Pricing basket spread options with default risk under Heston–Nandi GARCH models

In this paper, we investigate basket spread options under the Heston–Nandi GARCH model. Moreover, we adopt the reduced-form model to capture default risk, which is correlated with all underlying assets. Because of the nonexistence of the analytical fair values, we obtain a closed-form approximated pricing formula of basket spread options with default risk. Finally, we examine the accuracy of approximations and then use the proposed formulae to illustrate the effect of the number of the underlying assets and default risk as well.     

Analytical quasi maximum likelihood inference in multivariate volatility models

Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension of the parameter space is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian for a variety of multivariate GARCH models including the Vec and BEKK specifications as well as the recent dynamic conditional correlation model. By means of a Monte Carlo investigation of the BEKK–GARCH model we illustrate that employing analytical derivatives for inference is clearly preferable to numerical methods.     

BAYESIAN INFERENCE METHODS FOR UNIVARIATE AND MULTIVARIATE GARCH MODELS: A SURVEY

This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non‐parametric approaches for GARCH models that avoid imposing arbitrary parametric distributional assumptions. These novel approaches implicitly assume infinite mixture of Gaussian distributions on the standardized returns which have been shown to be more flexible and describe better the uncertainty about future volatilities. Finally, the survey presents an illustration using real data to show the flexibility and usefulness of the non‐parametric approach.     

Estimation of the Option Prime: Microsimulation of Backward Stochastic Differential Equations

A mathematical statistical model is needed to obtain an option prime and create a hedging strategy. With formulas derived from stochastic differential equations, the primes for US Dollar/Chilean Pesos currency options using a prime calculator are obtained. Furthermore, a backward simulation of the option prime trajectory is used with a numerical method created for backward stochastic differential equations. The use of statistics in finance is highly important in order to develop complex products.     

基于GARCH族模型的黄金价格收益率及波动性研究

文章应用GARCH族模型对黄金现货价格的收益率及波动性进行实证研究,实证结果表明黄金价格日收益率具有"尖峰厚尾"和"波动聚类"的特征。通过TGARCH及EGARCH模型发现我国黄金市场存在非对称性现象,正的冲击对黄金价格波动影响更大。     

基于动态VaR模型的我国银行间拆借市场风险度量研究

本文介绍了一种基于GARCH和非参数法的动态VaR模型——L_VaR模型,用来度量市场风险与流动性风险两者综合风险的大小。并通过采样我国银行间隔夜拆借的高频交易数据,以及SAS软件的数据处理分析发现,GARCH（1,1）模型能较好地拟合隔夜拆借利率的波动情况,而非参数估计法（Boot- strap）能较准确地估计拆借市场流动性的波动水平。实证结果表明。基于动态VaR模型对于市场风险与流动性风险两者综合风险的短期预测效果较为理想。     

基于VaR修正理论的投资组合优化模型

根据风险价值VaR的计算思路,本文提出了基于GARCH理论的风险计量投资组合优化模型;同时在修正的VaR——尾条件期望的基础上对证券组合投资的优化模型做了进一步的改进。     

Comparing forecasts from fixed and variable coefficient models: The case of money demand

In this paper we introduce a class of tentatively plausible, fixed-coefficient models of money demand and evaluate their forecast performance. When these models are reestimated allowing all coefficients to vary over time, the forecasting performance improves dramatically. Aside from offering insights about improved methods of analyzing time series data, the most promising direct use for point estimates derived from time-varying coefficients is as an aid in calibrating proposed models of the kind discussed here.     

我国沪、深股市的波动性研究——基于GARCH族模型

金融市场的波动性不仅是投资者关注的焦点之一,而且也是被研究的热点之一。中国股市还非常年轻,股票市场的价格常常表现出大幅波动的特征。本研究以上证综合指数和深圳成分指数为研究对象,分别运用GARCH模型、TARCH模型和EGARCH模型同时拟合,并对比分析了中国股市日收益率波动的动态特征;结果显示,EGACH模型能更有效拟合股市的波动性。     

Volatility and error transmission spillover effects: Evidence from three European financial regions

This study uses the multivariate GARCH-BEKK modelling approach to examine the transmission of news (both volatility and error) between portfolios of cross-listed equities within three European financial regions, that is, the Scandinavian (Denmark, Sweden, Finland and Norway), the Germanic (Austria, Switzerland and Germany) and the French area (Brussels, France, Italy, Holland and Spain). We find that the Finnish and Danish portfolios of cross-listed equities are the main transmitters of volatility relative to the Swedish and Norwegian portfolios of cross-listed equities. On the other hand, the Swiss portfolio of cross-listed equities is the major exporter of volatility and error to the other portfolios of cross-listed equities in the Germanic stock market area. Finally, the Paris, Amsterdam and Brussels stock exchanges are the major exporters of volatility and error to the portfolios of cross-listed equities traded on the Milan and Madrid stock exchanges.     

内蒙古稀土市场风险中的GARCH模型应用研究

我国是稀土资源大国,但各稀土产业企业对稀土市场缺乏合理的风险管控,导致稀土市场发展缓慢,规模不经济。文章尝试着对目前内蒙古有色金属稀缺资源之稀土市场风险管理系统构建合理的理论模型,并预测稀土价格变化频率,控制价格损失频率在较低范围内,为稀土投资者提供风险管理手段。     

企业负债经营风险及防范策略

企业负债经营,就必须承担筹资风险。只有对风险进行适当控制,才能使企业既获得负债经营带来的财务杠杆收益,同时将风险降低到最低限度。本文对负债经营的利弊和负债经营风险的防范策略进行了探讨。     

Portfolio optimization based on GARCH-EVT-Copula forecasting models

This study uses GARCH-EVT-copula and ARMA-GARCH-EVT-copula models to perform out-of-sample forecasts and simulate one-day-ahead returns for ten stock indexes. We construct optimal portfolios based on the global minimum variance (GMV), minimum conditional value-at-risk (Min-CVaR) and certainty equivalence tangency (CET) criteria, and model the dependence structure between stock market returns by employing elliptical (Student-$t$ and Gaussian) and Archimedean (Clayton, Frank and Gumbel) copulas. We analyze the performances of 288 risk modeling portfolio strategies using out-of-sample back-testing. Our main finding is that the CET portfolio, based on ARMA-GARCH-EVT-copula forecasts, outperforms the benchmark portfolio based on historical returns. The regression analyses show that GARCH-EVT forecasting models, which use Gaussian or Student-$t$ copulas, are best at reducing the portfolio risk.