Understanding the Relation Between Delta and Gamma in Option Chain

In options trading, two of the most important “Greeks” are Delta and Gamma. These metrics help traders measure risk, sensitivity, and how option prices may move when the underlying stock or index changes. To make better trading decisions, it is crucial to understand not only what Delta and Gamma mean but also how they are related mathematically.

What Is Delta?

Delta measures how much the premium (price) of an option changes when the underlying asset’s price changes by ₹1.

• Call Option Delta ranges from 0 to +1.

• Put Option Delta ranges from 0 to –1.

• For example, if a call option has a Delta of 0.5, and the stock price rises by ₹1, the option premium will rise by ₹0.5.

Delta also indicates the probability of expiring In-the-Money. For instance, a 0.7 Delta suggests roughly a 70% chance the option will finish ITM.

What Is Gamma?

Gamma measures how much Delta will change when the underlying price changes by ₹1.

• Gamma is always positive for both calls and puts.

• It is highest for At-the-Money (ATM) options and lowest for Deep ITM or OTM options.

Example: If a call option has a Delta of 0.5 and a Gamma of 0.1, and the stock rises ₹1, then:

• New Delta = 0.5 + 0.1 = 0.6

• Which means the option will now move ₹0.6 for every ₹1 move in the underlying.

Relation Between Delta and Gamma

• Delta tells you the direction and speed of option price changes.

• Gamma tells you the acceleration of Delta.

In other words:

• Delta = First derivative of option price with respect to stock price.

• Gamma = Second derivative of option price with respect to stock price.

This means Delta changes because of Gamma, and Gamma makes the option curve “non-linear.”

Calculation Example

Suppose:

• Nifty 50 = ₹25,000

• A 25,000 Call option has Premium = ₹300

• Delta = 0.5, Gamma = 0.05

➡ If Nifty rises by ₹10:

• Change in Delta = Gamma × Price change = 0.05 × 10 = 0.5

• New Delta = 0.5 + 0.5 = 1.0

➡ Effect on Premium:

• Premium change = Average Delta × Price change

• Here average Delta = (0.5 + 1.0)/2 = 0.75

• Premium change = 0.75 × 10 = ₹7.5

• New Premium ≈ ₹307.5

Thus, Gamma accelerated the growth of Delta, making the option more sensitive after the price movement.

Why It Matters to Traders

• High Gamma = Higher risk and reward. Small moves in the underlying can change Delta significantly.

• Gamma risk is most important for short option sellers because their Delta exposure can swing suddenly.

• Understanding Delta-Gamma together helps traders manage hedging, position sizing, and stop-loss planning effectively.

📌 Useful Links

• Investopedia – Delta vs Gamma Explained: https://www.investopedia.com

• NSE India – Option Chain Basics: https://www.nseindia.com/option-chain

• CME Group – Option Greeks Guide: https://www.cmegroup.com/education/courses/understanding-options/greeks.html

• Open your mutual funds account on below link & get your funds suggested by Dr. Vinay Prakash Tiwari: http://p.njw.bz/44600

• Open your demat account in Punch: https://punn.ch/ltp-on-punch

• Open a free demat account with Zerodha and start investing in stocks, derivatives, mutual funds, ETFs, bonds, IPOs, and more: https://zerodha.com/open-account?c=ZMPGFJ

Written by Dr. Vinay Prakash Tiwari, Founder – LTP Calculator Financial Technology Pvt. Ltd & Daddy’s International School & Hostel, Bishunpura Kanta, Chandauli, UP

⚠ Disclaimer: Mutual fund and stock market investments are subject to market risks. The examples and returns mentioned are purely illustrative. Future returns are uncertain — as per SEBI disclaimer, past performance does not guarantee future results. Please consult a SEBI-registered financial adviser before making any investment decisions.