混合分数布朗运动下亚式期权定价

运用混合分数布朗运动的Ito公式,将几何平均亚式期权定价化成一个偏微分方程求解问题,通过偏微分方程求解获得了几何平均型亚式看涨期权的定价公式.     

“亚式——阶梯”期权定价模型

本文结合亚式期权和阶梯期权的特点,构造出一种用于经理期权激励机制的新型期权——"亚式——阶梯"期权,建立相应的期权定价模型,运用偏微分方程方法,构造该期权价格所满足的具有恰当边值条件和终值条件的偏微分方程,并得出其精确解。     

双随机跳扩散模型下亚式期权的定价

研究了双随机跳扩散模型下的亚式期权的定价问题.首先引入一个双随机跳扩散过程.然后通过测度变换消除了亚式期权定价中的路经依赖性问题.最后利用鞅定价方法和Ito引理得到了跳扩散模型下的亚式期权价格必须满足的一个积微分方程.通过数值求解该积微分方程就可以得到了亚式期权的价格,供投资者参考.     

彩虹障碍期权的定价问题

采用偏微分方程方法研究了彩虹障碍期权的定价问题,推导出它满足的偏微分方程,通过求解这个偏微分方程得出了八种彩虹障碍期权的定价公式及四个看涨——看跌平价公式.     

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.     

分数布朗运动下几何平均亚式权证的定价

假设股票价格变化过程服从几何分数布朗运动,建立了分数布朗运动下的亚式期权定价模型.利用分数-It-公式,推导出分数布朗运动下亚式期权的价值所满足的含有三个变量偏微分方程.然后,引进适当的组合变量,将其定解问题转化为一个与路径无关的一维微分方程问题.进一步通过随机偏微分方程方法求解出分数布朗运动下亚式期权的定价公式.最后利用权证定价原理对稀释效用做出调整后,得到分数布朗运动下亚式股本权证定价公式.<正>~~     

基于跳扩散过程的欧式交换期权定价

考虑了股票价格服从带时滞泊松跳的跳扩散模型的欧式交换期权定价问题,运用无套利理论推导出期权价值微分方程,利用变换计价单位的方法,得到交换期权的显示定价公式.     

外汇期权的多维跳-扩散模型

本文建立了外汇期权的多维跳-扩散模型,在此模型下将外汇欧式未定权益的定价问题归结为一类倒向随机微分方程的求解问题,证明了这类倒向随机微分方程适应解的存在唯一性问题,并给出了一个关于外汇欧式未定权益的定价公式.     

浮动利率下基于不确定分数阶微分方程的期权定价研究

期权定价是金融数学领域中最复杂的问题之一.随着不确定理论公理化的建立,利用不确定理论进行期权定价的研究逐步展开,而分数阶微分方程的分数阶导数项可以很好地刻画金融市场的记忆特性.本文在机会空间中提出了一种新的不确定市场模型,假设股票价格满足Caputo型的不确定分数阶微分方程,且随机利率满足随机微分方程.基于该模型,利用Mittag-Leffler函数和微分方程的α-轨道我们给出了蝶式期权和欧式价差期权的定价公式及数值例子.     

带跳混合分数布朗运动下利差期权定价

在股票价格遵循带跳混合分数布朗运动过程假设下,得到了利差期权所满足的一般偏微分方程,并依据此偏微分方程获得了利差期权和标准欧式期权定价公式.推广了关于Black-Scholes期权定价的结论.     

Asymptotic approach to the pricing of geometric asian options under the CEV model

This paper studies the pricing of Asian options whose payoffs depend on the average value of an underlying asset during the period to a maturity. Since the Asian option is not so sensitive to the value of underlying asset, the possibility of manipulation is relatively small than the other options such as European vanilla and barrier options. We derive the pricing formula of geometric Asian options under the constant elasticity of variance (CEV) model that is one of local volatility models, and investigate the implication of the CEV model for geometric Asian options.     

An analytic formula for the price of an American-style Asian option of floating strike type

Average pricing is one of the main ingredients in determining the payoff associated with an Asian option. Since its beginnings in 1980 much has been written on the European-style Asian, especially with a fixed strike. In this article, we extend the work of Zhu to this exotic option. We present an analytic formula pricing an American-style Asian option of floating type. We also extend a symmetry result established by Henderson and Wojakowski.     

Optimal system of Lie group invariant solutions for the Asian option PDE

Asian options are useful financial products as they guard against large price manipulations near the termination date of the contract. In addition, they are often cheaper than their vanilla European counterparts. Previous analyses of the Asian option partial differential equation (PDE) have obtained analytical solutions for the fixed strike (arithmetically averaged) Asian option (and then only with certain assumptions on the boundary conditions). Using Lie symmetry analysis we obtain an optimal system of Lie point symmetries and demonstrate that many (usually ad hoc) reductions of the Asian option PDE are contained in this minimal set. We analyse each reduction member and the feasibility of its resulting invariant solution with the boundary conditions. We show that the numerical simulations on a reduced equation are more efficient than on the original specified problem. In addition, we have found new analytical solutions in terms of Fourier transforms for the floating strike Asian option as well as the fixed strike Asian option without the simplification of the domain. Copyright © 2011 John Wiley & Sons, Ltd.     

基于时变t-Copula的次贷危机前后亚洲股市相关结构的比较分析

将时变t-Copula函数与GARCH模型结合起来刻画金融市场间的相关结构并用于亚洲股市作实证研究.结果表明,次贷危机加剧了亚洲股市的波动溢出效应,提示次贷危机是亚洲股市相关结构的一个结构性变点.     

基于加权可能性均值的亚式期权模糊定价

主要探讨不确定环境下用模糊集理论处理亚式期权的定价问题.运用梯形模糊数来表示标的资产价格、无风险利率、红利率和波动率,建立了亚式期权的加权可能性均值模糊定价模型,得到连续几何和算术亚式期权的模糊价格公式.最后通过数值例子表明:亚式期权的加权可能性均值模糊定价模型具有很大的灵活性,更符合现实的不确定情况,具有较强的实用价值.     

Efficient pricing of discrete Asian options

Asian options are popular path-dependent financial derivatives. This paper uses lattices to price fixed-strike European-style Asian options that are discretely monitored. The algorithm proposed can also be applied to floating-strike Asian options as well because fixed-strike and floating-strike Asian options are related through an equation. The discretely monitored version is usually found in practice instead of the continuously monitored version usually encountered in the literature. This paper presents the first provably quadratic-time convergent lattice algorithm for pricing fixed-strike European-style discretely monitored Asian options. It is the most efficient lattice algorithm with convergence guarantees. The algorithm relies on the Lagrange multipliers to choose the number of states for each node of the lattice. Extensive numerical experiments and comparisons with many existing numerical methods confirm the performance claims and the competitiveness of our algorithm. This result places fixed-strike European-style discretely monitored Asian options in the same complexity class as vanilla options.     

Intended Treatments of Arithmetic Average in U.S. and Asian School Mathematics Textbooks

This study examined how selected U.S. and Asian mathematics curricula are designed to facilitate students' understanding of the arithmetic average. There is a consistency regarding the learning goals among these curriculum series, but the focuses are different between the Asian series and the U.S. reform series. The Asian series and the U.S. commercial series focus the arithmetic average more on conceptual and procedural understanding of the concept as a computational algorithm than on understanding the concept as a representative of a data set; however, the two U.S. reform series focus the concept more on the latter. Because of the different focuses, the Asian and the U.S. curriculum series treat the concept differently. In the Asian series, the concept is first introduced in the context of “equal‐sharing” or “per‐unit‐quantity,” and the averaging formula is formally introduced at a very early stage. In the U.S. reform series, the concept is discussed as a measure of central tendency, and after students have some intuitive ideas of the statistical aspect of the concept, the averaging algorithm is briefly introduced.     

Bounds for Asian basket options

In this paper we propose pricing bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework. We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151–168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3–33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55–57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51–90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1–52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity.