确定隐含波动率的总变分正则化方法

求解隐含波动率是一个典型的PDE反问题,传统的Tikhonov正则化方法往往导致解的过度光滑化.基于波动率的跳跃性、隔夜周末效应等及总变分正则化方法具有较好地保持图像边界的优点,本文以Black-Scholes理论为框架,把确定隐含波动率问题转化为一个抛物型方程的终端问题,进一步提出求解隐含波动率的总变分正则化方法,并证明了解的存在性.

Total Variation Regularization Method for Determining Implied Volatility

Implied volatilities are more efficient in the long-term prediction of volatilities than the series models.Solving the implied volatility is a typical PDE inverse problem.The traditional Tikhonov regularization method may over-smooth the solution.Considering the jump,overnight,weed-end effect of the volatility and the advantage of the total variation regularization which preserve the edge of the restored image,we put the problem of determining the implied volatility into a parabolic equation of the terminal problem under the Black-Scholes theoretical framework,propose the total variation regularization method and prove the existence to the solution.