The main reason why the yield curve of a call option is curve-shaped is due to the nonlinear characteristics of the option and the leverage effect.

Nonlinear characteristics: There is a nonlinear relationship between the return of an option and the change in the price of the underlying asset. When the price of the underlying asset is below the exercise price, the gain from the call option is zero because the holder will not exercise the right. When the price of the underlying asset exceeds the exercise price, the income from the call option will increase as the price of the underlying asset rises, but the increase will gradually decrease. When the price of the underlying asset is much higher than the exercise price, the return from the call option flattens out because exercising the right no longer makes much sense to the holder. This nonlinear relationship results in the curvilinear shape of the yield curve.

Leverage effect: Options have a leverage effect, which means that relatively large returns can be obtained with a small investment. When the price of the underlying asset rises, the income from the call option will increase accordingly, but the magnitude of this increase is usually greater than the magnitude of the increase in the price of the underlying asset. This is because call options only require payment of the premium, not the full value of the underlying asset. Therefore, for the same price increase of the underlying asset, the return of the call option will be relatively higher, resulting in the curvilinear shape of the return curve.

The yield curve of a call option is curve-shaped, which is caused by the nonlinear characteristics of the option and the leverage effect. This curve shape makes options flexible and potentially high-yield, and also provides investors with diversified investment strategy choices.