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Understanding the Nuances
of Option Delta

Presented By
Dan Passarelli

There are so many facets to options trading compared to say stock and futures trading. Getting a good grip on the option greeks, is mandatory to truly understanding how options function. For option traders both new and experienced, knowing what option delta is and what it means for your option position, can be the difference between a profitable and not so profitable position. Before we go further, let’s take a look below at the definition of option delta.


Different Definitions of Option Delta

Here are four definitions that will make understanding option delta a little easier.

  1. The rate of change of an option value relative to a change in the underlying price.
  2. The derivative of the graph of an option value in relation to the stock price.
  3. The equivalent of underlying shares represented by an option position.
  4. The estimate of the likelihood of an option expiring in-the-money (ITM).

Looking at the Delta Definitions in a Practical Sense

Long calls and short puts have positive deltas and benefit from a move higher in the underlying. Short calls and long puts have negative deltas and benefit from a move lower in the underlying. A long call with a positive delta of 0.70 should increase about 0.70 ($70 in real terms) if the underlying moved a dollar higher and vice-versa based on delta alone. Option gamma, theta and vega are also the other greeks that will contribute in a positive or negative way to the position as well.

Investors that smartly use options will often consider the 4th definition of delta listed above. If an investor sold a put option with a positive 0.15 delta, he or she might say that the option has an 85% (100 – 0.15) of expiring out-of-the-money (OTM) or worthless. Investors that often sell options will use delta as the probability of an option to expiring worthless at expiration. Other investors and often traders that use options will consider the current delta as the equivalent number of shares of stock. If a position has a negative 0.40 delta and the stock moves a dollar lower, the option should gain about 0.40 ($40 in real terms). This is like shorting (or selling short) 40 shares of stock with that same move of a dollar lower.


A Few Option Delta Benefits

Buyers of options know that using options can significantly reduce their outlay versus long or short stock positions. By using option delta as your guide, you can gauge your expected profit or loss based on the size of your delta which you can determine. This is done by buying or selling different strikes and different contract sizes as well. Everything about options is a tradeoff so the bigger the desired delta, the bigger the risk many times. If risk is not increased, other option greeks like theta are usually compromised. Either way, buying options will still be significantly less than say owning shares of stock. Delta is certainly not a fool-proof way to analyze an option. There are other important pricing factors that affect the value of an option, too. Time (theta) as mentioned above, volatility (vega) and more also play a very important role.


Option Delta Example

Suppose you have a bullish opinion about a stock over the next couple of weeks. With the stock trading just above $282 a share, the option trader decides he does not want to risk more than $1,100 on his position. Looking at the option chart below, he decides to buy the 280-strike put with 23 days to go to expiration for 10.50 or $1,050 in real terms.

Since the option position is bullish and a long call, the delta is a positive 0.56. Here is how to use delta to interpret the current position. If the stock moves a dollar higher based on current delta solely, the option premium should increase by about 0.56 ($56 in real terms). The option trader has a positive delta and a positive move in the stock which would increase the call premium since it is a debit position. The position now is more valuable than when it was purchased. If the stock moved $2 lower, the call option would lose a value of 1.12 (2 X 0.56) ($112 in real terms) based on delta alone. This is a fairly simplistic example but a fairly accurate depiction of what to expect based on delta and the movement of the stock in the above example.



Learning and understanding how delta functions can be pivotal for your success as an option trader. Option delta is fairly straightforward but there are several nuances involved. Gaining valuable experience either through trading and/or through studying screenshots of various option chains may be the best teacher of them all.

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