基于Monte-Carlo模拟的最小亏损套期保值策略研究

把终期的期望亏损定义为风险,研究了标的资产价格服从跳扩散结构时的自筹资最小亏损风险套期保值.首先通过Monte-Carlo模拟生成标的资产若干条价格路径并用所有路径上的终期亏损平均值作为优化目标期望值的估计,然后引入基函数作为套期保值头寸的近似逼近,最后通过数值方法得到最优套期保值策略.最后通过实例分析表明:1)套期保值头寸调整的频率相对较高时,可以更好地应对市场出现的价格波动,从而降低可能面临的损失风险,达到较好的保值效果;2)欧式看涨期权的交割价格与对冲头寸呈反向变化,交割价格越高,可适当调低持有的对冲头寸,反之则反,这样,即对冲风险又节约成本.     

具有变系数和红利的多维Black-Scholes模型

本文提出具有变系数和红利的多维Ｂｌａｃｈ－Ｓｃｈｏｌｅｓ模型,利用倒向随机微分方程和鞅方法,得到欧式未定权益的一般定价公式及套期保值策略,在具体金融市场,给出欧式期权的定价公式和套期保值策略,以及美式看涨期权价格的界。     

跳扩散结构下风险最小化动态套期保值策略研究

在标的资产价格服从跳-扩散过程情况下,研究了风险最小化动态套期保值问题.首先用MCMC方法估计得到模型参数值,克服了传统的直接用样本均值和样本方差进行参数估计值的不足,与市场实际更吻合;然后在风险最小目标下,采用逐步倒推法得到随时间改变的动态最优套期保值策略解析表达式,由此可以及时做出策略调整,达到既对冲风险又节约成本的目的.文章最后通过对比分析不同期限、不同策略调整频率情况下的费用投入,得出期限和策略调整频率之间的关系,为套期保值者根据不同情况做出合理的套保策略提供了参考,另外,为满足金融机构进行压力测试或投资者为适应费率调整的需要,也分析说明了不同交易费率和策略之间的关系.     

跳跃扩散型汇率过程的外汇期权定价

在完全外汇市场环境下 ,讨论了外汇汇率过程受 Brown运动和 Poisson过程共同驱动时外汇欧式未定权益的定价问题 ,并在常系数情形下获得了欧式外汇期权 Black- Scholes定价公式及其套期保值策略 ,最后给出了一种多汇率过程的线性组合式未定权益的定价     

分数布朗运动环境中欧式未定权益的定价

本文在标的资产价格服从几何分数布朗运动模型假设下，求出了在标的资产有红利支付时的欧式未定权益的一般定价公式及几种奇异期权的定价公式。     

有摩擦金融市场中的美式未定权益定价

本文研究了高借款利率下投资策略受限制的美式未定权益的定价问题. 文章通过引入反映上述金融市场摩擦的辅助的无摩擦金融市场类给出了美式未定权益的上下套期保值价格$h_{\text{up}}(K)$和$h_{\text{low}}(K)$的定价公式. 进一步, 在基于金融市场无套利的准则下证明了$[h_{\text{low}}(K),h_{\text{up}}(K)]$是美式未定权益的无套利价格区间. 最后在投资策略受到某些具体限制的情形下, 以美式看涨期权为例, 给出了上下套期保值价格的显式表达式或估计式.     

标的资产服从一类混合过程的欧式未定权益定价

文中假设标的资产价格服从受分数布朗运动和泊松过程共同驱动的一类混合模型，并给出了基于这一模型的欧式未定权益定价的基本公式，以及欧式看涨、看跌期权和上限型欧式期权的定价公式。     

标的资产服从混合过程的二种新型期权的定价

假设标的资产价格服从受多维分数布朗运动和泊松过程共同驱动的一类混合模型，通过这一模型的欧式未定权益的一般定价公式，求出了2种新型期权的定价公式．     

幂效用函数的无差别定价和套期保值

研究了多维扩散模型幂效用函数的无差别定价和套期保值.通过动态规划方法得到了未定权益的无差别定价和套期保值策略.并证明了无差别定价与风险厌恶指数无关的.     

标的资产价格服从跳-扩散过程的具有随机寿命的未定权益定价

本文在假设被终止或取消的风险与重大信息导致的标的资产价格跳跃的风险为非系统风险的情况下,应用无套利资本资产定价,推导出了标的的资产的价格服从跳-扩散过程具有随机寿命的未定权益满足的偏微分方程,然后应用Feynman-kac公式获得了未定权益的定价公式.     

Quadratic hedging for sequential claims with random weights in discrete time

We study a quadratic hedging problem for a sequence of contingent claims with random weights in discrete time. We obtain the optimal hedging strategy explicitly in a recursive representation, without imposing the non-degeneracy (ND) condition on the model and square integrability on hedging strategies. We relate the general results to hedging under random horizon and fair pricing in the quadratic sense. We illustrate the significance of our results in an example in which the ND condition fails.     

Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences

By applying the principle of equivalent forward preferences, this paper revisits the pricing and hedging problems for equity-linked life insurance contracts. The equity-linked contingent claim depends on, not only the future lifetime of the policyholder, but also the performance of the reference portfolio in the financial market for the segregated account of the policyholder. For both zero volatility and non-zero volatility forward utility preferences, prices and hedging strategies of the contract are represented by solutions of random horizon backward stochastic differential equations. Numerical illustration is provided for the zero volatility case. The derived prices and hedging strategies are also compared with classical results in the literature.     

NATURAL RESOURCE ECONOMICS UNDER UNCERTAINTY: EFFECT OF FUTURES MARKETS

The effects of hedging and time-dependent price and geological uncertainty on the behavior of a firm exploiting a nonrenewable natural resource are derived. Contrasts in behavior with and without hedging and uncertainty are identified and discussed. Much of the analysis centers on the firm's implicit value of its in situ reserves, marginal user cost. The main result is that time-dependent uncertainty lowers the implicit value of reserves. Hedging ameliorates this effect somewhat. Under some conditions even with risk reducing hedging, the firm tilts its extraction and development paths toward the present and may also shorten its decision-making time horizon.     

Mean-Variance Hedging on Uncertain Time Horizon in a Market with a Jump

In this work, we study the problem of mean-variance hedging with a random horizon T∧τ, where T is a deterministic constant and τ is a jump time of the underlying asset price process. We first formulate this problem as a stochastic control problem and relate it to a system of BSDEs with a jump. We then provide a verification theorem which gives the optimal strategy for the mean-variance hedging using the solution of the previous system of BSDEs. Finally, we prove that this system of BSDEs admits a solution via a decomposition approach coming from filtration enlargement theory.     

动态非短视资产负债管理

用均值-回复过程刻画股票价格变化,本文研究了股票收益可预测金融市场中的连续时间资产负债管理问题。运用动态规划方法,求得了最优资产负债管理策略的闭合解。结果表明,最优策略是风险溢价的线性函数,随着投资期限的缩短,股票上的投资金额不断降低。数值分析表明,投资期限、股票风险溢价和债务对于最优资产配置策略和股票风险溢价不确定性跨期对冲需求都存在显著影响。     

Valuing finite-lived Russian options

This paper deals with the valuation of the Russian option with finite time horizon in the framework of the Black–Scholes–Merton model. On the basis of the PDE approach to a parabolic free boundary problem, we derive Laplace transforms of the option value, the early exercise boundary and some hedging parameters. Using Abelian theorems of Laplace transforms, we characterize the early exercise boundary at a time to close to expiration as well as the well-known perpetual case in a unified way. Furthermore, we obtain a symmetric relation in the perpetual early exercise boundary. Combining the Gaver–Stehfest inversion method and the Newton method, we develop a fast algorithm for computing both the option value and the early exercise boundary in the finite time horizon.     

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.     

Local risk minimization for vulnerable European contingent claims on nontradable assets under regime switching models

This article focuses on an optimal hedging problem of the vulnerable European contingent claims. The underlying asset of the vulnerable European contingent claims is assumed to be nontradable. The interest rate, the appreciation rate and the volatility of risky assets are modulated by a finite-state continuous-time Markov chain. By using the local risk minimization method, we obtain an explicit closed-form solution for the optimal hedging strategies of the vulnerable European contingent claims. Further, we consider a problem of hedging for a vulnerable European call option. Optimal hedging strategies are obtained. Finally, a numerical example for the optimal hedging strategies of the vulnerable European call option in a two-regime case is provided to illustrate the sensitivities of the hedging strategies.     

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.