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Options Delta

Options Delta

Options Delta is a sensitivity measure of how the theoretical price of an option will change with changes in the price of the underlying asset, i.e. Delta changes in the same direction of the change in price of the underlying.  Delta is absolutely central to OM‘s market-neutral trading technique.

Options Delta is normalised: it is the change in an option’s theoretical value for a ONE point move in the price of the underlying.  Calls have a positive Delta; Puts have a negative Delta.Options Delta Curve

  • At-the-money (ATM) Delta is half-way i.e. ~50
  • In-the-money (ITM) Delta is high to very high
  • Out-of-the money (OTM) Delta is low to very low

Another way to think of Delta is the percentage chance (probability) the option will end up being In-the-Money (ITM).  As at Options Masters, strategies do not involve static or dynamic hedging, or balancing positions with underlying stocks, one can think of a 80-Delta Call as equivalent to owning 80 shares of the underlying at any one time (common multiplier for US options is 100).

Without going into details on Gamma on this page, one can already see on the right-hand side graph that Gamma is higher At-The-Money.

  • Options with Positive Delta will gain as the underlying asset increases in price.
  • Options with Negative Delta will gain as the underlying asset decreases in price.

Example: An option has a +56 delta, for every 1 point move up in the underlying the option will gain 56 dollars in value. For every move down in the underlying the option will lose 56 dollars.  For a lot of options traders, Delta actually becomes a proxy for the underlying’s movements.

For those who like a simple video instead of long sentences, please check Investopedia’s page on Delta.

Delta and TimeOptions Delta and Time

Greeks are interlinked, and the further out in time we go, the HIGHER the options delta for a given strike.

This makes intuitive sense. The longer the time until expiration of an option, the LESS its price is influenced by Vega, Theta and Gamma.

As an option gets closer to expiration, the in-the-money (ITM) options will have a HIGHER delta than the options that are further to expiration.  Other interactions can be seen on the Options Guide.

Calls and Puts

Calls are positively correlated to their underlying.  Therefore if you buy calls you are getting long deltas, if you are selling calls you are getting short deltas, just like buying and selling stock.

Puts are negatively correlated to the underlying.  Therefore if you buy puts you are getting short delta, if you sell puts you are getting long delta.

For a given strike, the total absolute value of the Delta (e.g. December 750 calls or puts) should add up to ~100, in other words Delta C + Delta P = 100 

Example: If the December 750 call has a 27 delta, then the December 750 put will have a -73 Delta

As options go from ITM to ATM to OTM their Deltas will decrease.

  • The lower (ITM) the Strike, the higher the Deltas of the call
  • The higher (OTM) the Strike, the lower the Deltas of the calls
  • The higher (ITM) the Strike, the higher the Deltas of the puts
  • The lower (OTM) the Strike, the lower the Deltas of the puts

Quick jargon reminder:

  • (ITM) = In-The-Money
  • (ATM) = At-The-Money
  • (OTM) = Out-The-Money
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