导　　师： 王晓天

学科专业： 070103

授予学位： 硕士

作　　者： ;

机构地区： 华南理工大学

摘　　要： 随着全球金融市场的蓬勃发展，为满足市场参与者的特殊要求，各种新型期权诸如障碍期权、回望期权和亚式期权等随之诞生。新型期权品种很多，它们的交易量及交易额都很大，内容形式也比较复杂，现在很多金融机构仍在不断创新推出新的新型期权。所以如何给这些新型期权定价是当前金融工程的热点和难点之一。本文主要研究的是障碍期权的定价问题。我们知道经典的Black-Scholes模型（简称B-S模型）假定标的资产价格收益率服从几何Brown运动，然而大量的实证研究表明：在实际市场中，标的资产价格分布不仅呈现高峰厚尾现象，而且还会受到一些突发事件的冲击产生跳跃。因此本文运用t-分布代替正态分布，来探讨对数t-分布下带跳的障碍期权的定价。 本文首先介绍了研究背景、选题意义和研究现状。接着简单介绍了与本文相关的行为金融知识，并回顾了经典Black-Scholes模型下连续及带跳情形的障碍期权定价。其次，研究了对数t-分布下欧式期权及一般连续情形下障碍期权的定价问题。最后是本文的主要研究成果：结合行为金融知识，运用条件delta规避策略得到了对数t-分布下带跳的障碍期权定价公式的解析解；用最小均方误差规避策略得到了不完全信息下障碍期权的市场价格，我们发现障碍期权的市场价格具有均值回归的特性，这与行为金融观点一致；我们还提出了一种新的估计波动率的方法——运用在险值VAR估计波动率参数：即在给定投资者风险置信水平下，使得定价误差最小化；另外，我们用数值方法估计出了对数t-分布模型下我们所得的相应的欧式期权的隐含波动率，并将之与Black-Scholes模型下的隐含波动率进行了比较，发现t-分布模型下的隐含波动率曲线更平缓。 With the vigorous development of the global financial markets, in order to satisfy thespecial requirements of the investors, a lot of exotic options have be born, such as Barrieroptions, Lookback options, Asian options and so on. These exotic options are more complexand profitable than vanilla options, and theirs trading numbers and transaction amounts arevery large, many financial institutions continue to innovate new exotic options. So how topricing these options has become a key topic in modern financial engineering. In this paperwe mainly study the pricing problem of barrier options. We know that the classicalBlack-Scholes model assumes that the underlying asset price obeys geometric Brown motion,however, a large number of empirical studies have shown that: in the actual market, thedistribution with a peak occurred fat tail phenomenon, and on the impact of some unexpectedevents the price generated jumps. So our article is using Student’s t-distribution instead of thenormal distribution, to pricing barrier option under a log Student’s t-distribution with jumps. In this paper, we first review the research on option pricing systematically, thenintroduce the behavior of financial knowledge briefly. Followed by the introduction of theclassical Black-Scholes model, we introduce the pricing of barrier option under the situationof continuous and discontinuous. Secondly, we introduce the pricing of European option andbarrier option under a log Student’s t-distribution. The last part is the main results of thispaper: Combinating with behavioral finance knowledge,we obtain the analytical solution ofthe barrier option pricing formula under a log Student’s t-distribution with jumps byconditional delta avoid strategy; We use the minimal mean-square-error avoid strategy to getthe market price of the barrier option under incomplete information., and we discover that theoption prices are mean reversion, which is in accord with the point of behavioral finance; Wealso propose a procedure to estimate the volatility parameterσ—using value at risk VAR toestimate volatility parameters; In addition, we compare the implied volatility between B-Smodel and Student’s t-distribution model, and find the implied volatility curve underStudent’s t-distribution model is more smooth.

关 键 词： 障碍期权定价 分布 条件 规避 最小均方误差规避 均值回归

分 类 号： [F224 F830.9]

领　　域： [经济管理] [经济管理]