Implied Volatility Surface Estimation via Quantile Regularization

Abstract

The implied volatility function and the implied volatility surface are both key tools for analyzing financial and derivative markets and various approaches were proposed to estimate theses quantities. On the other hand, theoretical, practical, and also computational pitfalls occur in most of them. An innovative estimation method based on an idea of a sparse estimation and an atomic pursuit approach is introduced to overcome some of these limits: the quantile LASSO estimation implies robustness with respect to common market anomalies; the panel data structure allows for a time dependent modeling; changepoints introduce some additional flexibility in order to capture some sudden changes in the market and linear constraints ensure the arbitrage-free validity; last but not least, the interpolated implied volatility concept overcomes the problem of consecutive maturities when observing the implied volatility over time. Some theoretical backgrounds for the quantile LASSO estimation method are presented, the idea of the interpolated volatilities is introduced, and the proposed estimation approach is applied to estimate the implied volatility of the Erste Group Bank AG call options quoted in EUREX Deutschland Market.