Estimation methods for stochastic volatility models: a survey

Abstract.  Although stochastic volatility (SV) models have an intuitive appeal, their empirical application has been limited mainly due to difficulties involved in their estimation. The main problem is that the likelihood function is hard to evaluate. However, recently, several new estimation methods have been introduced and the literature on SV models has grown substantially. In this article, we review this literature. We describe the main estimators of the parameters and the underlying volatilities focusing on their advantages and limitations both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.     

Dual long-memory, structural breaks and the link between turnover and the range-based volatility

This paper investigates the issue of temporal ordering of the range-based volatility and turnover volume in the Korean market for the period 1995–2005. We examine the dynamics of the two variables and their respective uncertainties using a bivariate dual long-memory model. We distinguish volume trading before the Asia financial crisis from trading after the crisis. We find that the apparent long-memory in the variables is quite resistant to the presence of breaks. However, when we take into account structural breaks the order of integration of the conditional variance series decreases considerably. Moreover, the impact of foreign volume on volatility is negative in the pre-crisis period but turns to positive after the crisis. This result is consistent with the view that foreign purchases tend to lower volatility in emerging markets—especially in the first few years after market liberalization when foreigners are buying into local markets—whereas foreign sales increase volatility. Before the crisis there is no causal effect for domestic volume on volatility whereas in the post-crisis period total and domestic volumes affect volatility positively. The former result is in line with the theoretical underpinnings that predict that trading within domestic investor groups does not affect volatility. The latter result is consistent with the theoretical argument that the positive relation between the two variables is driven by the uninformed general public.     

Why cryptocurrency markets are inefficient: The impact of liquidity and volatility

In this research, we study the multifractality, long-memory process, and efficiency hypothesis of six major cryptocurrencies (Bitcoin, Ethereum, Monero, Dash, Litecoin, and Ripple) using the time-rolling MF-DFA approach. For an in-depth analysis, this study uses the quantile regression approach to examine the determinants of efficient markets. The results show that all markets present evidence of long-memory property and multifractality. Furthermore, the inefficiency of cryptocurrency markets is time-varying, and Dash is the least inefficient market while Litecoin is the most inefficient. Finally, we find that higher liquidity improves but higher volatility weakens the efficiency of cryptocurrencies, depending on the quantiles. Therefore, we conclude that high liquidity with low volatility helps active traders to arbitrage away opportunities, resulting in market efficiency.     

中国股市长期记忆效应的实证研究

股票市场长期记忆效应问题一直是金融经济学家们倍感兴趣的一个研究热点。本文针对中国股票市场中价格指数与个股的日收益序列 ,在已有研究文献主要采用的经典R S分析方法基础上 ,引入修正R S分析与ARFIMA模型进行了实证研究。从研究结果来看 ,2 2个样本序列并不满足传统的正态分布假设 ,序列呈现出尖峰、肥尾、右偏等有偏特征以及独特的自相关与偏自相关结构 ,这些迹象预示着非线性动态系统的存在。而进一步的研究却表明 ,中国股市中代表市场总体的股价指数不存在长期记忆效应 ,而个股收益序列的分布特征存在着较大差异 ,仅少数个股存在长期记忆行为。这一结论明显地有别于以往那些由经典R S分析所得到的研究结果。     

Prediction from ARFIMA models: Comparisons between MLE and semiparametric estimation procedures

This paper considers the effects on multi-step prediction of using semiparametric local Whittle estimators rather than MLE for long memory ARFIMA models. We consider various representations of the minimum MSE predictor with known parameters. We then conduct a detailed simulation study for when the true parameters are replaced with estimates. The predictor based on MLE is found to be superior, in the MSE sense, to the predictor based on the two-step local Whittle estimation. The “optimal” bandwidth local Whittle estimator produces worse predictions than the local Whittle using an agnostic bandwidth of the square root of the sample size.     

A SHARP model of bid–ask spread forecasts

This paper proposes an accurate, parsimonious and fast-to-estimate forecasting model for integer-valued time series with long memory and seasonality. The modelling is achieved through an autoregressive Poisson process with a predictable stochastic intensity that is determined by two factors: a seasonal intraday pattern and a heterogeneous autoregressive component. We call the model SHARP, which is an acronym for seasonal heterogeneous autoregressive Poisson. We also present a mixed-data sampling extension of the model, which adopts the historical information flow more efficiently and provides the best (among all the models considered) forecasting performances, empirically, for the bid–ask spreads of NYSE equity stocks. We conclude by showing how bid–ask spread forecasts based on the SHARP model can be exploited in order to reduce the total cost incurred by a trader who is willing to buy or sell a given amount of an equity stock.     

Posterior analysis of mergers and acquisitions in the international financial market: A re-appraisal

Do mergers and acquisitions (M&A) improve the wealth status of investors, and if so, amidst persistence of volatility shocks? This paper tests these propositions by employing in the first step, a modified event study approach, and estimating a long-memory conditional volatility model, in the second step. The financial and policy implications of M&A are varied and contestable, yet, from an investor’s perspective, the long-term adjusted gain from M&A depends not only on the immediate growth of wealth, but also the fact that such a growth would accompany reduced rate of volatility persistence. Although in the beginning, a high persistence of volatility cannot be ruled out, its presence in the longer-run implies that the wealth gains from M&A are unstable, leading perhaps to a further collapse of both the merged/merger and acquired/acquiring firms. We estimate a long-memory Generalized Conditional Heteroscedasticity (GARCH) model with a Markovian transition for a number of international firms, specifically in Asia, to show in the first place, whether volatility shocks display differential memory in the pre- and post-M&A periods and whether the asymmetric high persistence is in the aftermath of M&A. Our results point at a significant ‘non-zero’ and positive gain for investors following M&A, but this is combined with greater volatility persistence.