Heston model: shifting on the volatility surface

Fitting the implied volatility surface is generally a complicated affair. Here, Claudio Pacati, Roberto Renò and Manola Santilli propose a simple extension of the Heston model that allows fast and arbitrage-free interpolation of the volatility surface with just one time-dependent parameter

Ideally, an option pricing model would have the following properties: it would be guaranteed to be free of arbitrage opportunities; it would provide simple (and fast) pricing and hedging formulas; it would readily fit the quoted volatility surfaces across both maturities and strikes; it would avoid overfitting, ie, keep the number of parameters parsimoniously small; and it would adequately