利用小波方差逼近数据波动率的改进BS模型(MBS)

Modified BS Model(MBS) Based on Using Wavelet Variance to Approach Real Volatility of Financial Process

利用小波分析的多尺度方法,描述了小波方差在金融数据中所反映的实际意义和在金融分析中的尺度选择条件,分析了数据发生过程中分解出的不同波动段对于整体波动性的贡献量,然后通过加权重构不同尺度段产生的小波方差来体现数据的波动情况,从而得到了一种新的计算Black Scholes模型中波动率的方法,最后利用MATLAB的模拟实证分析证明了其有效性.

In this article, we come up a new way to describe the volatility （considering the contribution of the wave motion situation of the time left to the expiration） and then modify the old BS model. Moreover, we describe the actual meaning of the wavelet variance toward financial data. At the same time, we illustrate the condition for choosing the scales when decomposing the process and get the wavelet variances. Firstly, we use the method named wavelet and multi-scale analysis to decompose the process, and find out the component scale contribution to the whole date wave process made by different wave motion components. And then, in order to fully reflect the real wave motion situation, considering the contribution made by the future time component （the time left to expiration） on the whole process, we reconstruct the volatility by making each component has different weight which is made according to the contribution toward the process. Finally, we use the new volatility to modify the Black Scholes Model. After the empirical analysis, we confirm that the new model MBS is valid.