模糊环境下美式看跌期权的定价研究

应用模糊集理论将无风险利率和波动率进行模糊化,以梯形模糊数替代精确值,将美式期权的定价模型扩展到美式期权模糊定价模型.得到了模糊风险中性概率表达式,并在此概率测度下推导出多期二叉树模糊定价模型,以及二叉树上各节点以梯形模糊数表示的模糊期权价值,以数值模拟演示了美式看跌期权的模糊定价过程.最后分析了不同风险偏好投资者在不确定环境下的套利决策行为,结果表明风险偏好大的投资者具有较高的置信水平、较小的主观模糊期权价格以及较大的无风险套利区间.     

固定执行价格下回望看涨期权保险精算定价

利用保险精算方法,将期权定价问题转化为纯保费确定问题,根据股票价格过程的实际概率测度推导出了无风险利率为常数时,固定执行价格下回望看涨期权定价公式,验证了当标的资产的期望收益率等于无风险利率时,保险精算定价和风险中性定价的一致性.最后通过实例分析了保险精算价格和风险中性价格的差异,并利用Matlab编程得到了保险精算价格与标的资产期望收益率之间的关系.     

分数布朗运动环境下欧式幂期权的定价

本文主要讨论了标的资产受多个分数布朗运动影响的欧式幂期权定价问题:基于风险中性概率测度,给出了在有红利支付且无风险利率及红利率为非随机函数的情况下的两类欧式幂期权定价公式,并分别求出了涨跌欧式幂期权的平价关系.     

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.     

无套利期权定价模型在一般均衡框架下的一致性研究

期权定价有无套利方法和一般均衡方法两种.本文在一般均衡框架下构造了一个允许连续消费的简单经济模型,并将基于无套利方法的期权定价模型中所假定的标的证券的价格变化动态过程内生化于理性预期均衡中.在常数相对风险厌恶(CRRA)的效用函数的条件下,我们推导出Merton(1973)期权定价公式,从而证明无套利方法与均衡方法的内在一致性,而CRRA这种类型的效用函数是无套利定价模型在一般均衡框架中成立的充分条件.本文进一步将此模型在一个简单经济中扩展到m种证券的情况,也得到相似的结论.     

广义交换期权定价

基于风险中性(等价鞅测度)定价理论和经典的Black-Scholes市场环境,我们给出了更一般情形下的欧式交换期权(ExchangeOption)封闭形式的解析定价公式,进而得出了欧式交换期权的价格公式、Black-Scholes期权定价公式.     

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.     

复合泊松过程和Meixner过程驱动下的期权定价

本文讨论了股票价格对数过程由复合泊松过程、Meixner过程驱动下的欧式看涨期权的定价问题.利用Esscher变换和风险中性Esscher测度得到了两类过程驱动下的期权定价公式,为实践者提供了理论上的参考价格.     

跳扩散模型下一种创新的重置期权定价

首先在风险中性测度下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的随机微分方程,利用期权定价的鞅方法推导得到了欧式重置看涨期权的价格以及一种创新的重置看涨期权的定价公式．最后给出了一个数值计算的例子,说明了创新的重置看涨期权价格要大于或等于传统的重置看涨期权和欧式看涨期权价格,并从理论上进行解释．     

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.     

Imposing no‐arbitrage conditions in implied volatilities using constrained smoothing splines

We apply constrained smoothing B‐splines to the construction of arbitrage‐free implied volatilities and derived measures. The constrained smoothing B‐splines allows the imposition of the constraints of monotonicity and convexity given by the no‐arbitrage conditions in the pricing function. We illustrate the methodology in the construction of implied volatilities and also in the construction of derived measures such as risk‐neutral densities, showing that it can be used as an effective tool for general treatment of option prices. Copyright © 2011 John Wiley & Sons, Ltd.     

The arbitrage pricing theorem with incomplete preferences

This paper proves existence of equilibrium and the arbitrage pricing theorem for an asset exchange economy, where individuals' preferences may be incomplete or intransitive. This extends existing results to more general preferences. We also prove the arbitrage pricing theorem for a theory of choice under uncertainty by Bewley [Bewley, T. F. (2002), Knightian decision theory: part I, Decisions in Economics and Finance 25, 79–110.]. These preferences model Knightian uncertainty by preferences which may be incomplete but satisfy independence.     

Valuation and hedging of contingent claims in the HJM model with deterministic volatilities

The aim of the present paper is mostly expository, namely, we intend to provide a concise presentation of arbitrage pricing and hedging of European contingent claims within the Heath, Jarrow and Morton frame-work introduced in Heath et al. (1992) under deterministic volatilities. Such a special case of the HJM model, frequently referred to as the Gaussian HJM model, was studied among others in Amin and Jarrow (1992), Jamshidian (1993), Brace and Musiela (1994a, 1994b). Here, we focus mainly on the partial differential equations approach to the valuation and hedging of derivative securities in the HJM framework. For the sake of completeness, the risk neutral methodology (more specifically, the forward measure technique) is also exposed.     

Valuing risky income streams in incomplete markets

A model for pricing and hedging in incomplete markets is proposed. This model is derived from expected utility theory, and a connection with the traditional no‐arbitrage framework is noted. It is shown that the CGM model can be implemented to value risky assets in incomplete markets.     

基于个体公平原则的寿险产品定价模型

在无套利框架的基础上,讨论基于个体公平原则下的寿险产品定价问题,即运用倒向随机微分方程理论,将投保人和保险人置于同一系统中进行考虑:首先,根据双方的随机投资决策目标分别建立无套利寿险定价模型和动态资产份额定价模型,得出两个特殊线性倒向随机微分方程的显式解;然后,建立基于个体公平原则的寿险定价模型,从投保人和保险人双方的角度对寿险产品进行公平定价,得出了从供需双方考虑的投资回报定价公式;最后,利用所建立的模型进行案例分析,计算出基于个体公平原则的保费及保险公司的投资策略.该寿险产品定价模型不仅考虑了保险人的意愿,还同时考虑了投保人的实际情况,因此,按此定价理念开发出的保险产品,不仅可以提高产品研发的成功率,而且使得研发出的新产品更能在竞争激烈的保险市场中站稳脚步.     

SDP Relaxation of Arbitrage Pricing Bounds Based on?Option Prices and Moments

This paper develops a semidefinite programming approach to computing bounds on the range of allowable absence of arbitrage prices for a European call option when option prices at other strikes and expirations are available and when moment related information on the underlying is known. The moment related information is incorporated in the problem through the fictitious prices of polynomial valued securities. The optimization then comes from relaxing a risk neutral pricing optimization problem in terms of moments of measures from a decomposition of the risk neutral pricing measure. We demonstrate this optimization formulation with computations using moment data from the standard Black-Scholes option pricing model and Merton’s jump diffusion model.     

On arbitrage‐free pricing of weather derivatives based on fractional Brownian motion

We derive an arbitrage‐free pricing dynamics for claims on temperature, where the temperature follows a fractional Ornstein–Uhlenbeck process. Using a fractional white noise calculus, one can express the dynamics as a special type of conditional expectation not coinciding with the classical one. Using a Fourier transformation technique, explicit expressions are derived for claims of European and average type, and it is shown that these pricing formulas are solutions of certain Black and Scholes partial differential equations. Our results partly confirm a conjecture made by Brody, Syroka and Zervos.