内部信息下的平方套期保值策略

建立了内部信息市场模型,提出并解决了内部信息投资者的平方最优套期保值问题.首先利用初始滤波扩张方法给出了内部信息市场中风险资产的价格动态.其次利用Ito公式和Galtchouk-Kunita-Watanabe分解给出了最优策略的显式表示.     

全时段最优套期保值模型及实证研究

针对传统套期保值模型只考虑套期保值资产在套期保值期末的风险及未能充分利用样本数据所提供的信息的问题,本文提出了一类同时考虑套期保值期内不同期限风险的全时段最优套期保值比率计算模型.全时段套期保值模型通过最小化套期保值资产在套期保值期内不同期限的风险将投资者面临的风险在整个套期保值期内稳定保持在一个较低的水平,并更充分的利用了资产历史价格样本数据所提供的信息.本文基于沪深300指数及其仿真股指期货的历史价格数据,对传统形式的三种套期保值模型与本文提出的三种全时段套期保值模型的套期保值效果进行了实证分析和比较,并使用GARCH模型比较分析了这些模型套期保值的动态效果,结果表明三种全时段模型的套期保值效果都要优于相应的传统模型,能有效地缓解提前终止套期保值时投资者所面临的风险.     

全时段最优套期保值模型及实证研

针对传统套期保值模型只考虑套期保值资产在套期保值期末的风险及未能充分利用样本数据所提供的信息的问题,本文提出了一类同时考虑套期保值期内不同期限风险的全时段最优套期保值比率计算模型.全时段套期保值模型通过最小化套期保值资产在套期保值期内不同期限的风险将投资者面临的风险在整个套期保值期内稳定保持在一个较低的水平,并更充分的利用了资产历史价格样本数据所提供的信息.本文基于沪深300指数及其仿真股指期货的历史价格数据,对传统形式的三种套期保值模型与本文提出的三种全时段套期保值模型的套期保值效果进行了实证分析和比较,并使用GARCH模型比较分析了这些模型套期保值的动态效果,结果表明三种全时段模型的套期保值效果都要优于相应的传统模型,能有效地缓解提前终止套期保值时投资者所面临的风险.     

不可交易资产的平方套期保值问题

提出并解决了不可交易资产的套期保值问题.基于金融实际构建了不可交易资产套期保值模型,在风险资产价格服从跳扩散模型的假设下提出了三个平方套期保值问题.借助于一个辅助过程和Hilbert空间投影定理,利用市场可观测量以后向形式给出了平方套期保值标准下的最优策略.最后通过Monte Carlo方法验证了套期保值策略的有效性.     

风险最小化套期保值比例估计:基于RV-Copula模型

随着中国第一只股指期货—沪深300股指期货合约的推出,基于沪深300的期货现货套期保值交易受到广泛关注。风险最小化套期保值比例估计成为影响套期保值交易有效性的关键问题。本文提出了基于已实现波动率和Copula(RV-Copula)相结合的风险最小套期保值比例估计方法,并基于沪深300指数期货和现货数据进行了实证分析。实证结果表明,相对于线性相关系数,本文提出的RV-Copula模型能够更准确地度量沪深300指数期货和现货价格的相关性,从而给出更合理的风险最小套期保值比例估计,提高套期保值交易有效性。本研究是对风险最小套期保值比例估计研究的有益补充,特别是对高频数据背景下的套期保值实践具有重要指导意义。     

基于整体风险最小的多阶段期货套期保值研究

对多阶段套期保值建立模型,综合考虑整体风险,以最终现货与期货的收益的方差建立目标函数.以多阶段整体风险最小为目标函数,考虑资金限制,建立套期保值模型来解决多阶段套期保值的套期保值比率问题.以资金限制为约束,避免了套期保值者因资金短缺而强制平仓造成的套保失败.利用差分算法和罚函数法进行求解.实证结果表明,多阶段的风险比逐个单阶段求得的风险明显的小,且整体套保的单位风险收益比单阶段的大很多,说明多阶段比单阶段能较好的实现套期保值.     

考虑结算风险的套期保值研究

期货市场的风险转移功能主要通过套期保值策略来实现,期货市场套期保值的关键问题是套期保值比率的确定。现有套期保值研究侧重于规避价格风险,忽略了期货市场另一个重要的风险因素-结算风险。本文通过建立考虑结算风险的期货套期保值决策模型,有效地平衡了套期保值过程中的价格风险与结算风险。具体特色一是将套保者的结算风险厌恶态度直接反映到套期比的计算中,体现了结算风险对套期保值决策的影响;二是在一定条件下,本模型的套期比趋近于最小方差套期比;三是利用ARMA时间序列方法预测期货与现货的价格走势,有效地反映了期货价格一阶平稳和季节性变化规律,使估计的套期比更加精确可靠。     

内部信息者的最小亏损风险策略

在一定的假设条件下,利用扩大信息流方法解决了跳扩散环境下内部信息者的最小亏损风险策略问题.首先构建了内部信息者最小亏损风险策略模型,证明了内部信息市场的完备性.然后利用风险资产价格的Markov性和鞅表示定理得到了线性损失函数下的最小亏损风险最优策略和相应的价值函数.     

期货套期保值的最小二阶矩方法

利用期货市场套期保值策略，企业可以避免或减少现货价值波动的风险。但是人们常常使用传统的最小方差法来求出套期保值率及其相应的套期保值风险。在本文我取小方差法存在的缺陷，提出了套期保值的最小二阶矩方法。导出新的套期保值率及其相应的套期保值总风险，空头套期保值风险和多头套期保值风险。为判断当前价格适合进行空头套期保值还是适合多头套期保值提供理论依据。     

基于风险约束的套期保值模型及沪深300股指实证研究

提出利用风险价值VaR建立套期保值资产组合的风险约束.以套期保值资产组合收益最大为目标,以控制套期保值资产组合风险为约束,建立了基于风险约束的套期保值模型.该模型在有效控制风险的基础上,可以大幅提高套期保值资产组合的收益.对沪深300股指现货和期货的数据进行了实证分析,对比了现有研究的最小二乘((OLS)、向量自回归(VAR)、向量误差修正(VEC)三种模型以及本文建立的基于风险约束的期货套期保值模型.样本内检验结果表明,本模型比现有研究模型的收益有大幅提高,平均增加81.6%.同时并没有失去对风险的控制,与现有研究模型只有5.32%的差别.对于样本外检验,模型在控制风险和提高收益两个方面都要优于现有研究模型.模型比现有研究模型平均可提高收益21.4%,平均降低风险3.61%.     

一般支付过程的局部风险最小对冲策略

本文主要研究对冲（套期保值）者的债务由一般的支付流描述时的局部风险最小对冲策略决定问题。我们在风险资产的价格过程在原概率测度下为半鞅的假设下，证明了局部风险最小对冲策略的存在性和唯一性。我们的结果包含了以前的局部风险最小对冲策略。在鞅的情形中，我们的局部风险最小对冲策略简化为Moller[5]的风险最小对冲策略。     

随机支付型未定权益的风险最小套期保值

讨论了具有随机支付型未定权益的风险最小套期问题.假定市场中存在两类具有不同市场信息的投资者,对于一个预先给定的随机支付流未定权益,利用Galtchouk-Kunita-Watanabe分解和L2空间投影定理证明了风险最小策略的存在性和唯一性,并给出了风险最小策略的构造方法.     

Hedging of defaultable claims in a structural model using a locally risk-minimizing approach

In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Föllmer–Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Lévy process and the claims pay a predetermined payout at maturity, contingent on no prior default. More precisely, in this particular framework, the locally risk-minimizing approach is carried out when the underlying process has jumps, the derivative is linked to a default event, and the probability measure is not necessarily risk-neutral.     

A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market

In [Riesner, M., 2006. Hedging life insurance contracts in a Lévy process financial market. Insurance Math. Econom. 38, 599–608] the (locally) risk-minimizing hedging strategy for unit-linked life insurance contracts is determined in an incomplete financial market driven by a Lévy process. The considered risky asset is not a martingale under the original measure and therefore, a change of measure to the minimal martingale measure is performed.The goal of this paper is to show that the risk-minimizing hedging strategy under the new martingale measure which is found in the paper cited above is not the locally risk-minimizing strategy under the original measure. Finally, the real locally risk-minimizing strategy is derived and a relationship between the number of risky assets held in the proposed portfolio cited in the above-mentioned paper and the one proposed here is given.     

Loss analysis of a life insurance company applying discrete-time risk-minimizing hedging strategies

The present paper investigates the net loss of a life insurance company issuing equity-linked pure endowments in the case of periodic premiums. Due to the untradability of the insurance risk which affects both the in- and outflow side of the company, the issued insurance claims cannot be hedged perfectly. Furthermore, we consider an additional source of incompleteness caused by trading restrictions, because in reality the hedging of the contingent claims is more likely to occur at discrete times. Based on Møller [Møller, T., 1998. Risk-minimizing hedging strategies for unit-linked life insurance contracts. Astin Bull. 28, 17–47], we particularly examine the situation, where the company applies a time-discretized risk-minimizing hedging strategy. Through an illustrative example, we observe numerically that only a relatively small reduction in ruin probabilities is achieved with the use of the discretized originally risk-minimizing strategy because of the accumulated extra duplication errors caused by discretizing. However, the simulated results are highly improved if the hedging model instead of the hedging strategy is discretized. For this purpose, Møller’s [Møller, T., 2001. Hedging equity-linked life insurance contracts. North Amer. Actuarial J. 5 (2), 79–95] discrete-time (binomial) risk-minimizing strategy is adopted.     

Discrete-time local risk minimization of payment processes and applications to equity-linked life-insurance contracts

We develop a theory of local risk minimization for payment processes in discrete time, and apply this theory to the pricing and hedging of equity-linked life-insurance contracts. Thus, we extend the work of Møller (2001a) in several directions: from risk minimization (which is done under a martingale measure) to local risk minimization (which is done under an arbitrary measure), from single claims to payment processes, from complete financial markets to possibly incomplete financial markets, from a single risky asset to several risky assets, and from finite state spaces to general state spaces.Moreover, we show that, when tradable financial assets are independent of mortality, a locally risk-minimizing hedging strategy for most claims in the combined financial and mortality market (such as those arising from equity-indexed annuities) may be expressed as the product of two simpler locally risk-minimizing hedging strategies: one for a purely financial claim, the other for a traditional (i.e. non-equity-linked) life-insurance claim.Finally, we also show, under general assumptions, that the minimal measure for the combined market is the product of the minimal measure for the financial market and the physical measure for the mortality.     

Risk minimizing hedging for a partially observed high frequency data model

Risk-minimizing hedging strategies for contingent claims are studied in a general model for intraday stock price movements in the case of partial information. The dynamics of the risky asset price is described throught a marked point process Y, whose local characteristics depend on some unobservable hidden state variable X. In the model presented the processes Y and X may have common jump times, which means that the trading activity may affect the law of X and could be also related to the presence of catastrophic events. The hedger is restricted to observing past asset prices. Thus, we are in presence not only of an incomplete market situation but also of partial information. Considering the case where the price of the risky asset is modeled directly under a martingale measure, the computation of the risk-minimizing hedging strategy under this partial information is obtained by using a projection result (M. Schweizer, Risk minimizing hedging strategies under restricted information, Mathematical Finance 4 (1994) 327–342). This approach leads to a filtering problem with marked point process observations whose solution, obtained via the Kushner-Stratonovich equation, allows us to provide a complete solution to the heding problem.     

Risk-minimization for life insurance liabilities with basis risk

In this paper we study the hedging of typical life insurance payment processes in a general setting by means of the well-known risk-minimization approach. We find the optimal risk-minimizing strategy in a financial market where we allow for investments in a hedging instrument based on a longevity index, representing the systematic mortality risk. Thereby we take into account and model the basis risk that arises due to the fact that the insurance company cannot perfectly hedge its exposure by investing in a hedging instrument that is based on the longevity index, not on the insurance portfolio itself. We also provide a detailed example within the context of unit-linked life insurance products where the dependency between the index and the insurance portfolio is described by means of an affine mean-reverting diffusion process with stochastic drift.     

Locally risk-minimizing hedging strategies for unit-linked life insurance contracts under a regime switching L��vy model

This paper extends the model and analysis in that of Vandaele and Vanmaele [Insurance: Mathematics and Economics, 2008, 42: 1128–1137]. We assume that parameters of the Lévy process which models the dynamic of risky asset in the financial market depend on a finite state Markov chain. The state of the Markov chain can be interpreted as the state of the economy. Under the regime switching Lévy model, we obtain the locally risk-minimizing hedging strategies for some unit-linked life insurance products, including both the pure endowment policy and the term insurance contract.