论文总字数：17070字

摘 要

股市是宏观经济的晴雨表。随着金融行业的不断发展，金融交易活动已经逐渐成为人们生活的重要组成部分。 据中国证监会发布的数据显示，中国股市投资者数量大幅增加，证券市场日成交量也在上升。股票市场发展潜力巨大， 金融活动交易量增长迅速，成绩显着。 然而，在这个阶段，中国证券市场仍然不完整，证券价格不时会出现较大波动。 为尽可能降低投资风险，许多证券公司向投资者发行衍生品，期货和其他金融衍生品。 因此，对于投资者而言，有必要找到合适的数学方法来对衍生品和其他金融衍生产品进行定价，从而合理投资和规避风险。

基于Black-Scholes定价模型，本文收集历史数据对上证50 ETF期权价格进行了实证研究，并分析各参数对期权价格的影响。数据收集根据上海证券交易所发布的最新上证 50ETF期权数据，选择不同的到期日和不同执行价的期权，将参数估计的结果纳入Black-Scholes公式，通过R软件，Matlab等一些软件对上证50ETF期权的价格进行实证研究。将B-S定价模型得到的期权理论的价格与期权的实际收盘价进行比较并对实际期权价格与理论价格产生的差异进行分析。将B-S定价模型得到的期权理论的价格与蒙特卡洛模拟方法的到的期权的理论价格进行比较。

关键词：期权价格, 参数估计，B-S模型, 蒙特卡洛模拟

Research on European option pricing based on B-S model

Abstract

The stock market is a barometer of the macro economy. With the continuous development of the financial industry, financial transactions have gradually become an important part of people's lives. According to the data released by the China Securities Regulatory Commission, the number of investors in China's stock market has increased significantly, and the daily turnover in the stock market is also rising. The development potential of the stock market is huge, and the volume of rapid growth can highlight its remarkable results. However, at this stage, China's stock market is still incomplete, and the price of securities will fluctuate from time to time. To minimize investment risks, many securities companies issue derivatives, futures and other financial derivatives to investors. Therefore, for investors, it is necessary to find the appropriate mathematical methods to price derivatives and other derivatives, so as to invest and avoid risk.

Based on the Black-Scholes pricing model, this paper collects historical data to make an empirical study on the price of Shanghai 50 ETF option, and analyzes the impact of the parameters on the option price. According to the latest 50ETF option data issued by the Shanghai stock exchange, the data is selected to choose different expiration date and different executive price options. The results of the parameter estimation are included in the Black-Scholes formula, and the price of the 50ETF option is empirically studied through some software such as R software and Matlab. The prices of the option obtained by the B-S pricing model are compared with the actual closing prices of the option, and the differences between the real option prices and the theoretical prices are analyzed. The prices of option derived from the B-S pricing model are compared with the theoretical prices of option calculated by Monte Carlo simulation.

Key Words: option price, parameter estimation, B-S model, Monte Carlo simulation

目 录

摘 要 I

Abstract II

第一章 引言 1

1.1 研究目的与意义 1

1.2国内外相关研究回顾 1

1.3创新点与研究方法 2

第二章 模型理论 3

2.1数据的说明 4

2.2 Black-Scholes定价模型的推导过程 4

2.3蒙特卡洛模拟......................................................................................................5

第三章 实证分析 6

3.1 数据选取与处理.........................................................................................................7

3.2 各因素对期权价格的影响.................................................................................... 7

3.3 B-S模型实证分析.................................................................................................10

3.4蒙特卡洛模拟定价分析........................................................................................11

3.5实证结果对比分析................................................................................................13

第四章 结论 15

4.1结论..........................................................................................................................15

4.2 下步研究.................................................................................................................................15

参考文献..................................................................................................16

附录 17

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