Accurate closed‐form approximation for pricing Asian and basket options

By approximating the distribution of the sum of correlated lognormals with some log‐extended‐skew‐normal distribution, we present closed‐form approximation formulae for pricing both Asian and basket options. Numerical comparison shows that our formulae provide both computational simplicity and accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

关于期权定价的一点注记

在介绍由随机波动源和异常波动源共同作用的波动源模型的基础上,对该模型进行了期权定价的研究,结果表明该模型只能比传统的对数正态分布模型更精确地描述现实市场中的股价波动规律而不能改善期权价值。     

Analytic bounds and approximations for annuities and Asian options

Even in case of the Brownian motion as most natural rate of return model it appears too difficult to obtain analytic expressions for most risk measures of constant continuous annuities. In literature the so-called comonotonic approximations have been proposed but these still require the evaluation of integrals. In this paper we show that these integrals can sometimes be computed, and we obtain explicit approximations for some popular risk measures for annuities.Next, we show how these results can be used to obtain fully analytic expressions for lower and upper bounds for the price of a continuously sampled European-style Asian option with fixed exercise price. These analytic lower bound prices are as sharp as those from [Rogers, L.C.G., Shi, Z., 1995. The value of an Asian option. J. Appl. Probab. 32, 1077–1088], if not sharper, but in contrast do not require any longer the evaluation of a two-dimensional or a one-dimensional integral.     

跳-扩散价格过程下有交易成本的期权定价研究

Black-Scholes模型成功解决了完全市场下的欧式期权定价问题.研究在不完全市场下的一类期权定价问题,即在假设交易过程有交易成本且标的资产价格服从跳-扩散过程下,推导出了在该模型下期权价格所满足的微分方程.     

“政策市”下的中国企业实物投资机理研究

在我国市场经济发展的过程中,某些具有不确定性和投资不可逆性的产业市场容易出现投资过热问题.这时政府往往频繁出台一系列宏观调控政策以规范市场,但效果不佳.为此从研究该类市场的投资主体—企业的投资决策机理的角度出发,通过引入实物期权的理论,给出了在完善和平稳发展的市场条件下及在政府政策冲击的市场条件下,价格分别服从单纯的几何布朗运动及混合的几何布朗运动/泊松跳跃过程的企业最佳投资规则及其临界价格,并进行了比较,结果表明:“政策市”下的企业投资更富“冒进性”.     

An inverse problem of determining the implied volatility in option pricing

In the Black-Scholes world there is the important quantity of volatility which cannot be observed directly but has a major impact on the option value. In practice, traders usually work with what is known as implied volatility which is implied by option prices observed in the market. In this paper, we use an optimal control framework to discuss an inverse problem of determining the implied volatility when the average option premium, namely the average value of option premium corresponding with a fixed strike price and all possible maturities from the current time to a chosen future time, is known. The issue is converted into a terminal control problem by Green function method. The existence and uniqueness of the minimum of the control functional are addressed by the optimal control method, and the necessary condition which must be satisfied by the minimum is also given. The results obtained in the paper may be useful for those who engage in risk management or volatility trading.     

基于价格均值回复与随机波动率的信用差价衍生产品定价

为了研究均值回复特征与随机波动率对金融衍生品定价的影响,考虑状态变量的均值回复特征与两种随机波动率过程:平方根过程与O rnste in-U h lenbeck过程,应用解偏微分与特征函数方法,分析衍生品的定价方程,推导出基于均值回复特征与随机波动率的信用差价期权、信用差价上限与下限的定价公式.结果表明,均值回复和随机波动率在衍生品定价中起重要影响.     

二元数字期权定价与copula的关系

首先简要介绍了 copula的一些基本概念和性质 ,然后探讨了一种多元未定权益——二元数字期权的价格与 copula的关系 .结论表明 ,一个二元数字期权的价格恰好是一个 copula函数 ,由此结论进而给出了根据实际数据获得二元数字期权价格的基本思路和步骤 .     

跳-扩散模型下的再装期权定价

本文建立股票价格的跳过程为Poisson过程,跳跃高度服从对数正态分布时股票价格过程的随机微分方程,在风险中性的假设下找到等价鞅测度,利用鞅方法,用较简单的数学推导得到了股票价格服从跳-扩散过程的欧式再装期权定价公式.