Black-Scholes期权定价公式推广

在Black-Scholes期权定价模型的基础上,进一步考虑标的资产受多个跳跃源影响的情况,用含有多维Poisson过程的Ito-Skorohod随机微分方程描述标的资产价格的动态运动,应用等价鞅测度变换方法导出一般形式的欧式期权定价公式,并讨论了利率,波动率不是常数情况下的拓广形式.     

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.     

On the asymptotic free boundary for the American put option problem

In practical work with American put options, it is important to be able to know when to exercise the option, and when not to do so. In computer simulation based on the standard theory of geometric Brownian motion for simulating stock price movements, this problem is fairly easy to handle for options with a short lifespan, by analyzing binomial trees. It is considerably more challenging to make the decision for American put options with long lifespan. In order to provide a satisfactory analysis, we look at the corresponding free boundary problem, and show that the free boundary—which is the curve that separates the two decisions, to exercise or not to—has an asymptotic expansion, where the coefficient of the main term is expressed as an integral in terms of the free boundary. This raises the perspective that one could use numerical simulation to approximate the integral and thus get an effective way to make correct decisions for long life options.     

On convergence of a semi-analytical method for American option pricing

We examine the valuation of American put options by a semi-analytical method, and obtain the prior estimate and the convergence of the approximate solution. Our proofs are based on the embedding theorem in Sobolev space and the theory of functional analysis, in particular, the theory of weak compactness. The results in this paper theoretically confirm empirical observations that these methods are accurate and computationally efficient.     

Black-Scholes期权定价公式的博弈论相关分析

从博弈论理论角度出发分析了B lack-Scho les期权定价公式的内容,把期权价格看作期权交易过程中依赖于股票价格的收益期望值,通过计算这个无限随机过程的密度函数得出B lack-Scho les期权定价公式.     

Multiperiod Portfolio Optimization with Terminal Liability: Bounds for the Convex Case

This paper is concerned with an investor trading in multiple securities over many time periods in order to meet an outstanding liability at some future date. The investor is concerned with maximizing the expected profits from portfolio rebalancing under an initial wealth restriction to meet the future liabilities. We formulate the problem as a discrete-time stochastic optimization model and allow asset prices to have continuous probability distributions on compact domains. For the case of Markovian price uncertainty and convex terminal liability, we develop a simplicial approximation, under which bounds on the problem can be computed efficiently. Computations only require evaluating a dynamic programming recursion, which thus, allows its application to problems with a large number of trading periods. The bounds are tight in that they are exact in certain cases. Numerical results are given to demonstrate the computational efficiency of the procedure.     

跳扩散模型中亚式期权的定价

本文研究一类跳扩散模型中亚式期权的定价问题，得到了关于算术平均亚式期权的一个简单而统一的算法，并用偏微分方程的技巧将其定价问题归结为一个与路径依赖量无关的一维积分-微分方程的求解问题．     

广义Black-Scholes模型期权定价新方法--保险精算方法

利用公平保费原则和价格过程的实际概率测度推广了Mogens Bladt和Tina Hviid Rydberg的结果．在无中间红利和有中间红利两种情况下，把Black-Scholes模型推广到无风险资产(债券或银行存款)具有时间相依的利率和风险资产(股票)也具有时间相依的连续复利预期收益率和波动率的情况，在此情况下获得了欧式期权的精确定价公式以及买权与卖权之间的平价关系．给出了风险资产(股票)具有随机连续复利预期收益率和随机波动率的广义Black-Scholes模型的期权定价的一般方法．利用保险精算方法给出了股票价格遵循广义Ornstein-Uhlenback过程模型的欧式期权的精确定价公式和买权和卖权之间的平价关系．     

Application of the Singularity-Separating Method to American Exotic Option Pricing

This paper is devoted to numerical methods for American barrier and lookback options, which are important examples of American exotic options. Since the singularity-separating method is adopted, accurate numerical results can be obtained very fast.     

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.