二次有限体积法定价美式期权

本文考虑二次有限体积法定价美式期权.构造了隐式欧拉和Crank-Nicolson两种全离散二次有限体积格式,并得到相应的线性互补问题.采用基于超松弛迭代的模方法求解线性互补问题,并与投影超松弛迭代法作数值比较.数值实验结果表明Crank-Nicolson二次有限体积格式的求解效率高于隐式欧拉格式,模方法的求解速度较快,二次有限体积法的求解精度较高.     

Front-fixing FEMs for the pricing of American options based on a PML technique

In this paper, efficient numerical methods are developed for the pricing of American options governed by the Black–Scholes equation. The front-fixing technique is first employed to transform the free boundary of optimal exercise prices to some a priori known temporal line for a one-dimensional parabolic problem via the change of variables. The perfectly matched layer (PML) technique is then applied to the pricing problem for the effective truncation of the semi-infinite domain. Finite element methods using the respective continuous and discontinuous Galerkin discretization are proposed for the resulting truncated PML problems related to the options and Greeks. The free boundary is determined by Newton’s method coupled with the discrete truncated PML problem. Stability and nonnegativeness are established for the approximate solution to the truncated PML problem. Under some weak assumptions on the PML medium parameters, it is also proved that the solution of the truncated PML problem converges to that of the unbounded Black–Scholes equation in the computational domain and decays exponentially in the perfectly matched layer. Numerical experiments are conducted to test the performance of the proposed methods and to compare them with some existing methods.     

An approach to the valuation and decision of ERP investment projects based on real options

The risks and uncertainties inherent in most enterprise resources planning (ERP) investment projects are vast. Decision making in multistage ERP projects investment is also complex, due mainly to the uncertainties involved and the various managerial and/or physical constraints to be enforced. This paper tackles the problem using a real-option analysis framework, and applies multistage stochastic integer programming in formulating an analytical model whose solution will yield optimum or near-optimum investment decisions for ERP projects. Traditionally, such decision problems were tackled using lattice simulation or finite difference methods to compute the value of simple real options. However, these approaches are incapable of dealing with the more complex compound real options, and their use is thus limited to simple real-option analysis. Multistage stochastic integer programming is particularly suitable for sequential decision making under uncertainty, and is used in this paper and to find near-optimal strategies for complex decision problems. Compared with the traditional approaches, multistage stochastic integer programming is a much more powerful tool in evaluating such compound real options. This paper describes the proposed real-option analysis model and uses an example case study to demonstrate the effectiveness of the proposed approach.     

美式看涨篮子期权解析近似定价模型

本文研究规范美式篮子看涨期权的定价问题.通常用来为美式看涨期权定价的格点法与蒙特卡罗模拟法,用于美式篮子看涨期权定价时,会产生"维数灾难".本文首先利用Vorst~([2])、Gentle~([3])以及Merton~([4,5])模型的结果,完成标的资产组合从算术平均向几何平均的转化;其次在Barone～Adesi和Whaley提出的单变量美式期权解析近似定价模型(以下简称BW模型)的基础上~([4]),提出了美式分红篮子看涨期权定价的一种解析近似方法.最后,进行了数值试验,取得了较好的结果.     

Stochastic models for bidding strategies on oligopoly electricity market

In this paper we consider the forward/futures contracts and Asian-type call options for power delivery as important components of the bidding strategies of the players’ profits on the electricity market. We show how these derivatives can affect their profit. We use linear asymmetric supply function equilibrium (SFE) and Cournot models to develop firms’ optimal bidding strategies by including forward/futures contracts and Asian-type options. We extend the methodology proposed by Niu et al. (IEEE Trans Power Syst 20(4):1859–1867, 2005), where only forward contracts for power delivery were considered in the SFE model.     

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??Model of option pricing driven by Brownian motion is the most classical model. However, it can not describe long-term property and invariance in a short period of time of asset price. In this article, option pricing model driven by sub-fractional Brownian motion is studied under time-transform with dividend-paying. Firstly, the model of diffusion B-S model of sub-fractional Brownian motion is build, and get option pricing formula with dividends. Secondly, statistical simulation is used by real data in finance and show that new model can reflect real financial assets.     

销售努力及双市场化期权下的三级供应链协调

本文针对需求随机且受到零售商销售努力影响的情况,研究了由制造商、分销商和零售商组成的三级供应链的协调问题。文章首先用双期权契约对三级供应链进行协调,即在制造商和分销商以及分销商和零售商之间都采用期权契约,发现在零售商独自承担努力成本的情况下仅通过双期权契约无法协调供应链。因此在双期权契约的基础上加入了努力成本共担契约,发现当期权价格满足某种线性关系以及零售商努力成本按特定比例分摊时,联合双期权契约和努力成本共担契约能顺利协调供应链。在此基础上,文章还引入了期权的市场化定价规则,研究了期权采用市场化定价规则对供应链协调产生的影响,研究表明,引入期权市场化定价规则增加了供应链协调需要满足的条件,降低了协调的可能性,且协调状态下的期权价格受到市场因素如利率、价格波动率等的影响。最后,文章给出了期权市场化定价规则下供应链协调的条件以及参数变化对协调的影响。     

信用风险下的变化类型权证期权定价

主要利用公司价值模型将信用风险引入到变化类型权证期权定价中,通过鞅和概率的方法,推导出信用风险下的变化类型权证期权的定价公式,给出了更切合实际的期权定价.     

随机波动率下股价服从O-U过程的期权定价

假设股票价格遵循指数O-U过程,利用随机分析中的鞅方法,得到了具有随机波动率的欧式期权的定价公式,推广了B-S模型.     

VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for pricing the European passport option is established. The pricing equation which is a fully nonlinear equation is derived using the dynamic programming principle. The comparison principle, uniqueness and convexity preserving of the viscosity solutions of related H J13 equation are proved. A relationship between the passport and lookback options is discussed.