Delta Neutral Option Trading

The delta of an option may be used in the following way for trading options. Robert used the Black Scholes model to determine the the­oretical price of a call to be $5 and the delta to be 1/2 but the actual market price is $4. The option is cheap according to his calculations, but if he buys the naked call (buying or selling an option alone) and the market drops the call will become even cheaper. He can neutralize the position by buying two calls, which is approximately equivalent to one future, and sell one future outright. In this way if the market drops the calls will lose approximately the same amount as the future gains. If the market rises the calls will make approximately what is lost from the future rising. He hopes the market will eventually revalue the call to the higher price so he can sell the call at $5 for a $1 profit and breakeven on the future.

The process of buying or selling options and buying or selling corresponding futures against the options is called delta neutral trading. This is often done in options trading to buy what are considered cheap options, or sell what are considered to be expensive options. Delta neutral trading is dynamic because the delta changes as the future price changes and as the volatility and time change.

Determination of the delta is also helpful in deciding how many options to buy or sell in various spreads. For example, if you want to buy the January 100-105 call backspread how many options should be bought and how many should be sold? If the delta on the January 105 call is 0.25 and the delta on the January 100 call is 0.5, then buying two January 105 calls for each January 100 call will delta neutralize the position.