Maintaining a neutral hedge

In our previous discussion of theoretical pricing models, we noted that the purchase or sale of a theoretically mispriced option requires us to establish a neutral hedge by taking an opposing position in the underlying contract.

When this is done correctly, for small changes in the price of the underlying contract, the increase or decrease in the value of the option position will exactly offset the decrease or increase in the value of the opposing position in the underlying contract.

Such a hedge is unbiased, or neutral, with respect to directional moves in the underlying contract.