variance. This shows that the structures of the forecast equations are identical, but with different dependencies on the forecast horizon. The process equations for the forward variance are induced by the process equations for an ARCH model, but postulated in a market model. In the ARCH case, they are different from the usual diffusive type. The conceptual differences between both approaches and their implication for volatility forecasts are analysed. The volatility forecast is compared with the realized volatility (the volatility that will occur between date t and t + ΔT), and the implied volatility (corresponding to an at-the-money option with expiry at t + ΔT). For the ARCH forecasts, the parameters are set a priori. An empirical analysis across multiple time horizons ΔT shows that a forecast provided by an I-GARCH(1) process (one time scale) does not capture correctly the dynamics of the realized volatility. An I-GARCH(2) process (two time scales, similar to GARCH(1,1)) is better, while a long-memory LM-ARCH process (multiple time scales) replicates correctly the dynamics of the implied and realized volatilities and delivers consistently good forecasts for the realized volatility.     

Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study

Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH specification of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We find this multivariate specification to be generally applicable once power, leverage and long-memory effects are taken into consideration. In addition, we find that both the optimal fractional differencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.     

Volume and Volatility: News or Noise?

This paper presents a market microstructure model that is consistent with several empirical regularities. The model embeds separate latent ARCH‐like volatility processes: one representing movements in the underlying fundamental and one representing noise caused by the trading process. This structure allows the regularities to depend either on news or noise. The heteroskedasticity and persistence in the data are due to both ARCH‐like processes. The model has difficulty in simultaneously capturing the size and persistence of trading volume. Several extensions of the basic model, particularly including a constant level of non‐informational trading, improve the model's ability to capture the relevant characteristics of the data.     

VOLATILITY FORECASTS,TRADING VOLUME,AND THE ARCH VERSUS OPTION‐IMPLIED VOLATILITY TRADE‐OFF

We investigate empirically the role of trading volume (1) in predicting the relative informativeness of volatility forecasts produced by autoregressive conditional heteroskedasticity (ARCH) models versus the volatility forecasts derived from option prices, and (2) in improving volatility forecasts produced by ARCH and option models and combinations of models. Daily and monthly data are explored. We find that if trading volume was low during period t?1 relative to the recent past, ARCH is at least as important as options for forecasting future stock market volatility. Conversely, if volume was high during period t?1 relative to the recent past, option‐implied volatility is much more important than ARCH for forecasting future volatility. Considering relative trading volume as a proxy for changes in the set of information available to investors, our findings reveal an important switching role for trading volume between a volatility forecast that reflects relatively stale information (the historical ARCH estimate) and the option‐implied forward‐looking estimate.     

Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects

This paper provides empirical support for the notion that Autoregressive Conditional Heteroskedasticity (ARCH) in daily stock return data reflects time dependence in the process generating information flow to the market. Daily trading volume, used as a proxy for information arrival time, is shown to have significant explanatory power regarding the variance of daily returns, which is an implication of the assumption that daily returns are subordinated to intraday equilibrium returns. Furthermore, ARCH effects tend to disappear when volume is included in the variance equation.     

Model-free versus Model-based Volatility Prediction

The well-known ARCH/GARCH models for financial time series havebeen criticized of late for their poor performance in volatilityprediction, that is, prediction of squared returns.¹ Focusingon three representative data series, namely a foreign exchangeseries (Yen vs. Dollar), a stock index series (the S&P500index), and a stock price series (IBM), the case is made thatfinancial returns may not possess a finite fourth moment. Takingthis into account, we show how and why ARCH/GARCH models—whenproperly applied and evaluated—actually do have nontrivialpredictive validity for volatility. Furthermore, we show howa simple model-free variation on the ARCH theme can performeven better in that respect. The model-free approach is basedon a novel normalizing and variance–stabilizing transformation(NoVaS, for short) that can be seen as an alternative to parametricmodeling. Properties of this transformation are discussed, andpractical algorithms for optimizing it are given.     

A long memory property of stock market returns and a new model

A ‘long memory’ property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return ¦r_t¦^d also has quite high autocorrelation for long lags. It is possible to characterize ¦r_t¦^d to be ‘long memory’ and this property is strongest when d is around 1. This result appears to argue against ARCH type specifications based upon squared returns. But our Monte-Carlo study shows that both ARCH type models based on squared returns and those based on absolute return can produce this property. A new general class of models is proposed which allows the power δ of the heteroskedasticity equation to be estimated from the data.     

Improving the Forecast of Longevity by Combining Models

Mortality is a dynamic process whose future evolution over time poses important challenges for life insurance, pension funds, public policy, and fiscal planning. In this paper, we propose two contributions: (1) a new dynamic corrective methodology of the predictive accuracy of the existing mortality projection models, by modeling a measure of their fitting errors as a Cox-Ingersoll-Ross process and; (2) various out-of-sample validation methods. Besides the usual static method, we develop a dynamic one allowing us to catch the change in behavior of the underlying data. For our numerical application, we choose the Cairns-Blake-Dowd (or M5) model. Using the Italian and French females mortality data and implementing the backtesting procedure, we empirically test the ex-post forecasting performance of the CBD model both for itself (CBD) and corrected by the CIR process (mCBD). We focus on age 65, but we show results for a wide range of ages, also much younger, and for cohort data. On the basis of average measures of forecasting errors and information criteria, we show that the mCBD model is parsimonious and provides better results in terms of predictive accuracy than the CBD model itself.     

Official interventions and the forward premium anomaly

This paper presents evidence that the forward premium anomaly intensifies during those times when a central bank intervenes. A model of exchange rate determination is presented to explain this and other features of the dollar–deutschemark and dollar–yen markets. In the model, the forward premium anomaly is caused by surprise central bank interventions in the foreign exchange market. Because interventions are pure surprises, the violations of uncovered interest parity that they create do not represent ex ante profit opportunities. Simulations of the model are found to match the forward premium anomaly and several other notable features of the data. The model also provides a theoretical basis for ARCH effects in exchange-rate returns.     

Conditional Heteroskedasticity and Global Stock Return Distributions

This paper investigates conditional return distribution characteristics for seven developed markets (DMs) and eight emerging markets (EMs). With the exception of Germany and Japan, the behavior of monthly returns of DM sample countries is similar to that of the U.S. In contrast, EM returns exhibit a substantially greater degree of serial correlation and a higher incidence of autoregressive conditional heteroskedasticity (ARCH) in monthly data. Aggregation of returns into two- and three-month holding periods decreases the significance of the ARCH effects. However, there are cross-sectional differences in the rate at which ARCH effects become insignificant. The findings of ARCH in monthly returns sample data is attributed to differences in the rate at which information arrives and is transmitted into prices in each market.     

Detecting ARCH Effects in Non-Gaussian Time Series

Engles ARCH test has become the standard test for ARCH effectsin applied work. Under non-normality the true rejection probabilityof this test can differ substantially from the nominal level,however. Bootstrap and Monte Carlo versions of the test maythen be used instead. This paper proposes an alternative testprocedure. The new test exploits the empirical distributionof the data and an extended probability integral transformation.The test is compared with the former tests in Monte Carlo experiments.Under normality, the new test works as well as the conventionalMonte Carlo test and the bootstrap. Under non-normality, thetest tends to be more accurate and more powerful than the bootstrappedARCH test. The procedure is then used to test for ARCH effectsin S&P 500 returns sampled at different frequencies. Incontrast to the standard and the bootstrapped ARCH tests, thenew test detects ARCH effects in the transformed low-frequencyreturns.     

Evaluation of Black-Scholes and GARCH Models Using Currency Call Options Data

This paper empirically examines the performance of Black-Scholes and Garch-M call option pricing models using call options data for British Pounds, Swiss Francs and Japanese Yen. The daily exchange rates exhibit an overwhelming presence of volatility clustering, suggesting that a richer model with ARCH/GARCH effects might have a better fit with actual prices. We perform dominant tests and calculate average percent mean squared errors of model prices. Our findings indicate that the Black-Scholes model outperforms the GARCH models. An implication of this result is that participants in the currency call options market do not seem to price volatility clusters in the underlying process.     

Volatility conditional on price trends

The influence of the past price behaviour on the realized volatility is investigated, showing that trending (driftless) prices lead to increased (decreased) realized volatility. This ‘volatility induced by trend’ constitutes a new stylized fact. The past price behaviour is measured by the product of two non-overlapping returns (of the form r × L[r] where L is the lag operator), and is different from the usual heteroskedasticity. The effect is studied empirically using USD/CHF foreign exchange data, in a large range of time horizons. On the modelling side, a set of ARCH based processes are modified in order to include the ‘volatility induced by trend’ effect, and their forecasting performances are compared. The aim is to understand the role and importance of the various terms that can be included in such a model. For a better forecast, it is shown that the main factor is the shape of the memory kernel (i.e. power law), and the next most important factor is the trend effect. The subtle role of mean reversion is also discussed.     

石油市场与黄金市场收益率波动溢出效应研究

在总结国内外相关研究的基础上,基于2002年12月2日到2010年9月30日的日数据,建立相应的ARCH族模型,并进行Granger因果关系检验,本文对石油市场和黄金市场收益的波动性、波动的非对称性及其波动溢出效应进行实证分析。结果表明:两市均具有显著的方差时变性及新信息对波动冲击的持续性;GARCH(1,1)模型能够很好地消除其ARCH效应;两市均存在明显的非对称性,即石油市场中利空消息引起的波动比同等利好消息引起的波动要大,而黄金市场相反;两市只存在从石油市场到黄金市场的单向波动溢出效应。研究结果对该领域投资者的相关投资及决策人的决策制定具有重要的参考价值。     

Estimating GARCH models using support vector machines*

Abstract

Support vector machines (SVMs) are a new nonparametric tool for regression estimation. We will use this tool to estimate the parameters of a GARCH model for predicting the conditional volatility of stock market returns. GARCH models are usually estimated using maximum likelihood (ML) procedures, assuming that the data are normally distributed. In this paper, we will show that GARCH models can be estimated using SVMs and that such estimates have a higher predicting ability than those obtained via common ML methods.     

Refining the Degree of Earnings Surprise: A Comparison of Statistical and Analysts' Forecasts

This paper compares the relative predictive ability of several statistical models with analysts' forecasts. It is one of the first attempts to forecast quarterly earnings using an autoregressive conditional heteroskedasticity (ARCH) model. ARCH and autoregressive integrated moving average models are found to be superior statistical forecasting alternatives. The most accurate forecasts overall are provided by analysts. Analysts have both a contemporaneous and timing advantage over statistical models. When the sample is screened on those firms that have the largest structural change in the earnings process, the forecast accuracy of the best statistical models is similar to analysts' predictions.     

Nonlinear modelling of the Finnish Banking and Finance branch index

It is well documented that daily returns of several financial assets cannot be modelled by pure linear processes. It seems to be generally accepted that many economic variables follow nonlinear processes. The sources of nonlinearity can be divided in two classes: those where nonlinearities stem from the conditional variance and those where non-linearities enter through the conditional mean. Efforts in modelling the former have resulted in development of the ARCH-family models. There is, however, less evidence on nonlinearity in the mean of financial time series. One family of models that is applied in finance is the STAR. In this paper some nonlinear modelling techniques are applied to a Finnish financial time series, the daily Banking and Finance branch index on the Helsinki Stock Exchange. The techniques include a variance-nonlinear model from the ARCH family, a mean-nonlinear model, namely Smooth Transition Autoregression (STAR)-model and a neural network. Linearity is tested for by standard autocorrelation tests, LM-tests against the specific nonlinear models and the BDS-test. The study provides supplements to a range of earlier research. It demonstrates that the stock series is both linearly and nonlinearly dependent. Adapting an ARCH(3) eliminates the dependencies most satisfactorily. The ARCH-models and STAR-models were estimated using the SHAZAM-package.     

Multivariate term structure models with level and heteroskedasticity effects

The paper introduces and estimates a multivariate level-GARCH model for the long rate and the term-structure spread where the conditional volatility is proportional to the γth power of the variable itself (level effects) and the conditional covariance matrix evolves according to a multivariate GARCH process (heteroskedasticity effects). The long-rate variance exhibits heteroskedasticity effects and level effects in accordance with the square-root model. The spread variance exhibits heteroskedasticity effects but no level effects. The level-GARCH model is preferred above the GARCH model and the level model. GARCH effects are more important than level effects. The results are robust to the maturity of the interest rates.