多分形波动率预测及其在B-S模型中的应用

发布时间：2018-05-04 01:22

本文选题：已实现波动率 + 多分形波动率　；参考：《浙江工商大学》2017年硕士论文

【摘要】：随着我国金融市场的发展,市场对金融衍生品的定价需求也越来越迫切,然而常用的经典B-S定价模型假定波动率为固定不变的常数,这显然不符合金融市场的实际情况。在以往的研究中,很多学者曾使用GARCH族模型来估计股票的波动率,然而,近年来针对我国金融市场的研究发现,金融市场具有多重分形性,即长记忆性。为了在B-S模型中反映我国市场的这一特性,本文将引入新的多分形波动率测度方法(MVM),并建立能够刻画时间序列长记忆性的ARFIMA模型,分析不同多分形波动率测度方法及其动力学模型对金融衍生品定价的影响。本文选取宝钢权证存续期间标的股票的5分钟高频数据作为研究样本,首先对样本区间内宝钢股票的收盘价、日收益率序列和已实现波动率序列的统计特征进行研究。研究结果发现样本的日收益率序列和已实现波动率序列均不服从正态分布,而是具有更为复杂的多重分形特征。为了能够建立准确的波动率预测模型,并结合序列的多分形特征,本文引入利用已实现波动率和多分形谱标准差作为修正参数计算基准的新的多分形波动率测度方法(MVM),并基于已实现波动率和新旧多分形波动率序列分别建立短记忆的ARMA模型(ARMA-LnRV、ARMA-LnMVM 等)和具有长记忆性的 ARFIMA模型(ARFIMA-LnRV、ARFIMA-LnMVM等)对股票收益未来10的波动率进行预测。最后,将上文不同模型预测得到的波动率作为真实波动率的代理变量分别代入B-S模型中,计算检验样本区间内权证的理论价格。并比较未来10天权证的理论价格和市场价格之间的差异,根据理论价格和市场价格的相对误差判断不同波动率预测模型对B-S模型定价精度的影响,最终发现新的多分形波动率测度方法及其动力学模型(ARFIMA-LnMVM)的预测效果是最优的。将利用该模型预测得到的波动率代入分形B-S模型中计算得到的权证价格更接近权证的市场价格。
[Abstract]:With the development of financial market in China, the demand for financial derivatives pricing is becoming more and more urgent. However, the classical B-S pricing model assumes that volatility is a constant constant, which obviously does not accord with the actual situation of financial market. In previous studies, many scholars have used the GARCH family model to estimate the volatility of stocks. However, in recent years, research on financial markets in China has found that financial markets have multifractal, that is, long memory. In order to reflect this characteristic of Chinese market in B-S model, a new multifractal volatility measurement method is introduced in this paper, and a ARFIMA model which can describe the long memory property of time series is established. The effects of different multifractal volatility measurement methods and their dynamic models on the pricing of financial derivatives are analyzed. In this paper, five minute high frequency data of the underlying stock in Baosteel warrant period is selected as the research sample. Firstly, the statistical characteristics of the closing price, the daily yield series and the realized volatility series of Baosteel stock in the sample interval are studied. It is found that both the daily rate of return series and the realized volatility series of samples are not subject to normal distribution, but have more complex multifractal characteristics. In order to establish an accurate volatility prediction model and combine the multifractal features of the series, In this paper, a new multifractal volatility measurement method based on realized volatility and multifractal spectral standard deviation is introduced. Based on realized volatility and new and old multifractal volatility series, a new multifractal volatility measurement method is introduced. The ARFIMA-LnRVV ARFIMA-LnMVM) and the long-memory ARFIMA model ARFIMA-LnRVMVM) are used to predict the volatility of stock returns in the next 10 years. Finally, the volatility predicted by different models above is substituted into B-S model as the proxy variable of real volatility, and the theoretical price of warrants in the test sample interval is calculated. The difference between the theoretical price and the market price of warrants in the next 10 days is compared, and the influence of different volatility forecasting models on the pricing accuracy of B-S model is judged according to the relative error between theoretical price and market price. Finally, it is found that the new multifractal volatility measurement method and its dynamic model ARFIMA-LnMVMM are the best. The volatility predicted by this model is substituted in the fractal B-S model to calculate the warrant price which is closer to the market price of warrant.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.51

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