Selecting the “Best” Delta

by Rob Roy

Selecting the strike that is best for each trading strategy will depend on several factors.  Straddles and Strangles are directional techniques and a trader can use the nature of how option prices change, via delta, to gain the best “bang for their buck.”  Hindsight will always show what the best strikes were for the trade, but all traders have to live without this ability to see into the future when placing their trade.  Though there are many variables that play into option pricing there do remain a few constants.

Through the option pricing model (the extremely complex formula used to create an options price), delta is one of these constants.  The delta changes after each $1.00 change in the stocks price.  This change comes from the gamma.  As the stock moves in the correct direction for the option to profit directionally, the delta gets larger.  As the stock moves adversely from the option, the delta gets smaller.  It is this changing of the delta that is key to how Straddles and Strangles profit.

Imagine a trader is in a Straddle or Strangle trade.  As the stock price increases (moves higher) the delta on the call side grows, while the delta on the put side shrinks.  Essentially the call is gaining more value at this point than the put is losing.  A table format like the one shown below makes it easier to see what is happening.

In the table the calls are on the left and the puts are on the right, with the stock price down the center.  Use it like a slide rule to see how the price of the trade changes with the delta.  The 50 strike will be highlighted in the assumption the trader decided to place the 50 strike Straddle at a cost of $4.00 ($2.00 call plus $2.00 put).

If the stock was to move higher in price from $50.00 to $51.00 (looking in the far right hand column showing the 50 strike Straddle’s value and delta), will show the trader that the Straddle will be worth $4.00.  The stock moved $1.00 in price yet the Straddle did not make any money.  The reason again is in the delta.  The 50 strike call had a .50 delta and the 50 strike put had a

-.50 delta.  When creating any position with options the trader needs to combine the deltas to arrive at what is called the “position delta.”  With a positive .50 delta and a -.50 delta, combing the two gives the Straddle a delta of .00.  That means, for the first $1.00 move either way, the Straddle value will not change.

After that first $1.00 move up in the stock, the call delta will increase to .58 and the put delta will reduce down to -.42.  The value of the Straddle remains $4.00.  For the second $1.00 move up in the stock, from $51.00 to $52.00, the call will gain $0.58 (from the .58 delta) and the put will lose $0.42 (from the -.42 delta), netting the position a gain of $0.16.  To state this more simply, the Straddle gained the value from the position delta of .16.  This process continues as the stock continues to move higher in price.

Let’s go back to the start price of $50.00.  If the stock were to move down in price the same effect would be seen.  For example, if the stock was to move from $50.00 down to $49.00, the Straddle would not make any profit as the position delta is .00.  The second $1.00 move down in the stock, from $49.00 to $48.00, the put delta being -.58 makes $0.58, while the call delta being .42 loses $0.42 of value, netting the Straddle a gain of $0.16 on the trade.  Directionally the Straddle or Strangle trader does not care which way the stock starts to trend.  Of course there are other factors that will give the trade a preference on which way they prefer the stock to trend.