Math is Beneficial for Option Trading

One of the greatest advantages for an option trader is the initial flexibility of the position and the ability to adjust a position to match the new outlook of the underlying. The option trader who limits his or her world to that of simply trading equities also limits the position and outlook to either long (bullish) or short (bearish) positions. A change in an outlook regardless of the reason often requires starting a new position or closing out the old one. The options trader can usually change with  the newly developed outlook with much more ease, often with a minor option adjustment on the position in order to achieve the right fit for the new outlook.

Option Adjustments
One concept with which the option trader needs to be familiar in order to construct a necessary option adjustment is that of the synthetic relationship. Most options traders neglect to familiarize themselves with this concept when learning to trade options. This concept arises from the fact that appropriately structured option positions are virtually indistinguishable in function from the corresponding long or short equity position. One approach to remembering the relationships is to memorize all of the relationships. It may be easier to do this by remembering the mathematical formula below and modifying as needed.

Synthetic Formula
For those who remember algebra probably that was taught back in high school, the fundamental equation expressing this relationship is S=C-P. The variables are defined as S=stock, C=call, and P=put. This equation states that stock is equivalent to a long call and a short put.

Using high school algebra to formulate this equation, the various equivalency relationships can easily be determined. Remember that we can maintain the validity of the equation by performing the same action to each of the two sides. This fundamental algebraic adjustment allows us, for example, to derive the structure of a short stock position by multiplying each side by -1 and maintain the equality relationship. In this case (S)*-1 =(C-P)*-1 or -S=P-C; short stock equals long put and short call.

Such synthetic positions are frequently used to establish option positions or to make an option adjustment either in whole or part. You might have not liked or did well with algebra when you were in school, but applying some of the formulas can help an option trader exponentially! 

John Kmiecik
Senior Options Instructor @
Market Taker Mentoring, Inc

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