  Panel data are modern statistical tools which are commonly used in all kinds
of econometric problems under various regularity assumptions. The panel data
models with changepoints are introduced together with atomic pursuit methods
and they are applied to estimate the underlying option price function. Robust
estimates and complex insight into the data are both achieved by adopting the
quantile LASSO approach. The final model is produced in a fully data-driven
manner in just one single modeling step. In addition, the arbitrage-free
scenarios are obtained by introducing a set of well defined linear constraints.
The final estimate is, under some reasonable assumptions, consistent with
respect to the model estimation and the changepoint detection performance. The
finite sample properties are investigated in a simulation study and proposed
methodology is applied for the Apple call option pricing problem.
