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 describe price and volatility risk.
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