Option Greek – Delta

What is Delta in Options?

Delta, the first of the option Greeks, reflects how much an option’s price changes with respect to a change in the underlying asset's price. It is expressed as:

Delta = Change in option price / Change in underlying price

Being derivatives, options are directly influenced by the movement of the underlying. Hence, understanding Delta is key to estimating how responsive an option is to these movements.

• Call options have a positive Delta because their value increases when the underlying price rises.
• Put options carry a negative Delta, as they gain value when the underlying price falls.

In simpler terms:

• Call options move in sync with the underlying.
• Put options move opposite to the underlying.

Deltas are typically expressed without decimals. For instance, a delta of 0.20 is often referred to as a 20-delta call, and a 0.20 delta for a put would be termed a 20-delta put.

Example – Delta in Action:

• Call Option:
  Nifty Call Option with a strike of 17,500, priced at ₹90 with a Delta of 0.60.
  If Nifty spot moves from 17,534 to 17,550 (up by ₹50), the call premium increases by ₹30 (50 × 0.60), moving the price to ₹120.
• Put Option:
  Nifty Put Option with a strike of 17,600, priced at ₹116 and Delta of 0.61.
  If the spot drops by ₹50, the option price increases by ₹30.5 (50 × 0.61), becoming ₹146.50.

Traders often rely on Delta to gauge the probability of an option expiring in-the-money.

Delta for Call Options

• Delta values for call options range between 0 and 1.
• At-the-money (ATM) calls have Delta close to 0.50, indicating a 50% probability of expiring in-the-money.
  • Example: An ATM August Nifty call with Delta 0.48 implies a 48% chance of expiring profitable.
• In-the-money (ITM) calls have Deltas ranging from 0.50 to 1. The deeper ITM the strike, the closer the Delta is to 1.
• Out-of-the-money (OTM) calls hold Delta between 0 and 0.50, with deep OTM calls nearing zero. These options have no intrinsic value and low sensitivity to price changes.

Delta for Put Options

• Delta values for put options fall between -1 and 0.
• ATM puts typically have a Delta around -0.50, suggesting a 50% chance of expiring in-the-money.
  • Example: An August Nifty put with a Delta of -0.52 suggests a 52% probability of ITM expiry.
• ITM puts hold Deltas from -0.50 to -1, with deeper ITM puts having Deltas closer to -1.
• OTM puts show Deltas from -0.50 to 0, with deep OTM puts approaching zero due to low sensitivity and minimal chance of ending in-the-money.

Option Chain Observation:

A glance at the Nifty options chain reveals that:

• Delta peaks for ITM options
• Delta is lowest for far OTM options
• From OTM to ATM, Delta climbs quickly
• From ATM to deep ITM, Delta increases gradually and then flattens

This natural progression helps traders assess position risk and exposure based on strike selection.

Time to Expiry & Volatility Impact on Delta

Both time to expiry and implied volatility heavily influence Delta.

• For ITM calls:
  • Longer time to expiry = Lower Delta
  • Shorter time to expiry = Higher Delta
• For OTM calls:
  • Longer expiry = Higher Delta
  • Shorter expiry = Lower Delta

As expiration approaches:

• ITM call Deltas move closer to 1
• ATM Deltas hover around 0.50
• OTM call Deltas drop toward 0

Role of Implied Volatility:

• When implied volatility increases, Delta for all strikes gravitates toward 0.50, due to rising chances of moneyness.
• When volatility decreases:
  • Delta for ITM calls trends toward 1
  • Delta for ITM puts trends toward -1
  • OTM Deltas (both calls and puts) tend toward zero

This relationship between volatility and Delta is crucial for adjusting strategies based on market expectations.

Conclusion

Delta is an essential tool for estimating how an option reacts to small changes in the underlying price. However, for larger price swings, another Greek, Gamma, becomes critical. While Delta measures speed, Gamma measures the acceleration of that speed. We will dive deeper into Gamma in the next chapter.

Points to Remember

• Delta measures how an option price changes with a change in the underlying’s price.
• It is expressed as:
  Delta = Change in option price / Change in underlying price
• Call options = Positive Delta
  Put options = Negative Delta
• Deltas are notated without decimals in conversation.
  For example: A 0.20 Delta = 20-delta option
• Delta is effective for forecasting small movements in price.
  For broader movements, Gamma takes centre stage.