A new type of American option has been developed where the holder pays a fee if they choose to exercise it early. The researchers found a way to calculate the value of this option, which is tricky because it involves figuring out when it's best to exercise it. They came up with a method to estimate the option's value and the best time to exercise it for options with short maturities. The results from their calculations were very accurate, showing that their approach works well for these types of options.