# Delta of an Option

Delta of an Option is the movement of option price by certain amount when underlying stock or index changes by 1 Dollar. Example delta 0.60 means for 1 dollar movement of underlying stock, option price has moved by 0.60 Dollar. Mathematically, Delta is first order derivative of Value “V” of an Option with respective to underlying stock price “S”

Δ =δV/δS

Delta is also called Delta Ratio and is used in Options for Hedging Risk. A Delta neutral portfolio is hedged in a way that a small changed stock price will not have any impact on the portfolio delta.

A strategy that maintains a delta neutral portfolio called Delta Hedging.

For example, a trader sell a Call Option on one stock of a company which will result in a negative delta. To mitigate this exposure, he will then buy more futures of same stock of that company. This way it will offset the short options negative delta. Sum of the short option and long futures of the same stock of this company will have zero delta

A Call Option will have a positive delta value from zero to 1.00 and a Put Option will have a negative delta value from zero to -1

At-the-money Call Option will have a delta around +0.50 and at-the-money put option will have a delta around -0.50

Delta will increase and move towards 1 for the Call Option when it gets deeper in-the-money and delta for a put option will decrease and move towards -1 when the option gets deeper in-the-money.

When the expiration is near, the delta of ITM Call Option will get closer to 1 and ITM Put Option will get closer to -1

When the expiry is near the delta of OTM Call Option and OTM Put Option, both approaches towards zero and on the day of expiry both becomes zero and Option becomes worthless.

When Volatility increases, delta of OTM Options increases and ITM Option delta value decreases.

Position Delta is the Delta of a Portfolio which is the sum of delta of each of the Options in the Portfolio. When Delta changes, position delta remains hedged for a shorter duration. This hedge needs to be adjusted from time-to-time. This activity is called rebalancing or dynamic hedging. If no rebalancing is done it is called static hedging or hedge and forget strategy.