The article shows that a European Call option with a higher strike price can be seen as a Call option on a Call option with a lower strike price. This means the prices of these contracts are the same. The researchers found new pricing functions for these options, including in the Black-Scholes model. They also discovered properties of the function that relates option prices to moneyness. Additionally, they developed a method to analyze implied volatility smiles for these options in the Black-Scholes model.