Estimating daily volatility in financial markets utilizing intraday data

This study proposes a new approach to the estimation of daily realised volatility in financial markets from intraday data. Initially, an examination of intraday returns on S&P 500 Index Futures reveals that returns can be characterised by heteroscedasticity and time-varying autocorrelation. After reviewing a number of daily realised volatility estimators cited in the literature, it is concluded that these estimators are based upon a number of restrictive assumptions in regard to the data generating process for intraday returns. We use a weak set of assumptions about the data generating process for intraday returns, including transaction returns, given in den Haan and Levin [den Haan, W.J., Levin, A., 1996. Inferences from parametric and non-parametric covariance matrix estimation procedures, Working paper, NBER, 195.], which allows for heteroscedasticity and time-varying autocorrelation in intraday returns. These assumptions allow the VARHAC estimator to be employed in the estimation of daily realised volatility. An empirical analysis of the VARHAC daily volatility estimator employing intraday transaction returns concludes that this estimator performs well in comparison to other estimators cited in the literature.     

Quadratic Hawkes processes for financial prices

We introduce and establish the main properties of QHawkes (‘Quadratic’ Hawkes) models. QHawkes models generalize the Hawkes price models introduced in Bacry and Muzy [Quant. Finance, 2014, 14(7), 1147–1166], by allowing feedback effects in the jump intensity that are linear and quadratic in past returns. Our model exhibits two main properties that we believe are crucial in the modelling and the understanding of the volatility process: first, the model is time-reversal asymmetric, similar to financial markets whose time evolution has a preferred direction. Second, it generates a multiplicative, fat-tailed volatility process, that we characterize in detail in the case of exponentially decaying kernels, and which is linked to Pearson diffusions in the continuous limit. Several other interesting properties of QHawkes processes are discussed, in particular the fact that they can generate long memory without necessarily being at the critical point. A non-parametric fit of the QHawkes model on NYSE stock data shows that the off-diagonal component of the quadratic kernel indeed has a structure that standard Hawkes models fail to reproduce. We provide numerical simulations of our calibrated QHawkes model which is indeed seen to reproduce, with only a small amount of quadratic non-linearity, the correct magnitude of fat-tails and time reversal asymmetry seen in empirical time series.     

Generative Bayesian neural network model for risk-neutral pricing of American index options

Financial models with stochastic volatility or jumps play a critical role as alternative option pricing models for the classical Black–Scholes model, which have the ability to fit different market volatility structures. Recently, machine learning models have elicited considerable attention from researchers because of their improved prediction accuracy in pricing financial derivatives. We propose a generative Bayesian learning model that incorporates a prior reflecting a risk-neutral pricing structure to provide fair prices for the deep ITM and the deep OTM options that are rarely traded. We conduct a comprehensive empirical study to compare classical financial option models with machine learning models in terms of model estimation and prediction using S&P 100 American put options from 2003 to 2012. Results indicate that machine learning models demonstrate better prediction performance than the classical financial option models. Especially, we observe that the generative Bayesian neural network model demonstrates the best overall prediction performance.     

A new closed-form solution as an extension of the Black–Scholes formula allowing smile curve plotting

In this paper, as a generalization of the Black–Scholes (BS) model, we elaborate a new closed-form solution for a uni-dimensional European option pricing model called the J-model. This closed-form solution is based on a new stochastic process, called the J-process, which is an extension of the Wiener process satisfying the martingale property. The J-process is based on a new statistical law called the J-law, which is an extension of the normal law. The J-law relies on four parameters in its general form. It has interesting asymmetry and tail properties, allowing it to fit the reality of financial markets with good accuracy, which is not the case for the normal law. Despite the use of one state variable, we find results similar to those of Heston dealing with the bi-dimensional stochastic volatility problem for pricing European calls. Inverting the BS formula, we plot the smile curve related to this closed-form solution. The J-model can also serve to determine the implied volatility by inverting the J-formula and can be used to price other kinds of options such as American options.     

Unconditional return disturbances: A non-parametric simulation approach

Simulation methods are extensively used in Asset Pricing and Risk Management. The most popular of these simulation approaches, the Monte Carlo, requires model selection and parameter estimation. In addition, these approaches can be extremely computer intensive. Historical simulation has been proposed as a non-parametric alternative to Monte Carlo. This approach is limited to the historical data available.In this paper, we propose an alternative historical simulation approach. Given a historical set of data, we define a set of standardized disturbances and we generate alternative price paths by perturbing the first two moments of the original path or by reshuffling the disturbances. This approach is either totally non-parametric when constant volatility is assumed; or semi-parametric in presence of GARCH(1, 1) volatility. Without a loss in accuracy, it is shown to be much more powerful in terms of computer efficiency than the Monte Carlo approach. It is also extremely simple to implement and can be an effective tool for the valuation of financial assets.We apply this approach to simulate pay off values of options on the S&P 500 stock index for the period 1982–2003. To verify that this technique works, the common back-testing approach was used. The estimated values are insignificantly different from the actual S&P 500 options payoff values for the observed period.     

Pricing under rough volatility

From an analysis of the time series of realized variance using recent high-frequency data, Gatheral et al. [Volatility is rough, 2014] previously showed that the logarithm of realized variance behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable timescale. The resulting Rough Fractional Stochastic Volatility (RFSV) model is remarkably consistent with financial time series data. We now show how the RFSV model can be used to price claims on both the underlying and integrated variance. We analyse in detail a simple case of this model, the rBergomi model. In particular, we find that the rBergomi model fits the SPX volatility markedly better than conventional Markovian stochastic volatility models, and with fewer parameters. Finally, we show that actual SPX variance swap curves seem to be consistent with model forecasts, with particular dramatic examples from the weekend of the collapse of Lehman Brothers and the Flash Crash.     

Power mapping with dynamical adjustment for improved portfolio optimization

For financial risk management it is of vital interest to have good estimates for the correlations between the stocks. It has been found that the correlations obtained from historical data are covered by a considerable amount of noise, which leads to a substantial error in the estimation of the portfolio risk. A method to suppress this noise is power mapping. It raises the absolute value of each matrix element to a power q while preserving the sign. In this paper we use the Markowitz portfolio optimization as a criterion for the optimal value of q and find a K/T dependence, where K is the portfolio size and T the length of the time series. Both in numerical simulations and for real market data we find that power mapping leads to portfolios with considerably reduced risk. It compares well with another noise reduction method based on spectral filtering. A combination of both methods yields the best results.     

Financial Modeling in a Fast Mean-Reverting Stochastic Volatility Environment

We present a derivative pricing and estimation methodology for a class of stochastic volatility models that exploits the observed 'bursty' or persistent nature of stock price volatility. Empirical analysis of high-frequency S&P 500 index data confirms that volatility reverts slowly to its mean in comparison to the tick-by- tick fluctuations of the index value, but it is fast mean- reverting when looked at over the time scale of a derivative contract (many months). This motivates an asymptotic analysis of the partial differential equation satisfied by derivative prices, utilizing the distinction between these time scales. The analysis yields pricing and implied volatility formulas, and the latter provides a simple procedure to 'fit the skew' from European index option prices. The theory identifies the important group parameters that are needed for the derivative pricing and hedging problem for European-style securities, namely the average volatility and the slope and intercept of the implied volatility line, plotted as a function of the log- moneyness-to-maturity-ratio. The results considerably simplify the estimation procedure. The remaining parameters, including the growth rate of the underlying, the correlation between asset price and volatility shocks, the rate of mean-reversion of the volatility and the market price of volatility risk are not needed for the asymptotic pricing formulas for European derivatives, and we derive the formula for a knock-out barrier option as an example. The extension to American and path-dependent contingent claims is the subject of future work. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multiresolution approximation for volatility processes

Abstract

We present an application of wavelet techniques to non-stationary time series with the aim of detecting the dependence structure which is typically found to characterize intraday stock index financial returns. It is particularly important to identify what components truly belong to the underlying volatility process, compared with those features appearing instead as a result of the presence of disturbance processes. The latter may yield misleading inference results when standard financial time series models are adopted. There is no universal agreement on whether long memory really affects financial series, or instead whether it could be that non-stationarity, once detected and accounted for, may allow for more power in detecting the dependence structure and thus suggest more reliable models. Wavelets are still a novel tool in the domain of applications in finance; thus, one goal is to try to show their potential use for signal decomposition and approximation of time-frequency signals. This might suggest a better interpretation of multi-scaling and aggregation effects in high-frequency returns. We show, by using special dictionaries of functions and ad hoc algorithms, that a pre-processing procedure for stock index returns leads to a more accurate identification of dependent and non-stationary features, whose detection results are improved compared with those obtained by other traditional Fourier-based methods. This allows generalized autoregressive conditional heteroscedastic models to be more effective for statistical estimation purposes.     

跨境资本流动会加大金融波动吗?

日益活跃的跨境资本流动与金融波动的关系备受学术界关注,"国际风险承担渠道效应"的提出使人们开始重视金融中介在其中发挥的重要作用。本文基于全球79个国家1996-2017年的面板数据,采用系统GMM估计方法,考察了跨境资本流动对金融波动的影响,以及"国际风险承担渠道效应"存在与否。研究结果表明:大规模的跨境资本流动会增大金融体系脆弱性,加剧金融波动,对一国金融稳定造成强有力的威胁;跨境资本巨额的流出与流入均无助于金融稳定;跨境资本流动会通过影响金融中介的风险感知来改变其风险承担行为,最终会进一步放大跨境资本流动对金融稳定的负向作用,即存在"国际风险承担渠道效应"。因此,中国应坚持完善跨境资本流动管理体系与健全宏观审慎监管框架,严守资本充足率这一重要风险防线,加强对跨境资本和金融中介行为的监管,维护金融稳定。     

Detecting volatility persistence in GARCH models in the presence of the leverage effect

Most asset prices are subject to significant volatility. The arrival of new information is viewed as the main source of volatility. As new information is continually released, financial asset prices exhibit volatility persistence, which affects financial risk analysis and risk management strategies. This paper proposes a nonlinear regime-switching threshold generalized autoregressive conditional heteroskedasticity model which can be used to analyse financial data. The empirical results based on quasi-maximum likelihood estimation presented in this paper suggest that the proposed model is capable of extracting information about the sources of volatility persistence in the presence of the leverage effect.     

Bivariate asymmetric GARCH models with heavy tails and dynamic conditional correlations

A bivariate generalized autoregressive conditional heteroskedastic model with dynamic conditional correlation and leverage effect (DCC-GJR-GARCH) for modelling financial time series data is considered. For robustness it is helpful to assume a multivariate Student-t distribution for the innovation terms. This paper proposes a new modified multivariate t-distribution which is a robustifying distribution and offers independent marginal Student-t distributions with different degrees of freedom, thereby highlighting the relationship among different assets. A Bayesian approach with adaptive Markov chain Monte Carlo methods is used for statistical inference. A simulation experiment illustrates good performance in estimation over reasonable sample sizes. In the empirical studies, the pairwise relationship between the Australian stock market and foreign exchange market, and between the US stock market and crude oil market are investigated, including out-of-sample volatility forecasts.     

Pricing exotic options using MSL-MC

Today, better numerical approximations are required for multi-dimensional SDEs to improve on the poor performance of the standard Monte Carlo pricing method. With this aim in mind, this paper presents a method (MSL-MC) to price exotic options using multi-dimensional SDEs (e.g. stochastic volatility models). Usually, it is the weak convergence property of numerical discretizations that is most important, because, in financial applications, one is mostly concerned with the accurate estimation of expected payoffs. However, in the recently developed Multilevel Monte Carlo path simulation method (ML-MC), the strong convergence property plays a crucial role. We present a modification to the ML-MC algorithm that can be used to achieve better savings. To illustrate these, various examples of exotic options are given using a wide variety of payoffs, stochastic volatility models and the new Multischeme Multilevel Monte Carlo method (MSL-MC). For standard payoffs, both European and Digital options are presented. Examples are also given for complex payoffs, such as combinations of European options (Butterfly Spread, Strip and Strap options). Finally, for path-dependent payoffs, both Asian and Variance Swap options are demonstrated. This research shows how the use of stochastic volatility models and the θ scheme can improve the convergence of the MSL-MC so that the computational cost to achieve an accuracy of O(ε) is reduced from O(ε^?3) to O(ε^?2) for a payoff under global and non-global Lipschitz conditions.     

Is more finance better? Disentangling intermediation and size effects of financial systems

Financial systems all over the world have grown dramatically over recent decades. But is more finance necessarily better? And what concept of financial system – a focus on its size, including both intermediation and other auxiliary “non-intermediation” activities, or a focus on traditional intermediation activity – is relevant for its impact on real sector outcomes? This paper assesses the relationship between the size of the financial system and intermediation, on the one hand, and GDP per capita growth and growth volatility, on the other hand. Based on a sample of 77 countries for the period 1980–2007, we find that intermediation activities increase growth and reduce volatility in the long run. An expansion of the financial sectors along other dimensions has no long-run effect on real sector outcomes. Over shorter time horizons a large financial sector stimulates growth at the cost of higher volatility in high-income countries. Intermediation activities stabilize the economy in the medium run especially in low-income countries. As this is an initial exploration of the link between financial system indicators and growth and volatility, we focus on OLS regressions, leaving issues of endogeneity and omitted variable biases for future research.     

股指期货市场金融加速器效应的实证分析

金融加速器理论认为,由于存在着摩擦成本,金融市场的波动可能是非对称的,体现为相对于扩张金融市场状态,紧缩金融市场状态下冲击的波动更加剧烈,由此产生加速效应。本文采用向量自回归模型系列对次贷危机期间S&P500股指期货市场波动状态进行了计量检验,验证了其非对称波动的金融加速器效应,揭示了股指期货市场与股票现货市场之间的风险衍生机制,旨在为我国沪深300指数期货交易的风险防范提供借鉴。     

Anomalies and financial distress

This paper explores commonalities across asset pricing anomalies. In particular, we assess implications of financial distress for the profitability of anomaly-based trading strategies. Strategies based on price momentum, earnings momentum, credit risk, dispersion, idiosyncratic volatility, and capital investments derive their profitability from taking short positions in high credit risk firms that experience deteriorating credit conditions. In contrast, the value-based strategy derives most of its profitability from taking long positions in high credit risk firms that survive financial distress and subsequently realize high returns. The accruals anomaly is an exception. It is robust among high and low credit risk firms in all credit conditions.     

Hierarchical GARCH

There is strong empirical evidence that the GARCH estimates obtained from panels of financial time series cluster. In order to capture this empirical regularity, this paper introduces the Hierarchical GARCH (HG) model. The HG is a nonlinear panel specification in which the coefficients of each series are modeled as a function of observed series characteristic and an unobserved random effect. A joint panel estimation strategy is proposed to carry out inference for the model. A simulation study shows that when there is a strong degree of coefficient clustering panel estimation leads to substantial accuracy gains in comparison to estimating each GARCH individually. The HG is applied to a panel of U.S. financial institutions in the 2007–2009 crisis, using firm size and leverage as characteristics. Results show evidence of coefficient clustering and that the characteristics capture a significant portion of cross sectional heterogeneity. An out-of-sample volatility forecasting application shows that when the sample size is modest coefficient estimates based on the panel estimation approach perform better than the ones based on individual estimation.     

中国金融发展与产业结构升级关系的实证研究

本文在国内外研究成果的基础上,针对中国的金融发展与产业结构升级的关系问题,系统分析金融发展与产业结构转变的内在联系,采用中国1978～2006年反映金融发展和产业结构升级的指标数据,利用非平稳时间序列分析方法进行定量描述。结果表明,产业结构升级指标和金融发展指标相互之间存在着长期均衡关系,金融相关率和金融市场化率对非农产业产值比重的提高有正向促进作用,并且金融相关率对产业结构升级的影响要强于金融相关率指标。中国产业结构的变化具有自身的惯性,中国的产业结构升级与金融发展的长短期关系是不一致的。产业结构升级和金融市场化比率之间存在双向的因果关系,而产业结构升级与金融相关比率以及金融相关比率和金融市场化比率之间只有单向的因果关系。     

Level changes in volatility models

Level shifts confound the estimation of persistence. This paper shows analytically, in simulations, and using high-frequency stock price data that models for financial volatility that feature a separate source of randomness in the volatility equation are less susceptible to this effect. Such models include recently proposed time series models for realized volatility, as opposed to GARCH models for daily observations, which are highly sensitive to unknown shifts, as has been shown before.     

金融开放背景下金融发展对跨境资本流动的影响研究

金融开放能够促进跨境资本流动,也具有引发跨境资本流动失衡和波动性增加的风险,而一国金融发展水平在其金融开放效应中发挥着重要作用。本文基于58个国家及地区1999-2016年的数据建立动态面板模型,研究金融开放背景下金融发展对直接投资和证券投资流入、流出以及总跨境资本流动波动性的影响。研究结果表明:金融开放本身有可能造成跨境资本流出大于流入的失衡现象,并显著增加跨境资本流动波动性风险,而金融发展水平的提高有助于在一定程度上抑制金融开放带来的跨境资本流动失衡现象和波动性风险。因此,在扩大金融开放进程中,为获得跨境资本流动的积极效应,应密切关注跨境资本流向和资本波动性变化,提高国内金融发展水平,使之与金融开放水平相匹配。