Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.

Some Explicit Formulae for the Hull and White Stochastic Volatility Model

An explicit formula for the transition probability density function of the Hull and White stochastic volatility model in presence of nonzero correlation between the stochastic differentials of the Wiener processes on the right hand side of the model equations is presented. This formula gives the transition probability density function as a two dimensional integral of an explicitly known integrand. Previously an explicit formula for this probability density function was known only in the case of zero correlation. In the case of nonzero correlation from the formula for the transition probability density function we deduce formulae (expressed by integrals) for the price of European call and put options and closed form formulae (that do not involve integrals) for the moments of the asset price logarithm. These formulae are based on recent results on the Whittaker functions [1] and generalize similar formulae for the SABR and multiscale SABR models [2]. Using the option pricing formulae derived and the least squares method a calibration problem for the Hull and White model is formulated and solved numerically. The calibration problem uses as data a set of option prices. Experiments with real data are presented. The real data studied are those belonging to a time series of the USA S&P 500 index and of the prices of its European call and put options. The quality of the model and of the calibration procedure is established comparing the forecast option prices obtained using the calibrated model with the option prices actually observed in the financial market. The website: http://www.econ.univpm.it/recchioni/finance/w17 contains some auxiliary material including animations and interactive applications that helps the understanding of this paper. More general references to the work of the authors and of their coauthors in mathematical finance are available in the website: http://www.econ.univpm.it/recchioni/finance.

The Calibration of Some Stochastic Volatility Models Used in Mathematical Finance

Stochastic volatility models are used in mathematical finance to describe the dynamics of asset prices. In these models, the asset price is modeled as a stochastic process depending on time implicitly defined by a stochastic differential Equation. The volatility of the asset price itself is modeled as a stochastic process depending on time whose dynamics is described by a stochastic differential Equation. The stochastic differential Equations for the asset price and for the volatility are coupled and together with the necessary initial conditions and correlation assumptions constitute the model. Note that the stochastic volatility is not observable in the financial markets. In order to use these models, for example, to evaluate prices of derivatives on the asset or to forecast asset prices, it is necessary to calibrate them. That is, it is necessary to estimate starting from a set of data the values of the initial volatility and of the unknown parameters that appear in the asset price/volatility dynamic Equations. These data usually are observations of the asset prices and/or of the prices of derivatives on the asset at some known times. We analyze some stochastic volatility models summarizing merits and weaknesses of each of them. We point out that these models are examples of stochastic state space models and present the main techniques used to calibrate them. A calibration problem for the Heston model is solved using the maximum likelihood method. Some numerical experiments about the calibration of the Heston model involving synthetic and real data are presented.

Dynamic Hedging Based on Markov Regime-Switching Dynamic Correlation Multivariate Stochastic Volatility Model

It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-DC-MSV model were used to calculate the time-varying hedging ratios and compare the hedging performance. The Markov chain Monte Carlo( MCMC) method was used to estimate the parameters. The results showed that,there were obviously two economic states in Chinese financial market. Two models all did well in hedging,but the performance of MRS-DCMSV model was better. It could reduce risk by nearly 90%. Thus,in the hedging period,changing states is a factor that cannot be neglected.

Market Risk Evaluation on Single Futures Contract:SV-CVaR Model and Its Application on Cu00 Data

A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC）simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk（GARCH-VaR）model.Empirical study suggests that this model is better than GARCH-VaR model in this field.

Study of Volatility Stochastic Processes in the Context of Solvency Forecasting for Sri Lankan Life Insurers

The main business of Life Insurers is Long Term contractual obligations with a typical lifetime of 20 - 40 years. Therefore, the Solvency metric is defined by the adequacy of capital to service the cash flow requirements arising from the said obligations. The main component inducing volatility in Capital is market sensitive Assets, such as Bonds and Equity. Bond and Equity prices in Sri Lanka are highly sensitive to macro-economic elements such as investor sentiment, political stability, policy environment, economic growth, fiscal stimulus, utility environment and in the case of Equity, societal sentiment on certain companies and industries. Therefore, if an entity is to accurately forecast the impact on solvency through asset valuation, the impact of macro-economic variables on asset pricing must be modelled mathematically. This paper explores mathematical, actuarial and statistical concepts such as Brownian motion, Markov Processes, Derivation and Integration as well as Probability theorems such as the Probability Density Function in determining the optimum mathematical model which depicts the accurate relationship between macro-economic variables and asset pricing.

Stock Exchanges Comparison between China's Mainland and H.K. Based on the SVL Model

In this paper, we consider the leverage effect on the CSI 300 Index yield and Hong Kong Hang Seng Index yield. It is modeled by the SV model with leverage. In this model, we compare the mainland and the Hong Kong stock market with stock market long-term effect, the degree on fluctuation reply and leverage effect so on. The analysis results show that the leverage stochastic volatility model can well fitting rate of return on the CSI300 index and the Hang Seng index in Hong Kong;The Shanghai and Shenzhen stock market volatility and leverage effect obviously stronger than the Hong Kong stock market.

基于跳聚集现象随机波动率短期利率模型的影响研究

构建了具有自我激励机制跳的随机波动率短期利率模型,应用Hawkes过程描述自我激励机制的跳,从而刻画了跳的聚集现象。基于微分算子展开给出精确的矩函数,进一步应用广义矩方法给出模型的参数估计值和统计推断。实证结果揭示了在随机波动模型条件下,引入自我激励机制跳的模型将不会明显地改变了拟合效果,但是在统计意义上接受强度满足Hawkes过程,而且所构建的模型也能很好地刻画跳的聚集现象。最后,使用过滤方法给出随机波动率、跳的幅度、跳的概率和随机跳强度的估计,特别是跳的概率估计值可作为市场压力测试的一个重要指标。

基于SV模型的风速时间序列峰度分析

风速预测是风力发电领域的重要课题之一。风速波动剧烈,预测难度大,深入发掘风速数据波动性特征对于提高风速预测的准确性有积极意义。根据随机波动(SV)模型的峰度分析技术,研究风速时间序列的高峰度特征。基于电力系统领域对峰度的定义,理论推导并证明SV超峰度定理的衍生形式,建立适应风速预测的SV风速模型,模拟风速数据的整体峰度。在分析SV-t族模型的基础上,为选择适当的SV风速预测模型的条件分布类型提供了一种有效方案。实际风电场数据算例分析表明,该方法能有效建立高峰度特征的实际风速模型,对实际风速建模有一定的实用意义。

具有杠杆效应SV模型的贝叶斯分析及其应用

对具有杠杆效应的 SV模型进行了的贝叶斯分析 ,使用基于 Gibbs取样的 BUGS软件对模型的参数进行了估计。用上海和深圳股市的指数收益时间序列对杠杆效应 SV模型进行检验 ,指出沪。

基于VS-MSV模型的金融市场波动溢出分析及实证研究

对于动态投资组合与风险管理来说,测定波动溢出效应是非常重要的。已有的资料显示SV模型比GARCH模型能够更好地刻画金融市场的波动,使用SV模型研究两个金融市场间波动溢出的文献并不多见,而使用多元SV模型研究多个金融市场间波动溢出则属空白。为了同时研究分析金融市场之间的波动溢出,作者在研究多元SV模型的基础上,建立了能分析判断波动溢出的模型——VS—MSV模型,并进行了实证分析。

扩展SV模型及其在深圳股票市场的应用

在金融风险的研究中很重要的一个领域就是量测金融风险的波动性。本文所研究的这种波动性指的是资产收益的方差随时间不断变化 ,这在计量经济学中称之为异方差问题。许多高频的金融时间序列都具有异方差现象。对于波动性的量测 (即异方差的量测 ) ,主要有两种模型方法 :其一是 ARCH模型族的量测方法 ,它包括 Engle的 ARCH模型 (1982 )、Bollerslev的 GARCH模型 (1986 )以及在此基础上提出的其他扩展模型 ;另外一种方法就是SV(Stochastic Volatility)模型。本文提出扩展的 SV模型及其参数估计方法和波动估计方法 ,并进行蒙特卡罗试验 ,最后利用扩展 SV模型对深圳股票市场的波动性进行了实证研究 ,说明扩展 SV模型比标准 SV模型描述金融波动性的优越性。

基于SV模型的深圳股市波动的预测

首次应用基本SV(stochasticvolatility)模型及其扩展ASV(asymmetricstochasticvolatility)模型来预测深圳股市的波动,并根据对称和非对称两类评价准则,对SV类模型的预测效果与常用模型的预测效果做了比较。结果表明,对于深圳股市基本SV模型具有最好的预测效果;ASV模型的表现稍差于基本SV模型,但好于GARCH模型;GARCH模型的预测效果不稳定,随评价准则的不同而有显著差别。

SV模型参数估计的经验特征函数方法

计算基本SV模型和杠杆效应SV模型的联合特征函数,借助经验特征函数方法估计这两个SV模型。使用上海和深圳股票指数收益数据进行实证研究,结果表明经验特征函数方法是一种简单易行的估计SV模型的方法。

ARCH模型与SV模型之间的关系研究

讨论了在金融时间序列中广泛应用的两类波动性模型,即自回归条件异方差(ARCH)模型和随机波动(SV)模型的关系问题.通过随机微分方程研究了GARCH模型和SV模型的相互联系并得到结论:一个离散的EGARCH(1,1)模型在弱GARCH过程的条件下与一个离散的SV模型是一一对应的.在此基础上进一步讨论了EGARCH(1,1)模型和SV模型的单位根问题,结果表明,两类模型的单位根存在对应的关系,即二者的持续性能够通过随机微分方程的形式来传递,这一性质表明了二者之间存在本质的联系.

具有杠杆效应的非线性SV模型及其应用

提出一类非线性SV模型,许多离散时间SV模型都是它的特例。这类模型的优点在于用它可以检验不同函数形式的随机波动,该模型的检验仅基于一个单独参数δ。在非线性SV模型的基础上,进一步把它扩展为具有杠杆效应的非线性SV模型。使用沪、深股市的指数日收益数据进行了实证分析,借助BUGS软件,利用Gibbs取样的MCMC方法对模型进行了贝叶斯参数估计,证明了应拒绝对数正态SV模型,而使用非线性SV模型。

基于贝叶斯SV模型的通货膨胀水平与不确定性关系研究

针对我国通货膨胀水平与不确定性的时变性特征,分别建立了随机波动均值模型和非对称随机波动均值模型,在MCMC稳态模拟的框架下研究了我国通货膨胀水平与不确定性的动态关系。研究结果表明:我国通货膨胀不确定性中具有明显的持续性特征,并且通胀水平中虽然不存在与金融资产价格运动类似的杠杆效应,但是正向冲击增加了经济行为主体对未来不确定性的预期,由此将导致明显的"示范效应"和"追涨效应";特别是风险溢出系数的贝叶斯估计为正,反映了通胀不确定性对通胀水平的正向影响作用,说明我国目前的货币政策框架中含有相机抉择的成分因素。

基于SV-Copula模型的相关性分析

本文结合SV模型和Copula技术,建立两变量金融时间序列的Copula-SV模型,并以上海综合指数和深圳成分指数为例利用建立的模型进行分析,根据采用不同的Archimedean Copula函数,通过使用K-S检验说明用Clayton Copula研究上证综指和深圳成指的下尾相关性,用Gumbel Copula研究上证综指和深圳成指的上尾相关性是合适的,从而风险管理者就可以根据尾部相关性,定量的研究两个市场的相关性及预测市场的变化。

基于SV模型时变参数的中国股市政策效应研究

政策效应是一种广泛的现象,但在我国尤为突出。文章通过对SV模型参数集的时变特性研究表明,时变的参数能够有效地反映我国股市的动态过程。SV模型的这一特性,能够检验我国股票市场的政策效应现象,并解释金融时间序列数据的“杠杆效应”。实证得出我国股市政策效应正逐渐减弱,杠杆效应逐渐显著的结论,表明我国股市逐渐走向成熟和完善,与我国股市发展的历史和现状相符。

厚尾SV模型的贝叶斯分析及其应用研究

SV模型在实际应用中大多都假定以潜在波动为条件的收益的分布是正态的,本文分析并比较了正态SV模型和具有厚尾分布,特别是t分布的SV模型。为了估计SV模型的参数,我们使用了BUGS软件,该软件借助Gibbs取样(一种MCMC方法)方法对模型进行贝叶斯分析。用上海和深圳的股票指数数据对两种SV模型进行了检验,认为厚尾SV模型可以更好地刻画收益的尖峰厚尾以及波动高的持续性。最后提出了使用BUGS软件对SV扩展模型进行估计的展望。