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硕士学位论文
基于Black-Scholes模型的认股权证定价实证研究 姓名：方璐
申请学位级别：硕士
专业：西方经济学
supercapture指导教师：李天有
20070521
摘要
一般来说，期权定价的常用模型有三种，分别是二叉树模型、蒙特卡罗模拟和Black－Scholes模型。二叉树模型是用离散的随机游走模拟资产价格连续变动的可能路径，并利用二元树状图求出到期日的资产价格，从而计算出当前期权价格；蒙特卡罗模拟是一种通过模拟标的资产价格随机运动路径计算出期权 期望值的数值算法，是一种应用较广泛的期权定价方法，它在每次的模拟环境中都会产生一个价格，其与真实价格的误差会随着模拟次数的增加逐渐缩小；Black－Scholes模型是一种解析模型，在给定输入参数的情况下能够得到确定的解析解，该模型的提出对于期权定价理论是一个突破性的进展。但由于其建立在极其严格的假设条件上，因此应用范围也相对较窄。
认股权证本质上是一种公司发行的看涨期权，因此，可以利用期权定价模型对其进行定价研究。本文的主要工作是利用Black－Scholes模型，结合国内市场上的认股权证国电JTB1进行认股权证定价的实证研究，对理论价格与实际价格的差异原因进行分析，并对在目前我国权证市场上使用Black－Scholes模型的合理性作了初步探讨。 本文的理论部分主要由两大块组成：一是Black－Scholes模型的建立、推导与求解；二是波动率预测。在第一块中，首先对Black－Scholes 模型得以成立的三大理论基石分别做了阐述，即无套利均衡原理、风险中性原理以及有效市场假说。随后进一步阐述了在弱有效市场假说下股票价格的行为模式——几何布朗运动，并且得到了对数价格的分布特征。在模型推导部分，首先介绍了建模的基本思想——“动态复制”，然后在此基础上推导出了Black－Scholes偏微分方程，并对方程的形式进行了讨论，采用风险中性定价的方法求解出了Black －Scholes欧式期权定价公式。最后，笔者对于目前普遍遵从的考虑股本摊薄效应的认股权证定价模型进行了介绍，并且对其适用性提出质疑。
波动率预测部分主要分常数波动率与时变波动率两种情况讨论，并且分别给出了两种情形下的预测模型，其中以时变波动率模型为阐述重点。在时变波动率预测部分中，本文介绍了两种方法，移动平均法与条件异方差模型，其中以条件异方差模型为阐述重点。在条件异方差模型中又分ARCH族模型与随机波动率模型两类模型进行讨论。在随机波动率模型中，由于存在资产价格和瞬背心式连衣裙
时方差两个状态变量，自融资组合策略失效，因此不能应用Black－Scholes公式定价，所以本文以ARCH族模型为论述重点。在ARCH族模型中，重点介绍了ARCH模型、GARCH模型、GARCH－M模型以及EGARCH 模型。本章最后阐述了隐含波动率的概念，并且认为在目前我国权证市场上，Black－Scholes模型自身假设得不到满足，应用隐含波动率预测必然有很大偏差。
本文的实证工作主要分两步进行，第一步是Black－Scholes模型的参数估计，即波动率估计；第二步是结果差异分析。在估计波动率时，首先分析了标的股的收益率特征，验证了ARCH效应的存在；在对 GARCH（1，1）模型和GARCH（1，1）－M模型的估计效果进行对比后选择GARCH（1，1）模型对收益率建模。在结果差异分析部分，引入溢价率，打平点等指标，发现
Black-Scholes模型对认股权证价格存在严重低估。随后，围绕市场本身的非理性与模型本身假设与现实情况的不一致对差异原因进行了讨论，并且认为我国目前没有建立真正的卖空机制是应用Black－Scholes模型失效的最重要原因。
和谐农村关键词：Black－Scholes模型；波动率；ARCH；卖空电力安全性评价
Abstract
Generally Speaking, there are three categories of models for Option-Pricing: Binomial Option Pricing Model, Monte Carlo Simulation and Black-Scholes Model. BOPM focuses on simulating continuous-varying asset price in a discrete time model. Monte Carlo Simulation resorts to computer to simulate almost all the routes followed by asset price, and give different values as the conditions changes. As it is limited by the least preconditions among the three models, it is applied the most widely. The coming up of Black-Scholes Model greatly progressed the research of Option-Pricing, as this model is an analytic model basically, which means an exact numerical value can be acquired when parameters are given. However，as it has strict preconditions, the application is limited.
As Warrant is a kind of Call Option issued by company in essence, it can be priced in all above models. The main purpose of the thesis is to apply Black-Scholes Model to price Warrant of GuoDian which is being listed in China derivatives product market, and try to find the factors causing the theoretical price deviating from the real market price. Empirical study shows Black-Scholes Model undevalues the warrant, and our analysis focuses on two kinds of reasons behind the deviatio
n: one is that China derivative product market is irrational; the other is the incorrectness of model itself, which is our analysis emphasis. The irrational market features too many speculations, which are largely attributed to the absence of nescesary institutions. The incorrectness of the model is due to the preconditions can not be met in China market. The forbidden of short sale poses a fatal impact on Black-Scholes Model, because the unlimited short sale ensures risk-free arbitrage can be effectively conducted, and risk-free arbitrage is the footstone of the whole model. Based on the analysis, we conclude that Black-Scholes Model is not an effective approach to find the reasonable price of Warrant in China market, therefore the implied volatility can not pose effective forecast for the trend of underlying stock. At the end of the thesis,
河北人事厅we propose that the mechanism of short sell should be introduced as soon as possible so that the price of financial derivatives products can return to its reasonable price and our derivatives product market can grow mature.
Key Words：Black-Sholes Model; V olatality; ARCH; Short Sale
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