Delta

Delta is a fascinating Greek value that is used several different ways in trading.  In general the delta is a measure of how an option’s value changes as the price of the underlying goes up or down.  However, the delta represents more than that as it includes probability of an ITM Strike Price and also serves as a comparison to stock ownership.  One of the most important aspects of delta is that it is an estimation.  It is NOT an exact.  


Delta has a lower boundary of 0 and an upper boundary of 100.  Most traders will write delta as a decimal and so we will do the same.  A typical delta, for example 60, will be written as 0.60.  For Calls, the Delta is positive, for Puts it is Negative.  A Put with a delta of 72 would be written as -0.72.  The negative sign indicates that the change of the  Option will be in the opposite direction of the market.


The first aspect of Delta is using it as a measurement of the change in an Options value as compared to the movement of the stock.  A Call Option with a Delta of 0.35 can be expected to change its value at 35% of the rate of the underlying.  If the underlying were to rise $1.00, then the Option value can be expected to rise approximately $0.35.  If the underlying were to fall $1.00, then the Option value can be expected to drop approximately $0.35.  Call and Put Options that are close to being or are At-the-Money have Delta values that are very close to, if not at, 0.50.


Another aspect of the Delta is that it gives us the probability that the Strike Price will be In-the-Money (ITM) at expiration.  If, for example, the $50 Call on XYZ Corporation has a 0.75 delta, then we have a 75% probability that the $50 Call will expire In-the-Money (ITM).  What is nice about this is using this as we short or sell our Options.  If we have constructed, for example, a Bull Put Spread completely Out-of-the-Money, and we want it to remain OTM to expiration, then we want to find a small Delta on our short Put.  If we find a 0.18 Delta on our short Put, then we have a 82% probability that the Put will be OTM at expiration.


One important safety factor of the Delta is that it can help us hedge our positions.  The Delta can help us determine the ratio of Stock to Option Contracts.  Remember that the Delta of Stock is always 1.00.  If we want to hedge our Option positions with underlying Stock we will divide 100 by the Option's Delta.  If, for example, we have an Option that has a Delta of 0.50, then the proper hedge is 100/50, or 2/1.  For every two Options that we purchase, we can sell one hundred shares of Stock.  This will help us establish a neutral hedge.


Delta can aid the trader in establishing probabilities and also give an estimate as to growth in value as the underlying moves in the appropriate direction.  It can also aid us in hedging our positions.