基于贝叶斯的期权定价方法及实证

发布时间：2018-04-28 22:05

本文选题：贝叶斯方法 + 期权定价　；参考：《湖南大学》2013年硕士论文

【摘要】：随着金融衍生品市场的发展,金融衍生品交易的规模不断扩大,同时也出现了一些衍生品的定价方法.多年以来,有很多学者在经典统计学的框架下对B-S模型进行了研究,但是同时也存在着一些不足,模型当中的资产价格以及波动率的随机性问题一直没有得到较好的解决.考虑到贝叶斯统计所具有的诸多优点,本文在贝叶斯统计的框架下结合B-S模型对期权的价格进行推断.首先采用Fisher信息矩阵来确定无风险资产回报率和波动率的无信息先验,并且将资产价格和波动率都看成是随机变量,然后运用无风险资产回报率和波动率的无信息先验并结合适当的似然函数,得出欧式看涨期权的先验密度以及后验密度函数的表达式. 本文采用中国的欧式认购权证“鞍钢JTC1”的日收盘价格数据以及其标的资产的日收盘价格数据进一步进行了实证研究.在计算方面,考虑到蒙特卡罗模拟方法(MC)整体的运算较为有效,且适用于标的资产的预期收益率和波动率的函数形式比较复杂的情况,所以本文运用蒙特卡罗算法(MC)来获得期权价格的估计值以及其它的数值特征,例如均值、方差等等,并且根据计算所得到的结果进行了分析,分析表明随着时间的增大,期权价格密度函数的收敛性增强.然后,将计算得出的理论价格与相应的实际价格进行比较.最后,为了衡量出权证的市场价格与理论价格的偏离程度,本文采用了偏离度进行分析研究.实证的结果表明:当时间接近于到期日的时侯,权证的实际价格与其理论价格趋于一致,偏离度逐渐趋近于零.由此可以看出:权证标的股票的交易者与权证的交易者对标的股票价格的预期逐渐趋于一致.
[Abstract]:With the development of financial derivatives market, the scale of financial derivatives trading is expanding, and some derivatives pricing methods have emerged. For many years, many scholars have studied the B-S model under the framework of classical statistics, but at the same time, there are some shortcomings, the problem of asset price and volatility randomness in the model has not been solved. Considering the many advantages of Bayesian statistics, this paper inferred the price of options under the framework of Bayesian statistics combined with B-S model. Firstly, the Fisher information matrix is used to determine the non-information prior to the return and volatility of risk-free assets, and the asset price and volatility are regarded as random variables. Then the prior density and posteriori density function of European call options are obtained by using the non-information priori of risk-free return on assets and volatility and the appropriate likelihood function. This paper makes a further empirical study on the daily closing price data of the European subscription warrant "Angang JTC1" and the daily closing price data of its underlying assets. In terms of calculation, considering that the Monte Carlo simulation method / MCMC) is more effective in overall operation and is applicable to the complex function forms of the expected return and volatility of the underlying asset, So this paper uses Monte Carlo algorithm to get the estimated value of option price and other numerical characteristics, such as mean value, variance and so on, and according to the results of the calculation, the analysis shows that with the increase of time, The convergence of the option price density function is enhanced. Then, the calculated theoretical price is compared with the corresponding actual price. Finally, in order to measure the deviation degree between the market price and the theoretical price, the deviation degree is analyzed. The empirical results show that when the time is close to the maturity date, the actual price of warrant tends to be consistent with its theoretical price, and the deviation gradually approaches zero. It can be seen that the traders of the underlying stocks and the traders of warrants tend to converge on the price of the underlying stocks.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224

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