含交易费用的二元市场上的期权定价研究

发布时间：2018-06-06 21:09

本文选题：二元市场 + 交易费用　；参考：《华中师范大学》2013年硕士论文

【摘要】：当考虑股票价格是连续随机过程时,若给定股票现价,那么它在未来某一时刻的价格是对数正态分布的,这样得到了期权的Black-Scholes定价公式。当考虑股票价格是离散随机过程时,可构造二叉树图即Cox-Ross-Rubinstein模型(以下简称CRR模型)对期权进行估值,此树图可显示股票价格在期权的有效期内可能遵循的路径。我们在为基于股票价格的衍生证券定价时,可以假设这个世界是风险中性的,即无套利的。这就意味着我们可以假设股票的预期收益率为无风险利率,然后以无风险利率贴现期望收益。本论文是在完全市场、满足无套利假设条件下研究只含债券和股票的二元市场上的期权定价问题。该研究的主要方法是二叉树模型和复制期权的思想,建立了含交易费用的二元市场期权定价模型。在原CRR模型的基础上,将证券交易附加一定比例交易费用,并且假使股价在不同时间节点上的涨、跌幅不一致。由于在完全市场里,在风险中性即无套利假设及其它限制条件下,任何一个未定权益,总存在惟一的自融资策略来复制这个权益,从而,通过对基于股票价格的未定权益期权进行自融资策略的复制,推得其价值等于自融资策略中投资组合的初始成本,从而得到期权的定价公式。
[Abstract]:When the stock price is considered as a continuous stochastic process, if the present price of the stock is given, then the price of the stock is logarithmic normal distribution at a certain time in the future. Thus, the Black-Scholes pricing formula of the option is obtained. When considering that the stock price is a discrete stochastic process, a binary tree graph, Cox-Ross-Rubinstein model (CRR model), can be constructed to estimate the option. This tree diagram can show the path that the stock price may follow during the period of validity of the option. In pricing derivative securities based on stock prices, we can assume that the world is risk-neutral, that is, arbitrage free. This means that we can assume that the expected rate of return on stocks is risk-free and then discount the expected return at a risk-free rate. Under the assumption of no arbitrage, the option pricing problem in a dualistic market with only bonds and stocks is studied. The main methods of this study are binary tree model and the idea of replicating option. A dual market option pricing model with transaction costs is established. On the basis of the original CRR model, a certain proportion of transaction costs are added to the stock exchange, and if the stock price rises at different time points, the decline is inconsistent. Because in a complete market, under the risk-neutral assumption of no arbitrage and other restrictions, there is always a unique self-financing strategy to replicate this equity, so that, By replicating the self-financing strategy of the contingent equity options based on the stock price, the paper deduces that the value of the option is equal to the initial cost of the portfolio in the self-financing strategy, and then obtains the pricing formula of the option.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

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