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。     

Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns

In this work, we investigate sequential Bayesian estimation for inference of stochastic volatility with variance‐gamma (SVVG) jumps in returns. We develop an estimation algorithm that combines the sequential learning auxiliary particle filter with the particle learning filter. Simulation evidence and empirical estimation results indicate that this approach is able to filter latent variances, identify latent jumps in returns, and provide sequential learning about the static parameters of SVVG. We demonstrate comparative performance of the sequential algorithm and off‐line Markov Chain Monte Carlo in synthetic and real data applications.     

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.     

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.     

多元波动率模型的一些新进展

对多个资产收益率的协方差矩阵建立动态模型是一个非常重要的问题。本文就近些年来该方面研究的一些主要进展进行了综述,特别地介绍了几种基于数据降维技术发展起来的能够适用于高维情形的多元GARCH模型,另外,对于多元波动率的模型诊断与比较方法以及条件协方差矩阵的预测等方面的研究成果也作了分析。     

Bayesian modeling of financial returns: A relationship between volatility and trading volume

The modified mixture model with Markov switching volatility specification is introduced to analyze the relationship between stock return volatility and trading volume. We propose to construct an algorithm based on Markov chain Monte Carlo simulation methods to estimate all the parameters in the model using a Bayesian approach. The series of returns and trading volume of the British Petroleum stock will be analyzed. Copyright © 2009 John Wiley & Sons, Ltd.     

证券价格长期波动控制系统的最优控制策略

探讨证券价格长期波动控制系统的最优控制问题.建立了在有效市场条件下证券价格长期波动的控制系统模型.为了使证券价格和内在价值按照人们预期的目标变化,探讨了对它们服从的系统采用经典信息结构下的随机最优控制策略问题.设计了使系统的输出跟踪证券内在价值的估计值,同时使调节控制的幅度尽可能小的性能指标,给出了最优控制策略的求解公式和计算过程,并给出了考虑系统性能的计算过程,对相应结果进行了分析.主要结论是:当价值对价格的均衡回归调整不足,或投资者对前期价值的增值预期乐观时,最优控制策略所起的作用在加强;而当价值对价格的均衡回归调整过度,或投资者对前期价值的增值预期悲观时,最优控制策略所起的作用在减弱.这些结果可以为完善证券市场和上市公司的监管提供理论依据     

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。