Nonlinear reserving and multiple contract modifications in life insurance

Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications.     

Pricing of American lookback spread options

We find the closed form formula for the price of the perpetual American lookback spread option, whose payoff is the difference of the running maximum and minimum prices of a single asset. We solve an optimal stopping problem related to both maximum and minimum. We show that the spread option is equivalent to some fixed strike options on some domains, find the exact form of the optimal stopping region, and obtain the solution of the resulting partial differential equations. The value function is not differentiable. However, we prove the verification theorem due to the monotonicity of the maximum and minimum processes.     

看涨期权契约与看跌期权契约对比分析研究

在面临相同随机市场需求的情况下,本文对期权契约中的看涨期权与看跌期权契约进行了对比分析,以期为决策者在实际采购活动中选择不同类型的期权契约时提供决策依据。通过模型建立与求解分析,本文得出了销售商接受期权契约时,契约参数需要满足的条件及相应的订购策略;并进一步得出了两种期权契约下,供应链达到协调状态时的具体条件,分析了此时契约参数对供销双方利润的影响,继而给出了两种期权契约的适用范围以及供销双方的契约选择偏好。在此基础上,本文还给出了不同期权契约下,供销双方各自利润均不低于其自身保留利润时契约参数的取值范围,并证明了两种期权契约均可有效提高销售商的利润水平。最后,本文通过算例对上述结论进行了验证。     

非仿射随机波动率的欧式障碍期权定价

研究非仿射随机波动率模型的欧式障碍期权定价问题时,首先介绍了非仿射随机波动率模型,其次利用投资组合和It^o引理,得到了该模型下扩展的Black-Schole偏微分方程.由于这个方程没有显示解,因此采用对偶蒙特卡罗模拟法计算欧式障碍期权的价格.最后,通过数值实例验证了算法的可行性和准确性.     

离散分红下障碍期权的间接级数展开定价方法

人们投资股票市场的最大动力,除了从股票本身的升值中获利,还包括收益分红.提出了带有离散分红的障碍期权的一种新型的近似方法,以向上敲出看涨障碍期权为例,固定分红的次数,通过泰勒级数展开得到关于关键变量的仿射函数,给出了一个只带有一维积分的定价公式,提高了计算速度.该方法还可以用于回望期权等其它衍生品的定价,对在市场上进行期权交易有一定指导意义.     

基于减排成本共担期权契约的供应链协调

考虑消费者具有低碳产品偏好的情况,研究需求随机且受减排影响的期权契约,建立了由单个制造商和单个零售商组成的供应链模型。该模型中制造商处主导地位,零售商处追随地位,制造商首先提出期权契约,零售商购买期权。求解发现,由于传统双重边际化效应的存在,只有当零售价格等于期权执行价格时,才能达到供应链的协调,这时零售商利润为负,不满足参与约束。为此,从降低期权执行价格的角度,对期权契约进行补充,增加了成本共担条款。研究表明,减排成本共担的期权契约能够实现供应链的协调。最后利用算例验证了结论,计算了制造商和零售商利润及零售商分担的减排成本比例随期权价格和期权执行价格的变化情况,并对减排难度系数的敏感性做了分析。     

跳扩散模型下美式期权的对称性

利用分析方法得到了跳扩散模型下美式看涨、看跌期权的价格和最佳实施边界间的对称性公式．美式看涨和看跌期权价格问的对称关系通常是利用概率理论得到,这里给出了这些结果在跳扩散模型下的另一种证明．此外,由本文所得结果和偏微分方程理论,可以得到跳扩散模型下美式看涨期权的最佳实施边界以及永久美式期权的若干性质．     

An analytic formula for the price of an American-style Asian option of floating strike type

Average pricing is one of the main ingredients in determining the payoff associated with an Asian option. Since its beginnings in 1980 much has been written on the European-style Asian, especially with a fixed strike. In this article, we extend the work of Zhu to this exotic option. We present an analytic formula pricing an American-style Asian option of floating type. We also extend a symmetry result established by Henderson and Wojakowski.     

What types of investors generate the two-phase phenomenon?

We examine the two-phase phenomenon described by Plerou, Gopikrishnan, and Stanley (2003)  [1] in the KOSPI 200 options market, one of the most liquid options markets in the world. By analysing a unique intraday dataset that contains information about investor type for each trade and quote, we find that the two-phase phenomenon is generated primarily by domestic individual investors, who are generally considered to be uninformed and noisy traders. In contrast, our empirical results indicate that trades by foreign institutions, who are generally considered informed and sophisticated investors, do not exhibit two-phase behaviour.     

倒向随机微分方程与巴黎期权的非线性定价

巴黎期权是一种复杂的奇异期权. 本文基于倒向随机微分方程, 定义了巴黎期权的非线性价格过程, 分析其性质, 并且给出巴黎期权非线性定价的偏微分方程表达式. 在金融市场收益率不确定的情形以及存贷利率不同的情形下分别对连续巴黎期权进行定价和具体的数值分析, 结论显示巴黎期权的非线性定价机制更具合理性.