分数跳-扩散模型下的互换期权定价

用保险精算法,在标的资产价格服从分数跳-扩散过程,且风险利率、波动率和期望收益率为时间的非随机函数的情况下,给出了一类多资产期权——欧式交换期权的定价公式．该公式是标准跳扩散模型下的欧式期权及欧式交换期权定价公式的推广．     

服从分数跳-扩散过程的复合期权定价

用保险精算法,在标的资产价格服从分数跳-扩散过程,且风险利率、波动率和期望收益率为时间的非随机函数的情况下,给出了欧式复合期权的定价公式.结果推广了Gukhal以及Li等关于传统跳-扩散模型下的欧式复合期权的定价公式.     

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.     

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.     

标的资产服从一类混合过程的欧式未定权益定价

文中假设标的资产价格服从受分数布朗运动和泊松过程共同驱动的一类混合模型，并给出了基于这一模型的欧式未定权益定价的基本公式，以及欧式看涨、看跌期权和上限型欧式期权的定价公式。     

新的广义欧式期权定价模型及其性质

本文提出一种新型期权,称之为随机到期时刻的广义欧式期权.我们证明了新的期权是欧式期权和美式期权的推广.在市场为无摩擦且完备无套利的连续市场时,我们构建了两个理论模型,导出了广义欧式期权的鞅方法定价公式,在适当的条件下,证明了两个模型的结果是一致的.当随机到期时刻与标的资产价值不独立时,给出了几种情形下的广义欧式期权定价公式.针对利率、资产价格、到期时刻等随机因素,定义了两个具体市场模型,导出了在Vasicek短期利率模型下,标的资产价值服从一般It过程等的广义欧式期权定价公式.     

跳-扩散碳排放市场模型下的碳配额价格与期权定价

研究碳排放市场中碳配额价格与期权定价的相关问题.通过引入基于跳-扩散过程建模碳排放量过程与相应的违约事件.利用风险中性定价理论,刻画碳配额期货价格公式.最后,研究以期货合约为标的资产的欧式期权定价问题.     

服从跳-扩散过程的几种资产的最大值的期权定价

本文利用了关于 Black- scholes方程的直观解释 ,以及采用了 Margrabe在推导交换期权定价公式时的手段 ,研究了 Merton跳 -扩散过程期权定价的一个特殊情况 ,并得到服从跳 -扩散过程的几种资产最大值的欧式看涨期权定价公式     

利用Laplace变换研究基于一个双跳模型的脆弱期权定价问题

本文针对欧式脆弱期权首先给出一个定价模型.在该模型中,期权对手方的企业资产价值服从双指数跳跃-扩散过程并且与期权标的资产的价格相关.双跳过程能够刻画对手方资产价值的突然提高或下降,从而对脆弱期权的定价提供更深层次的经济学解释.基于我们推导出的关于双跳过程的首次到达时间与相关Brownian运动的联合Laplace变换的显性表达式,并结合提前违约条件,本文通过二维Laplace变换给出关于欧式脆弱期权价格的的一个简单公式.采用数值Laplace逆变换方法,可实现利用该公式对欧式脆弱期权的定价.数值计算的结果表明,我们得到的定价公式是正确和有效的.     

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.     

Local risk minimization for vulnerable European contingent claims on nontradable assets under regime switching models

This article focuses on an optimal hedging problem of the vulnerable European contingent claims. The underlying asset of the vulnerable European contingent claims is assumed to be nontradable. The interest rate, the appreciation rate and the volatility of risky assets are modulated by a finite-state continuous-time Markov chain. By using the local risk minimization method, we obtain an explicit closed-form solution for the optimal hedging strategies of the vulnerable European contingent claims. Further, we consider a problem of hedging for a vulnerable European call option. Optimal hedging strategies are obtained. Finally, a numerical example for the optimal hedging strategies of the vulnerable European call option in a two-regime case is provided to illustrate the sensitivities of the hedging strategies.     

Contingent claim pricing using probability distortion operators: methods from insurance risk pricing and their relationship to financial theory

This paper considers the pricing of contingent claims using an approach developed and used in insurance pricing. The approach is of interest and significance because of the increased integration of insurance and financial markets and also because insurance-related risks are trading in financial markets as a result of securitization and new contracts on futures exchanges. This approach uses probability distortion functions as the dual of the utility functions used in financial theory. The pricing formula is the same as the Black-Scholes formula for contingent claims when the underlying asset price is log-normal. The paper compares the probability distortion function approach with that based on financial theory. The theory underlying the approaches is set out and limitations on the use of the insurance-based approach are illustrated. The probability distortion approach is extended to the pricing of contingent claims for more general assumptions than those used for Black-Scholes option pricing.     

标的资产价格服从跳-扩散过程的具有随机寿命的未定权益定价

本文在假设被终止或取消的风险与重大信息导致的标的资产价格跳跃的风险为非系统风险的情况下,应用无套利资本资产定价,推导出了标的的资产的价格服从跳-扩散过程具有随机寿命的未定权益满足的偏微分方程,然后应用Feynman-kac公式获得了未定权益的定价公式.     

标的资产服从混合过程的二种新型期权的定价

假设标的资产价格服从受多维分数布朗运动和泊松过程共同驱动的一类混合模型，通过这一模型的欧式未定权益的一般定价公式，求出了2种新型期权的定价公式．     

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.     

On valuing and hedging European options when volatility is estimated directly

We quantify the effects on contingent claim valuation of using an estimator for the unknown volatility σ of a geometric Brownian motion (GBM) process. The theme of the paper is to show what difficulties can arise when failing to account for estimation risk. Our narrative uses a direct estimator of volatility based on the sample standard deviation of increments of the underlying Brownian motion. After replacing the direct estimator into the GBM, we derive the resulting distribution function of the approximated GBM for any time point. This allows us to present post-estimation distributions and valuation formulae for an assortment of European contingent claims that are in accord with many of the basic properties of the underlying risk-neutral process, and yet better reflect the additional uncertainties and risks that exist in the Black-Scholes-Merton paradigm.     

有交易费的未定权益无套利定价区间

本文首先给出了有交易费资产模型下套利机会的定义,利用辅助鞅和资产折算函数等方法,讨论了该模型下未定权益无套利定价问题,得到的结果是有交易费的未定权益无套利定价区间.     

A Model with Interacting Assets Driven by Poisson Processes

Abstract

An extension with noise given by Poisson processes of a model of financial market with several assets that are interacting, i.e., influencing each other (even in the absence of noise) is given. We present explicit formulae for the stock price process as well as for the prices of European multi-asset contingent claims based on a residual risk minimization approach. We also provide an explicit hedging formula.     

Incomplete financial markets and contingent claim pricing in a dual expected utility theory framework

This paper investigates the price for contingent claims in a dual expected utility theory framework, the dual price, considering arbitrage-free financial markets. A pricing formula is obtained for contingent claims written on n underlying assets following a general diffusion process. The formula holds in both complete and incomplete markets as well as in constrained markets. An application is also considered assuming a geometric Brownian motion for the underlying assets and the Wang transform as the distortion function.     

Infinite-Dimensional Black-Scholes Equation with Hereditary Structure

This paper considers the option pricing problem for contingent claims of the European type in a (B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary structures. The Black-Scholes equation for the classical option pricing problem is generalized to an infinite-dimensional equation to include the effects of time delay in the evolution of the financial market as well as a very general payoff function. A computational algorithm for the solution is also obtained via a double sequence of polynomials of a certain bounded linear functional on a Banach space and the time variable.