实物期权定价与风险对冲方法研究

实物期权定价面临的一个主要问题是其基本资产不可交易问题，在这种情况下，通常的解决办法是在市场中寻找一个与该基本资产最为相关的可交易资产，利用可交易资产的价格信息来对特定实物期权进行定价和风险对冲．利用随机动态规划法，本文得到基本资产不可交易时实物期权的最优风险对冲策略，在一定条件下还可以得到近似定价．     

具有跳跃特征的资产价格过程的期权定价模型研究

资产价格具有跳跃特征时，衍生于该资产的期权就不能利用传统的Black-Schoels公式进行定价。本主要研究基于Poisson过程和固定跳跃Merton模型的期权定价与风险对冲问题，利用e-套利定价法，得到期权的风险对冲策略所满足的偏微分方程和近似期权定价。     

基于模糊Black-Scholes模型的螺纹钢期权定价

能源金融和大宗商品的衍生品交易已逐渐成为金融领域的前沿热点问题。钢铁类金融衍生品定价和能源金融风险研究,对能源资产证券化和金融的发展有着重要意义。本文在现有的期权定价模型下,结合影响螺纹钢实物期权价格的因素,优化经典的Black-Scholes实物期权定价模型,得到螺纹钢模糊B-S实物期权定价模型,并结合VaR方法,研究螺纹钢实物期权的定价机制,量化钢铁类金融风险,从而合理的控制风险传播。     

Black-Scholes期权定价的风险(英文)

Black-Scholes期权定价的推导假定对冲是连续的以达到无风险. 但事实上, 股市收市后将不再有交易, 所以投资者不能连续的调整其投资组合, 故期权定价的风险是存在的. 本文讨论了这种不连续对冲带来的期权定价的风险, 并以美国股市的几种指标股为例, 给出其比率. 比率多在5%以上, 有的可以达到38%, 可见传统期权定价的风险不容小觑.     

基于混合规避策略的期权定价及其数值分析

考虑现实市场中红利的存在、波动率等参数随时间变化以及交易时间不连续产生的对冲风险不可忽略,研究离散时间、支付红利条件下基于混合规避策略的期权定价模型.由平均自融资-极小方差规避策略得到相应欧式看涨期权定价方程,并且分别使用偏微分方法和概率论方法得到统一的闭形解.数值分析表明,与经典的期权定价模型相比,新模型中的期权价格更接近对冲成本.     

有交易成本的回望期权定价研究

基于标的资产价格的几何布朗运动假设，Black—Seholes模型运用连续交易保值策略成功解决了完全市场下的欧式期权定价问题。然而，在实际的金融市场中，存在着数量可观的交易成本。本文主要研究了在不完全市场下有交易成本的回望期权的定价问题，并且利用Ito公式，得到了在该模型下期权价格所满足的微分方程。     

量子金融的意义

金融市场中的风险资产的演化过程遵从某种统计规律。这种统计规律通常是采用经典概率理论来加以阐述的。最近, 作者提出了从量子力学的角度来探讨金融问题的设想［1］,［2］,［3］。其中, 作者不仅从量子力学的角度用Maxwell Boltzmann统计重新推导了著名的Cox Ross Rubinstein期权定价公式，而且还用量子力学中的Bose Einstein统计(不可分辨粒子模型)得到了一个新的期权定价公式。这表明在理论上存在着一套关于金融市场的和谐的“量子理论”——量子金融。本文从对冲的角度来阐述这种潜在理论的金融意义和可能的实际内涵。作者给出了对冲定价的量子方案，详细讨论了单期金融市场的量子对冲问题。最后，作者解释了为什么（某些）金融市场在物理上要遵循量子规律，而不是经典统计规律。     

次分数Vasicek随机利率模型下的欧式期权定价

本文对经典的B-S模型的假设条件进行放松,在假定利率为随机波动情况下对欧式期权定价进行讨论.作为利率的载体,本文首先对零息票债券进行定价,得出利率风险的市场价格的含义.其次,利用投资组合的?对冲原理构造无风险资产,求得欧式期权在次分数布朗运动驱动的随机利率模型下所满足的偏微分方程.最后,经过变量替换转化为经典的热传导方程,获得了欧式期权定价公式.     

不完全市场定价与对冲方法

在经典的完全市场中,根据无套利原理,能够为期权提供唯一的价格同时可以完全对冲风险.在这样的理论假设下,没有理由管理不好相关衍生产品的风险.但是在现实的金融市场中,有关衍生产品风险管理失败的案例时有发生,特别是最近的金融危机使人们认识到,现实的金融市场是非常复杂而不完全的.在这样的市场中,风险不能完全对冲,定价与对冲问题也变得不易处理,至今还没有一致接受的理论.为了促进更深入的研究,综述了各种在不完全市场中的定价与对冲方法,侧重于基本思想和基本模型.同时也探讨了各种方法的优缺点,以及它们之间的联系,突出了优化理论和方法在解决这类问题中的关键作用,同时也分析了一些需要进一步研究的问题及方法上的空白点.     

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.     

A note on convergence of an approximate hedging portfolio with liquidity risk

When the underlying asset price depends on activities of traders, hedging errors include costs due to the illiquidity of the underlying asset and the size of this cost can be substantial. Cetin et al. (2004), Liquidity risk and arbitrage pricing theory, Finance and Stochastics, 8(3), 311-341, proposed a hedging strategy that approximates the classical Black–Scholes hedging strategy and produces zero liquidity costs. Here, we compute the rate of convergence of the final value of this hedging portfolio to the option payoff in case of a European call option; i.e. we see how fast its hedging error converges to zero. The hedging strategy studied here is meaningful due to its simple liquidity cost structure and its smoothness relative to the classical Black–Scholes delta.     

Large investor trading impacts on volatility

We begin with this paper a series devoted to a tentative model for the influence of hedging on the dynamics of an asset. We study here the case of a “large” investor and solve two problems in the context of such a model namely the question of the fair value (or liquidative value) of a “large” position and the question of pricing or hedging an option. In order to do so, we use a utility maximization approach and some new results in stochastic control theory.     

A possible way of estimating options with stable distributed underlying asset prices

Option pricing theory is considered when the underlying asset price satisfies a stochastic differential equation which is driven by random motions generated by stable distributions. The properties of the stable distributions are discussed and their connection with the theory of fractional Brownian motion is noted. This approach attempts to generalize the classical Black–Scholes formulation, to allow for the presence of fat tails in the distribution of log prices which leads to a diffusion equation involving fractional Brownian motion. The resulting option pricing via a hedging strategy approach is independently derived by constructing a backward Kolmogorov equation for a simple trinomial model where the probabilities are assumed to satisfy a particular fractional Taylor series due to Dzherbashyan and Nersesyan. To effect this development, some knowledge of fractional integration and differentiation is required so this is briefly reviewed. Consideration is also given to a different hedging strategy approach leading to a fractional Black–Scholes equation involving the market price of risk. Modification to the model is also considered such as the impact of transaction costs. A simple example of American options is also considered.     

G框架下的欧式期权定价公式

用G几何布朗运动描述标的资产的价格变动,得到了欧式看涨期权定价的动态公式,并给出了动态复制策略的显示表达.     

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.     

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.     

Hedging with a correlated asset: Solution of a nonlinear pricing PDE

Hedging a contingent claim with an asset which is not perfectly correlated with the underlying asset results in unhedgeable residual risk. Even if the residual risk is considered diversifiable, the option writer is faced with the problem of uncertainty in the estimation of the drift rates of the underlying and the hedging instrument. If the residual risk is not considered diversifiable, then this risk can be priced using an actuarial standard deviation principle in infinitesimal time. In both cases, these models result in the same nonlinear partial differential equation (PDE). A fully implicit, monotone discretization method is developed for solution of this pricing PDE. This method is shown to converge to the viscosity solution. Certain grid conditions are required to guarantee monotonicity. An algorithm is derived which, given an initial grid, inserts a finite number of nodes in the grid to ensure that the monotonicity condition is satisfied. At each timestep, the nonlinear discretized algebraic equations are solved using an iterative algorithm, which is shown to be globally convergent. Monte Carlo hedging examples are given to illustrate the profit and loss distribution at the expiry of the option.     

对数正态随机波动率期权局部风险最小定价与风险对冲

随机波动率模型是著名的Black-Scholes模型的推广,该模型描述的市场是不完备的,相应期权的定价与保值和投资者的风险态度有关．本文假设标的资产波动率为对数正态过程,根据局部风险最小准则,运用梯度算子方法,得到了欧式看涨期权的局部风险最小定价及套期保值策略的显式解．