最优波动率模型选择及其在黄金市场中的应用

文章先总结了波动率模型过去的研究，并对不同波动率模型的评估提出三种方法，然后讨论了这些方法在黄金市场波动率预测中的应用。通过分析黄金市场1975年到2004年的数据，得出的结论是，如果基于样本外四期预测误差的评估，EWMA模型较优；如果基于样本外四期预测的R平方的评估，T-GARCH模型较优；如果基于VAR损失函数的真实性检验评估，EWMA模型较优。最后对未来关于金融市场波动率的研究提出一些建议。     

我国上海股票市场GARCH效应实证研究

对我国上海股票市场的GARCH效应进行了实证研究，包括3个方面的内容：应用GARCH模型对股票收益率进行事前估计分析；对模型参数进行估计与最优选择；应用GARCH模型进行事后估计分析，结果表明我国上海股票上益率序列的波动具有显著性的异方差性，可以用GARCH（1，1）进行拟合。     

The properties and mechanism of long-term memory in nonparametric volatility

Recent empirical literature documents the presence of long-term memory in return volatility. But the mechanism of the existence of long-term memory is still unclear. In this paper, we investigate the origin and properties of long-term memory with nonparametric volatility, using high-frequency time series data of the Chinese Shanghai Composite Stock Price Index. We perform Detrended Fluctuation Analysis (DFA) on three different nonparametric volatility estimators with different sampling frequencies. For the same volatility series, the Hurst exponents reduce as the sampling time interval increases, but they are still larger than 1/2, which means that no matter how the interval changes, it still cannot change the existence of long memory. RRV presents a relatively stable property on long-term memory and is less influenced by sampling frequency. RV and RBV have some evolutionary trends depending on time intervals, which indicating that the jump component has no significant impact on the long-term memory property. This suggests that the presence of long-term memory in nonparametric volatility can be contributed to the integrated variance component. Considering the impact of microstructure noise, RBV and RRV still present long-term memory under various time intervals. We can infer that the presence of long-term memory in realized volatility is not affected by market microstructure noise. Our findings imply that the long-term memory phenomenon is an inherent characteristic of the data generating process, not a result of microstructure noise or volatility clustering.     

Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility

This paper investigates the open-loop equilibrium reinsurance-investment (RI) strategy under general stochastic volatility (SV) models. We resolve difficulties arising from the unbounded volatility process and the non-negativity constraint on the reinsurance strategy. The resolution enables us to derive the existence and uniqueness result for the time-consistent mean variance RI policy under both situations of constant and state-dependent risk aversions. We apply the general framework to popular SV models including the Heston, the 3/2 and the Hull–White models. Closed-form solutions are obtained for the aforementioned models under constant risk aversion, and the non-leveraged models under state-dependent risk aversion.     

Optimal kernel estimation of spot volatility of stochastic differential equations

A unified framework to optimally select the bandwidth and kernel function of spot volatility kernel estimators is put forward. The proposed models include not only classical Brownian motion driven dynamics but also volatility processes that are driven by long-memory fractional Brownian motions or other Gaussian processes. We characterize the leading order terms of the mean squared error, which in turn enables us to determine an explicit formula for the leading term of the optimal bandwidth. Central limit theorems for the estimation error are also obtained. A feasible plug-in type bandwidth selection procedure is then proposed, for which, as a sub-problem, a new estimator of the volatility of volatility is developed. The optimal selection of the kernel function is also investigated. For Brownian Motion type volatilities, the optimal kernel turns out to be an exponential function, while, for fractional Brownian motion type volatilities, easily implementable numerical results to compute the optimal kernels are devised. Simulation studies further confirm the good performance of the proposed methods.     

随机环境下具有最低担保约束的DC养老金鲁棒投资策略

针对近年来养老金管理遇到的问题,基于模型不确定性,考虑随机环境和退休保障限制的DC型养老金最优投资策略具有重要意义.以养老金的最终价值相对于退休后年金担保的不变相对风险厌恶期望效用最大化为目标,利用随机动态规划的方法,求出鲁棒最优投资策略及相应的价值函数.最后,通过数值分析,得到各参数对最优投资策略的影响.     

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。     

基于双因子已实现GARCH模型的波动率预测研究

准确地预测金融市场的波动率对市场管理者和参与者而言都是至关重要的。本文在标准已实现GARCH模型基础上,将条件方差乘性分解为长期方差和短期方差两部分,分别构造包含杠杆函数的长期方差方程和短期方差方程,用以捕捉波动率的长记忆性和短期微观波动。运用上证综指和日经指数的日收盘价、已实现方差和已实现核波动此类高频数据进行实证分析,结果表明:与标准已实现GARCH模型相比,两指数的双因子已实现GARCH模型在样本内表现出更大的似然估计值;通过样本外误差函数分析和DM检验,双因子已实现GARCH模型也取得更好表现。     

随机波动率与投资中的q理论

本文将随机波动率引入托宾q模型,讨论生产率冲击的波动率大小对公司价值与投资决策的影响.研究发现,公司托宾q值会受到生产率冲击波动率的显著影响,波动率的增大会降低托宾q值,且该影响会随着波动率的增大而加剧.此外,波动率对托宾q值的影响也会传导到公司的投资决策上来,托宾q降低会使得投资额减小,该影响同样会随波动率的增大而加剧.本文还考虑了波动率对公司在用资产与成长机会价值的影响,更为合理地刻画了公司生产过程中生产率冲击的波动率为随机的假设现实情况,所得结论对公司估值及投资决策均有一定的参考价值.     

基于Heston随机波动率模型和风险偏好视角的资产负债管理

本文研究基于Heston随机波动率模型的资产负债管理问题。假设金融市场由一个无风险资产和一个风险资产构成,投资者的目标是最大化其终端财富的期望效用。应用随机控制方法,得到了该问题最优资产配置策略的解析表达式和相应值函数的解析解,通过数值算例分析了Heston模型主要参数以及债务对最优资产配置策略的影响。结果表明:配置到风险资产的比例对Heston模型中的参数非常敏感;为了对冲债务风险,负债的引入使得配置到风险资产的比例比无负债情形下的高;在风险厌恶系数变大时,无论投资者是否有负债,其投资到风险资产的比例则越来越低。