Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation

In this paper, we present a power penalty function approach to the linear complementarity problem arising from pricing American options. The problem is first reformulated as a variational inequality problem; the resulting variational inequality problem is then transformed into a nonlinear parabolic partial differential equation (PDE) by adding a power penalty term. It is shown that the solution to the penalized equation converges to that of the variational inequality problem with an arbitrary order. This arbitrary-order convergence rate allows us to achieve the required accuracy of the solution with a small penalty parameter. A numerical scheme for solving the penalized nonlinear PDE is also proposed. Numerical results are given to illustrate the theoretical findings and to show the effectiveness and usefulness of the method. This work was partially supported by a research grant from the University of Western Australia and the Research Grant Council of Hong Kong, Grants PolyU BQ475 and PolyU BQ493.     

Stochastic Optimization Algorithms for Pricing American Put Options Under Regime-Switching Models

This work provides a Markov-modulated stochastic approximation based approach for pricing American put options under a regime-switching geometric Brownian motion market model. The solutions of pricing American options may be characterized by certain threshold values. Here, a class of Markov-modulated stochastic approximation (SA) algorithms is developed to determine the optimal threshold levels. For option pricing in a finite horizon, a SA procedure is carried out for a fixed time T. As T varies, the optimal threshold values obtained via SA trace out a curve, called the threshold frontier. Numerical experiments are reported to demonstrate the effectiveness of the approach. Our approach provides us with a viable computational tool and has advantage in terms of the reduced computational complexity compared with the variational or quasivariational inequality methods for optimal stopping.Communicated by C. T. LeondesThis research was supported in part by the National Science Foundation under Grant DMS-0304928, and in part by the National Natural Science Foundation of China under Grant 60574069.     

基于跳跃波动率的未定权益定价模型

讨论了具有随机波动率的未定权益定价问题,建立了两状态波动率的股票价格行为模型,在股票价格过程是连续过程、跳风险不可定价的假设下,推导出未定权益的定价公式.     

管理人因素对风险项目期权估值的影响

本基于对风险项目及其“孪生证券”风险和收益特性的分析，认为真正的“孪生证券”实际中很难存在，进而提出利用“近似孪生证券”与无风险证券构造资产组合来复制实物期权收益特征，利用无风险套利分析确定项目实物期权价值的方法。但考虑到管理人因素造成的实物期权内部风险特征的不可复制性，本进一步提出利用“确定性等值”将内部风险价值V1具体化，从而实现对“近似孪生证券”方法进行修正。     

Pensions modelling

Valuable insights into the problem of how to fund defined benefitpension schemes can be obtained by analysis using the standardBlack–Scholes/Merton option pricing model, consideringthe pension fund finances jointly with those of the sponsoringcompany. The nature of the fund assets and liabilities is completelydifferent, and this lies behind current controversies aboutthe appropriate discount rate, valuation, financial accountingand preferential status for pension fund claimants in insolvency.     

基于期望损失厌恶的供应链期权契约协调研究

以一个损失厌恶销售商与一个损失中性供应商组成的两级供应链为背景,利用期望损失厌恶理论对销售商在期权契约下的最优采购策略进行了研究,并证明了期望损失厌恶理论能有效克服传统基于前景理论的研究中因参考点外生且固定假设带来的弊端。在此基础上,进一步给出了供销双方在期权契约下实现协调共赢的条件,分析了销售商损失厌恶程度,期权契约价格等参数对供应链协调共赢机制的影响。结果显示:销售商的损失厌恶偏好并不会改变权利金分配整体供应链利润的作用,但会增强销售商分享收益的能力,改变供销双方利润或效用水平对权利金,产品销售价格和生产成本的敏感程度,且较高的损失厌恶偏好还会阻碍供销双方协调共赢目标的达成。     

基于不确定指数O-U过程带有浮动利率模型的亚式期权定价

不确定金融是不确定理论在现代金融领域的一种应用,在解决金融问题中发挥着越来越重要的作用。而利率是一个重要的经济指标,经常受到一些不确定因素的影响,在研究期权定价时,有必要考虑浮动利率。本文提出了一种新的不确定指数Ornstein-Uhlenbeck过程模型,假设利率服从不确定均值回复过程,研究了期权定价问题,运用α-轨道方法,分别推导了亚式看涨期权和看跌期权定价公式。最后,设计了计算期权价格的数值算法,并给出数值算例。     

Repetitive impact exposure and characterization of stress-whitening of an American football helmet outer shell material

Mechanical stress exerted upon impact-modified polycarbonate (PC) and poly(ethylene terephthalate) (PET) blends has been reported to generate microscopic voids via rubber-toughener (RT) particle cavitation which can macroscopically manifest to visibly whiten the material. Previous work has revealed a whitening phenomenon in collegiate American football helmet outer shells after a single season and in helmet-grade plaques following linear impact testing. The purpose of this research was to quantify the effects of repetitive linear drop exposures on the (i) impact performance; (ii) physical and thermal properties; and (iii) surface and tensile mechanical properties of a stress-whitened American football helmet outer shell material. Statistically significant changes in plaque impact performance corresponded to substantial stress-whitening that penetrated up to 40–45% into the plaque thickness and elicited shifts in surface and tensile mechanical properties. Nanoscale microscopy revealed elongation of the PC/PET matrix and delamination at the RT-matrix interface. Thermal property analysis suggested the concomitant occurrence of RT cavitation and strain-induced PET crystallization. Overall, the research identified a battery of diagnostic tools to characterize material property changes of stress-whitening in rubber-toughened helmet outer shell materials.     

Infinite-Dimensional Black-Scholes Equation with Hereditary Structure

This paper considers the option pricing problem for contingent claims of the European type in a (B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary structures. The Black-Scholes equation for the classical option pricing problem is generalized to an infinite-dimensional equation to include the effects of time delay in the evolution of the financial market as well as a very general payoff function. A computational algorithm for the solution is also obtained via a double sequence of polynomials of a certain bounded linear functional on a Banach space and the time variable.     

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.