The article shows that the price of a European Call option with a higher strike can be seen as the price of a Call option on a Call option with a lower strike. This means the prices of these two contracts are the same. The researchers studied how the price of the Call on Call option relates to the underlying Call option, and found new pricing formulas. They also looked at how the price changes with the moneyness of the option. In the Black-Scholes model, they explored the properties of implied volatility smiles for Calls on Calls.