Semi-parametric quantile estimation for double threshold autoregressive models with heteroskedasticity

Compared to the conditional mean or median, conditional quantiles provide a more comprehensive picture of a variable in various scenarios. A semi-parametric quantile estimation method for a double threshold auto-regression with exogenous regressors and heteroskedasticity is considered, allowing representation of both asymmetry and volatility clustering. As such, GARCH dynamics with nonlinearity are added to a nonlinear time series regression model. An adaptive Bayesian Markov chain Monte Carlo scheme, exploiting the link between the quantile loss function and the asymmetric-Laplace distribution, is employed for estimation and inference, simultaneously estimating and accounting for nonlinear heteroskedasticity plus unknown threshold limits and delay lags. A simulation study illustrates sampling properties of the method. Two data sets are considered in the empirical applications: modelling daily maximum temperatures in Melbourne, Australia; and exploring dynamic linkages between financial markets in the US and Hong Kong.     

Falling and explosive,dormant, and rising markets via multiple‐regime financial time series models

A multiple‐regime threshold nonlinear financial time series model, with a fat‐tailed error distribution, is discussed and Bayesian estimation and inference are considered. Furthermore, approximate Bayesian posterior model comparison among competing models with different numbers of regimes is considered which is effectively a test for the number of required regimes. An adaptive Markov chain Monte Carlo (MCMC) sampling scheme is designed, while importance sampling is employed to estimate Bayesian residuals for model diagnostic testing. Our modeling framework provides a parsimonious representation of well‐known stylized features of financial time series and facilitates statistical inference in the presence of high or explosive persistence and dynamic conditional volatility. We focus on the three‐regime case where the main feature of the model is to capturing of mean and volatility asymmetries in financial markets, while allowing an explosive volatility regime. A simulation study highlights the properties of our MCMC estimators and the accuracy and favourable performance as a model selection tool, compared with a deviance criterion, of the posterior model probability approximation method. An empirical study of eight international oil and gas markets provides strong support for the three‐regime model over its competitors, in most markets, in terms of model posterior probability and in showing three distinct regime behaviours: falling/explosive, dormant and rising markets. Copyright © 2009 John Wiley & Sons, Ltd.     

基于信息溢出网络的我国行业关联性研究

行业信息溢出网络是各行业之间风险关联的载体,其信息溢出的方向和强度与行业的风险传染特征密切相关。运用广义方差分解对申银万国行业一级指数同时构建行业收益率溢出网络和行业波动率溢出网络,分别从静态和动态角度分析我国行业信息溢出的总体情况和动态演化。研究发现:我国各行业间信息溢出水平较高,整体信息联动能力强,但各行业信息溢出随时间变化具有波动性和不确定性。长期情形下,收益率溢出网络和波动溢出网络对系统性重要行业的识别排序具有高度一致性,但短期内两者存在较大差异。长期内,银行业和非银行金融业是系统性重要(信息)接受行业,机械设备业是系统性重要(信息)传播行业;短期内,银行、非银行金融、国防军工、食品饮料及家用电器业是系统性重要行业,但它们的具体角色(信息接受或者传播)具有不确定性。研究结论对于政府产业政策制定及产业监管具有重要的现实意义。     

Doubly stochastic models with GARCH innovations

A rapid development of time series models and methods addressing volatility in computational finance and econometrics are recently reported in the financial literature. This paper considers doubly stochastic volatility models with GARCH errors. General properties for process mean, variance and kurtosis are derived as these results can be used in model identification.     

经济政策不确定性与数字货币市场波动影响研究——基于比特币市场的实证分析

本文运用混频模型(GARCH-MIDAS)实证研究了全球和7个国家的经济政策不确定性指标(EPU)对比特币市场的波动率影响。样本内结果表明,全球和七个国家的EPU指数对未来比特币市场波动率有显著的影响,EPU在样本内能提升比特币波动率的预测效果,且美国和澳大利亚的EPU与比特币市场波动率呈正相关,其余EPU与之呈负相关。然后运用模型置信集合(MCS)样本外检验发现,美国经济政策不确定性指标相比其他EPU指标更能提高对比特币市场波动率的预测精度。进一步指出,了解全球以及七国经济政策不确定性对数字货币市场的影响,有助于监管机构和政策制定者判断数字货币市场的未来走向,从而防范数字货币市场引发的金融风险。     

Robust static hedging of barrier options in stochastic volatility models

Static hedge portfolios for barrier options are extremely sensitive with respect to changes of the volatility surface. In this paper we develop a semi-infinite programming formulation of the static super-replication problem in stochastic volatility models which allows to robustify the hedge against model parameter uncertainty in the sense of a worst case design. From a financial point of view this robustness guarantees the hedge performance for an infinite number of future volatility surface scenarios including volatility shocks and changes of the skew. After proving existence of such robust hedge portfolios and presenting an algorithm to numerically solve the underlying optimization problem, we apply the approach to a detailed example. Surprisingly, the optimal robust portfolios are only marginally more expensive than the barrier option itself.     

广义双曲线分布模型在我国证券市场风险度量中的应用研究

经济的全球化、衍生产品的大量出现以及因此导致的金融市场的动荡使得金融机构越来越需要更有效的风险管理方法。而如何精确度量风险是风险管理的关键问题。本文试图从金融收益分布假设着手改善风险度量的精度。国外学者研究发现广义双曲线分布比其它分布形式可以更好地拟合实际收益分布特征。本文首次把广义双曲线分布应用到VaR的分析方法中计算我国股票指数的VaR。实证结果表明，基于广义双曲线分布的方法得到了较好的预测结果。     

Mean-reverting stock model with floating interest rate in uncertain environment

As an application of uncertainty theory in the field of finance, uncertain finance is playing a more and more important role in solving the financial problems. This paper proposes a mean-reverting stock model with floating interest rate to investigate the uncertain financial market. The European option and American option pricing formulas of the stock model are derived by using the Yao–Chen formula. Besides, some numerical algorithms are designed to compute the prices of these options based on the pricing formulas.     

快速均值回归随机波动率模型参数估计及应用

基于快速均值回归随机波动率模型, 研究双限期权的定价问题, 同时推导了考虑均值回归随机波动率的双限期权的定价公式。 根据金融市场中SPDR S&P 500 ETF期权的隐含波动率数据和标的资产的历史收益数据, 对快速均值回归随机波动率模型中的两个重要参数进行估计。 利用估计得到的参数以及定价公式, 对双限期权价格做了数值模拟。 数值模拟结果发现, 考虑了随机波动率之后双限期权的价格在标的资产价格偏高的时候会小于基于常数波动率模型的期权价格。     

A model of speculative behaviour with a strange attractor

An asset pricing model for a speculative financial market with fundamentalists and chartists is analysed. The model explains bursts of volatility in financial markets, which are not well explained by the traditional finance paradigms. Speculative bubbles arise as a complex non-linear dynamic phenomenon brought about naturally by the dynamic interaction of heterogeneous market participants. Depending on the time lag in the formation of chartists' expectations, the system evolves through several dynamic regimes, finishing in a strange attractor. Chaos provides a self-sustained motion around the rationally expected equilibrium that corresponds to a speculative bubble. In order to explain the role of Chartism, chaotic motion is a very interesting theoretical feature for a speculative financial market model. It provides a complex non-linear dynamic behaviour around the Walrasian equilibrium price produced by deterministic interactions between fundamentalists and chartists. This model could be a link between two opposite views over the behaviour of financial markets: the theorist's literature view that claims the random motion of asset prices, and the chartist's position extensively adopted by market professionals.     

互联网金融与传统金融业双向风险溢出效应研究

基于2013-2019年互联网金融指数和申万行业指数的日收盘价数据，采用GARCH族模型结合CoVaR方法，从定量计量和动态特征分析两方面入手，考察了互联网金融行业与传统金融业之间的双向风险溢出效应.结果表明，互联网金融与各传统金融业之间均存在双向不对称的正向风险溢出且传统金融业对互联网金融的风险溢出强度显著高于互联网金融对传统金融业的风险溢出强度；从整体来看，互联网金融与银行业之间双向风险溢出效应最强，但从局部分析，互联网金融可能会对证券业造成“激增式”风险溢出，不可掉以轻心；此外，互联网金融与各传统金融业之间的风险溢出还具有周期性特征.     

Modelling LGD for unsecured personal loans: decision tree approach

The New Basel Accord, which was implemented in 2007, has made a significant difference to the use of modelling within financial organisations. In particular it has highlighted the importance of Loss Given Default (LGD) modelling. We propose a decision tree approach to modelling LGD for unsecured consumer loans where the uncertainty in some of the nodes is modelled using a mixture model, where the parameters are obtained using regression. A case study based on default data from the in-house collections department of a UK financial organisation is used to show how such regression can be undertaken.     

HMM based scenario generation for an investment optimisation problem

The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, important features of the time series, like extreme behaviour or volatility clustering cannot be captured. We propose an approach by which the parameters of the GBM are able to switch between regimes, more precisely they are governed by a hidden Markov chain. Thus, we model the financial time series via a hidden Markov model (HMM) with a GBM in each state. Using this approach, we generate scenarios for a financial portfolio optimisation problem in which the portfolio CVaR is minimised. Numerical results are presented.     

Black swans and white eagles: on mathematics and finance

It is often objected that we cannot use mathematical methods in finance because (1) finance is dominated by unpredictable unique events (the black swans), (2) there are qualitative effects that cannot be quantified, and (3) the laws themselves of finance keep on changing. In this paper we discuss these three objections, offering arguments to reject them. We begin by reviewing the development of the physical sciences, pointing out parallels that are relevant for our discussion. Modern science has abandoned the objective of describing reality and has adopted an operational point of view that regards physical laws as tools to connect observations. Modern science is no longer deterministic, but has accepted a fundamental uncertainty in physical laws both at micro and macroscopic levels. Unpredictable pivotal events exist in the physical sciences as well in finance but this does not lead us to question the use of mathematics in the physical sciences. On the contrary, using principles of safe design, we try to understand how to avoid and contain unpredictability. Financial markets are manmade artifacts with, as actors, a large number of interacting agents. If we so wish, we can reduce the level of uncertainty present in markets: But if we try to do so describing financial markets with simple mathematical laws, we find that these laws are not stable but change over time, eventually with sudden structural breaks. This makes the use of mathematical finance difficult but not impossible. We can forecast human decision-making processes, crucial in forecasting financial markets, at the statistical level in aggregate. From an operational point of view, we have the tools to understand and describe the behavior of large number of interacting agents. At the present stage of development of our science, we need to use the mathematics of adaptive systems, changing mathematical models in function of different market states. However, reductionism to a small number of basic laws remains a fundamental objective of financial economics as it is in the physical sciences.     

Common volatility and correlation clustering in asset returns

We present a new multivariate framework for the estimation and forecasting of the evolution of financial asset conditional correlations. Our approach assumes return innovations with time dependent covariances. A Cholesky decomposition of the asset covariance matrix, with elements written as sines and cosines of spherical coordinates allows for modelling conditional variances and correlations and guarantees its positive definiteness at each time t. As in Christodoulakis and Satchell [Christodoulakis, G.A., Satchell, S.E., 2002. Correlated ARCH (CorrARCH): Modelling the time-varying conditional correlation between financial asset returns. European Journal of Operational Research 139 (2), 350–369] correlation is generated by conditionally autoregressive processes, thus allowing for an autocorrelation structure for correlation. Our approach allows for explicit out-of-sample forecasting and is consistent with stylized facts as time-varying correlations and correlation clustering, co-movement between correlation coefficients, correlation and volatility as well as between volatility processes (co-volatility). The latter two are shown to depend on correlation and volatility persistence. Empirical evidence on a trivariate model using monthly data from Dow Jones Industrial, Nasdaq Composite and the 3-month US Treasury Bill yield supports our theoretical arguments.     

Modelling dynamic portfolio risk using risk drivers of elliptical processes

The situation of a limited availability of historical data is frequently encountered in portfolio risk estimation, especially in credit risk estimation. This makes it difficult, for example, to find statistically significant temporal structures in the data on the single asset level. By contrast, there is often a broader availability of cross-sectional data, i.e. a large number of assets in the portfolio. This paper proposes a stochastic dynamic model which takes this situation into account. The modelling framework is based on multivariate elliptical processes which model portfolio risk via sub-portfolio specific volatility indices called portfolio risk drivers. The dynamics of the risk drivers are modelled by multiplicative error models (MEMs)-as introduced by Engle [Engle, R.F., 2002. New frontiers for ARCH models. J. Appl. Econom. 17, 425-446]-or by traditional ARMA models. The model is calibrated to Moody’s KMV Credit Monitor asset returns (also known as firm-value returns) given on a monthly basis for 756 listed European companies at 115 time points from 1996 to 2005. This database is used by financial institutions to assess the credit quality of firms. The proposed risk drivers capture the volatility structure of asset returns in different industry sectors. A characteristic cyclical as well as a seasonal temporal structure of the risk drivers is found across all industry sectors. In addition, each risk driver exhibits idiosyncratic developments. We also identify correlations between the risk drivers and selected macroeconomic variables. These findings may improve the estimation of risk measures such as the (portfolio) Value at Risk. The proposed methods are general and can be applied to any series of multivariate asset or equity returns in finance and insurance.     

On theoretical pricing of options with fuzzy estimators

In this paper we present an application of a new method of constructing fuzzy estimators for the parameters of a given probability distribution function, using statistical data. This application belongs to the financial field and especially to the section of financial engineering. In financial markets there are great fluctuations, thus the element of vagueness and uncertainty is frequent. This application concerns Theoretical Pricing of Options and in particular the Black and Scholes Options Pricing formula. We make use of fuzzy estimators for the volatility of stock returns and we consider the stock price as a symmetric triangular fuzzy number. Furthermore we apply the Black and Scholes formula by using adaptive fuzzy numbers introduced by Thiagarajah et al. [K. Thiagarajah, S.S. Appadoo, A. Thavaneswaran, Option valuation model with adaptive fuzzy numbers, Computers and Mathematics with Applications 53 (2007) 831–841] for the stock price and the volatility and we replace the fuzzy volatility and the fuzzy stock price by possibilistic mean value. We refer to both cases of call and put option prices according to the Black & Scholes model and also analyze the results to Greek parameters. Finally, a numerical example is presented for both methods and a comparison is realized based on the results.     

基于异质交易者定价模型的资产价格泡沫内生机理研究

资产价格泡沫等市场异常现象使得有效市场假说理论受到质疑,研究者们更多的是从行为金融学的角度对这些现象进行解释,认为是由市场投资者的非理性因素所造成的。本文考虑了市场中投资者决策的异质性,构建了含有长期基础投资者和短期技术投资者的异质交易模型,以说明在投资者均具有理性预期的条件下,有效市场假说理论同样可以解释泡沫的产生。具体而言,技术投资者的交易行为使价格产生波动,基础投资者的存在则对波动起到放大作用,并会进一步导致泡沫的出现,随着基础投资者所占的比例增大,泡沫膨胀的速度加快,由此导致市场的波动越剧烈。研究结果为市场监管者提供了有益的启示:与其设置壁垒限制技术投资者的加入及交易活动,不如让越来越多的技术投资者加入到市场中来,这样更有益于市场的稳定。     

Strategic real options with stochastic volatility in a duopoly model

The investment-timing problem has been considered by many authors under the assumption that the instantaneous volatility of the demand shock is constant. Recently, Ting et al. (2013) [12] carried out an asymptotic approach in a monopoly model by letting the volatility parameter follow a stochastic process. In this paper, we consider a strategic game in which two firms compete for a new market under an uncertain demand, and extend the analysis of Ting et al. to duopoly models under different strategic game structures. In particular, we investigate how the additional uncertainty in the volatility affects the investment thresholds and payoffs of players. Several numerical examples and comparison of the results are provided to confirm our analysis.     

Simulated likelihood inference for stochastic volatility models using continuous particle filtering

Discrete-time stochastic volatility (SV) models have generated a considerable literature in financial econometrics. However, carrying out inference for these models is a difficult task and often relies on carefully customized Markov chain Monte Carlo techniques. Our contribution here is twofold. First, we propose a new SV model, namely SV–GARCH, which bridges the gap between SV and GARCH models: it has the attractive feature of inheriting unconditional properties similar to the standard GARCH model but being conditionally heavier tailed. Second, we propose a likelihood-based inference technique for a large class of SV models relying on the recently introduced continuous particle filter. The approach is robust and simple to implement. The technique is applied to daily returns data for S&P 500 and Dow Jones stock price indices for various spans.