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Black Scholes Option Formula

The Black Scholes Option Formula has been widely used by traders for decades due to its consistency and accuracy. There are some significant limitations to the formula making it important for traders to use it to approximate option prices. It is important to understand the limitations of the Black Scholes Option Formula in order to use it properly. Using the Black Scholes Option Formula without taking into consideration its limitations increases the risk significantly.
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Black Scholes Option Formula Limitation 1

The first limitation of the Black Scholes Option Formula is the fact that it creates tail risk by not correctly estimating the effects of extreme moves. The underestimation can cause serious repercussions to traders blindly following the formula.

Black Scholes Option Formula Limitation 2

The second limitation of this formula is that it creates volatility risk by assuming it is a stationary process. Assuming this puts the formula at risk and creates the possibility for volatility hedging. Traders should be aware of this limitation and keep this risk in mind when employing the Black Scholes Option Formula.

Black Scholes Option Formula Limitation 3

The third limitation to this formula is the assumption that trading is instantaneous and has no cost. This results in a liquidity risk and that is very challenging to hedge.
Black Scholes Option Formula Limitation 4
The final limitation in the Black Scholes Option Formula discussed here is the yielded gap risk that results from the assumption that trading and time are continuous. Gamma hedging can hedge this gap risk and it should be noted by traders.
Considerations of the Black Scholes Option Formula
There are many considerations of the Black Scholes Option Formula and these assumptions and limitations should be weighed and evaluated by traders. This particular formula is consistent and accurate when these limitations are accounted for. When they arenŐt the risk level of using this formula skyrockets. Traders should realize that there are many risks in reality that are not addressed by the Black Scholes Option formula despite the ability to perfectly hedge options with the model.