基于模糊集合论的实物期权定价方法

实物期权的定价在风险投资决策过程中具有重要意义.传统的实物期权定价方法忽略标的资产价值和投资成本的模糊性,从而可能导致错误的投资决策.本文主要研究了具有模糊标的的资产价值和投资成本情形时的实物期权定价模型.文中将这些模糊因素分别视为模糊数和模糊变量,然后运用模糊集合论,结合B-S期权定价理论,对实物期权进行定价,得到了基于模糊集合论的实物期权定价模型.     

双指数跳扩散模型下奇异期权的定价

在双指数跳扩散模型下,利用已建立的欧式期权定价公式讨论了三种常见的奇异期权——简单任选期权、上限型买权和滞后付款期权的期权定价,得到了这些期权定价的解析公式.这是对双指数跳扩散模型期权定价的补充.     

分数布朗运动环境下上证50ETF期权定价的实证研究

合理的期权价格是期权交易的前提.基于上证50ETF期权的最新数据,运用经典的BlackScholes定价模型、蒙特卡洛模拟期权定价方法和分数布朗运动定价模型对上证50ETF期权价格进行实证研究.结果表明:分数布朗运动定价模型相比较经典的Black-Scholes定价模型和蒙特卡洛方法在接近期权的实际成交价格时均方误差和均方比例误差更小,能够较为准确地、有效地模拟出上证50ETF期权的价格,从而对投资者的期权交易行为具有一定的指导作用,也为国内其他品种的期权定价研究提供参考.     

几何平均下的水平重置期权定价

针对重置期权的风险对冲△跳现象,研究了一种亚式特征的水平重置期权的定价问题.首先在BS模型下用股票的几何平均价格作为水平重置期权执行价格重置与否的统计量,然后运用测度变换和鞅定价方法得到了风险中性定价公式,最后利用风险中性定价公式得出风险对冲△值的显示解,改进了水平重置期权的部分已有结果.     

股票价格遵循几何分式Brown运动的期权定价

讨论了股票价格过程遵循几何分式B row n运动的欧式期权定价.由于该过程存在套利机会使得传统的期权定价方法(如资本资产定价模型(CAPM),套利定价模型(APT),动态均衡定价理论(DEPT))不可能对该期权定价.利用保险精算定价法,在对市场无其它任何假设条件下,获得了欧式期权的定价公式.并讨论了在有效期内股票支付已知红利和红利率的推广公式.     

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.     

体制转换市场中股价服从带门限均值回复过程的期权定价

体制转换和门限特征是资产定价过程中的两个重要特征.本文在股价服从带门限均值回复过程而折现率含有状态切换的情况下对欧式看涨期权进行定价.首先给出股价服从无门限均值回复过程的欧式期权定价;然后,结合风险中性定价原理、超合流函数、Laplace变换等方法,给出股价服从一般情形的Volterra积分形式的欧式期权定价公式.为了进一步说明所得结论的适用性,本文最后给出了欧式看涨期权定价的差分格式解.     

“降价补差”承诺期权定价分析

综合应用Δ对冲技巧以及It引理,在风险中性意义的前提下建立了房产开发商"降价补差"承诺期权的偏微分方程定价模型.根据"降价补差"承诺能否在到期前任何一天履约,分别建立了欧式承诺期权定价模型和美式承诺期权定价模型.对于欧式承诺期权,得到了期权价格的解析公式;对于美式承诺期权,采用基于自适应的有限差分法对上述定价模型进行数值计算,得到了相应的期权价格.并以欧式承诺期权为例,分析了期权价格对参数的依赖关系.最后对两个具体的"降价补差"承诺期权案例进行了期权价格计算.     

倒向随机微分方程与巴黎期权的非线性定价

巴黎期权是一种复杂的奇异期权. 本文基于倒向随机微分方程, 定义了巴黎期权的非线性价格过程, 分析其性质, 并且给出巴黎期权非线性定价的偏微分方程表达式. 在金融市场收益率不确定的情形以及存贷利率不同的情形下分别对连续巴黎期权进行定价和具体的数值分析, 结论显示巴黎期权的非线性定价机制更具合理性.     

结构转换条件下债券期权定价研究

从利率动态变化、结构转换和期权定价三个方面进行分析,对结构转换下的债券和债券期权进行定价,考虑了结构转换对利率衍生物定价的影响,利用Ito引理获得债券定价的偏微分方程,并得到债券期权定价的特征函数与递归等式.结构转换下债券期权定价的灵敏度分析表明期权价值与初始状态概率、结构的持续性和结构波动率有关.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

<正>~~     

Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.