基于非对称漂移双gamma跳-扩散过程的创新幂型期权定价模型

针对假设股价的对数收益率布朗运动在期权定价时产生的无法解释股价对数收益率的尖峰厚尾和序列相关性的缺陷,采用了Zhang提出的非对称漂移双gamma跳-扩散过程来描述资产(股价)的对数收益率运动形态(该过程是kou提出的双指数跳-扩散过程的推广),并利用Esscher风险中性变换,研究了幂型期权的定价公式.还设计了两种创新的幂型期权,在非对称漂移双gamma跳-扩散过程下给出了相应的定价公式.     

再装股票期权的Esscher变换定价

近年来,公司为了吸引和激励股票的执行者而引入了一系列的非传统期权.本文将讨论其中的一种:再装期权,运用Esscher变换给出了再装期权(只装一次)的闭式解,并提供了数值计算的例子,为实践者提供了理论上的参考价格.     

On the consistency of credibility premiums regarding Esscher principle

In this paper, we investigate the problems of convergence of experience-based ratemakings regarding the Esscher principle. In addition to the Bayes and the classical credibility premiums, we suggest a new credibility formula for the Esscher premium. Then we show the convergence of the Bayes and the newly defined credibility premiums towards the individual premium and point out that the classical credibility premium does not generally converge to the individual premium by presenting a sufficient and necessary condition under which the classical credibility Esscher premium converges to the individual premium. A simulation study is carried out to illustrate the theoretical conclusions.     

隐含风险中性分布在巨灾超额损失再保险定价中的应用

通过与标的风险相关的期权市场估计出隐含变换系数,然后以Esscher变换为工具,将巨灾损失统计分布风险中性化,从而对以该非交易风险为标的的巨灾超额损失再保险进行定价.同时,从期权定价的角度,结合Weibull极值分布和超额损失再保险的特点,给出了巨灾超额损失再保险定价的闭型表达式.     

Large deviations: An introduction to 2007 Abel prize

2007 Abel prize has been awarded to S R S Varadhan for creating a unified theory of large deviations. We attempt to give a flavour of this branch of probability theory, highlighting the role of Varadhan.     

Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models

The structure of various Gerber-Shiu functions in Sparre Andersen models allowing for possible dependence between claim sizes and interclaim times is examined. The penalty function is assumed to depend on some or all of the surplus immediately prior to ruin, the deficit at ruin, the minimum surplus before ruin, and the surplus immediately after the second last claim before ruin. Defective joint and marginal distributions involving these quantities are derived. Many of the properties in the Sparre Andersen model without dependence are seen to hold in the present model as well. A discussion of Lundberg’s fundamental equation and the generalized adjustment coefficient is given, and the connection to a defective renewal equation is considered. The usual Sparre Andersen model without dependence is also discussed, and in particular the case with exponential claim sizes is considered.     

Optimal Upper and Lower Bounds for the Upper Tails of Compound Poisson Processes

A compound Poisson process is of the form where Z, Z ₁, Z ₂, are arbitrary i.i.d. random variables and N is an independent Poisson random variable with parameter . This paper identifies the degree of precision that can be achieved when using exponential bounds together with a single truncation to approximate . The truncation level introduced depends only on and Z and not on the overall exceedance level a.     

欧式向下敲出看涨幂期权的Esscher变换定价

首先根据障碍期权的不同类型,对普通欧式向下敲出看涨幂期权、部分时间开始、部分时间结束、一般部分时间欧式向下敲出看涨幂期权给出定义.通过E sscher变换分别给出定价公式.另外,对两资产欧式向下敲出幂期权也给出了定价公式,为实践者提供了理论上的参考价格.最后,阐述了此方法的优点.     

Pricing currency options under two-factor Markov-modulated stochastic volatility models

This article investigates the valuation of currency options when the dynamic of the spot Foreign Exchange (FX) rate is governed by a two-factor Markov-modulated stochastic volatility model, with the first stochastic volatility component driven by a lognormal diffusion process and the second independent stochastic volatility component driven by a continuous-time finite-state Markov chain model. The states of the Markov chain can be interpreted as the states of an economy. We employ the regime-switching Esscher transform to determine a martingale pricing measure for valuing currency options under the incomplete market setting. We consider the valuation of the European-style and American-style currency options. In the case of American options, we provide a decomposition result for the American option price into the sum of its European counterpart and the early exercise premium. Numerical results are included.