Options Greeks :: 

Options Greeks are quantitative measures that show how an option’s price will react to changes in price, time, volatility, and interest rates. Understanding them is critical for Nifty/Bank Nifty options risk management and strategy design.

• Delta (Δ): Sensitivity of option price to underlying price changes.​

• Gamma (Γ): Sensitivity of delta to underlying price changes.​

• Theta (Θ): Sensitivity of option price to passage of time (time decay).​

• Vega (V): Sensitivity of option price to implied volatility changes.​

• Rho (ρ): Sensitivity of option price to interest rate changes.​

Delta – Direction & Probability

• Meaning: Delta measures how much the option price should move for a 1-point move in the underlying.​

• Range:

  • Calls: 0 to +1 (e.g., +0.50 means option gains ₹0.50 for each ₹1 rise in stock).​

  • Puts: 0 to −1 (e.g., −0.40 means option loses ₹0.40 for each ₹1 rise).​

• Use cases:

  • Gauges directional exposure of a position (net delta).​

  • Approximates probability of expiring ITM (e.g., 0.30 delta ≈ 30% ITM chance).​

Gamma – Stability of Delta

• Meaning: Gamma measures how much delta changes for a 1-point move in the underlying.​

• Behaviour:

  • Highest for at-the-money options, lower for deep ITM/OTM.​

  • Short-dated weekly options show very high gamma, causing fast delta swings.​

• Use cases:

  • Long gamma (buying options) helps in fast markets, as delta moves in your favour quickly.​

  • Short gamma (selling options) is risky near expiry due to sudden P&L swings.​

Theta – Time Decay

• Meaning: Theta is the daily loss in option value from time passing, holding price and volatility constant.​​

• Sign:

  • Long options: negative theta (you lose value each day).​​

  • Short options: positive theta (you earn time decay).​

• Behaviour:

  • Decay accelerates as expiry nears, especially for at-the-money options.​

• Use cases:

  • Income strategies (credit spreads, iron condors) are theta positive.​

  • Intraday scalping is less affected by theta than multi-day option holding.

Vega – Volatility Sensitivity

• Meaning: Vega measures how much the option price changes for a 1% change in implied volatility.​​

• Behaviour:

  • Highest for at-the-money and longer-dated options.​

  • Event days (results, RBI, budget) cause large IV spikes and vega impact.​

• Use cases:

  • Long vega (buying options) benefits from IV increase (e.g., before news).​

  • Short vega (selling options) benefits from IV crush after events.

Rho – Interest Rate Sensitivity

• Meaning: Rho measures change in option price for a 1% change in interest rates.​

• Behaviour:

  • Matters more for long-dated options (LEAPS) than weeklies.​

  • Call options usually gain when rates rise; puts often lose slightly.​

• Use cases:

  • Relevant for portfolio hedging and longer-term positions around rate cycles.​

Greeks in Risk Management

• Position Greeks: Sum of deltas, gammas, thetas, vegas, and rhos across all options gives your portfolio exposure.​

• Practical rules:

  • Keep net delta aligned with your directional view; avoid accidental large one-sided exposure.​

  • Control theta when buying options by not holding too close to expiry without strong momentum.​​

  • Watch vega around high-IV events (e.g., results day for Nifty stocks) to avoid IV crush losses.​

Scenarios ::

1. Delta – Price Sensitivity & Direction

• Example (Nifty Call):

  • Nifty spot = 22,000

  • You buy 22,000 ATM Call at premium = ₹200

  • Delta = 0.50 (typical ATM).​

  • If Nifty goes up 100 points to 22,100, expected option change ≈ 

  • 0.5×100=50

  • 0.5×100=50.

  • New premium ≈ ₹250 (ignoring other Greeks).​

• Example (Bank Nifty Put):

  • Bank Nifty = 48,000

  • You buy 48,000 ATM Put at ₹300, Delta = −0.50.​

  • If Bank Nifty falls 200 points to 47,800, expected option change ≈ 

  • −0.5×−200=+100

  • −0.5×−200=+100.

  • New premium ≈ ₹400.​

Use: Delta shows directional exposure and rough ITM probability (e.g., 0.30 delta ≈ 30% chance of expiring ITM).

2. Gamma – How Fast Delta Changes

• Nifty Call example:

  • Nifty = 22,000, 22,000 Call premium = ₹200

  • Delta = 0.50, Gamma = 0.01.​

  • If Nifty moves up 100 points, Delta increase ≈ 

  • 0.01×100=1.0

  • 0.01×100=1.0.

  • New Delta ≈ 1.50 (theoretical; in practice capped near 1).​

• Interpretation:

  • High Gamma (weekly ATM) → Delta changes very fast; short option sellers can see P&L swing sharply on quick moves.​

  • Low Gamma (far OTM or far ITM) → Delta is more stable.​

Use: For Nifty/Bank Nifty intraday, avoid selling very high‑gamma strikes near expiry unless risk is tightly controlled.​

3. Theta – Time Decay per Day

• Nifty Intraday/Short-term:

  • Nifty = 22,000

  • You buy 22,000 weekly Call at ₹200

  • Theta = −8 per day.​

  • If price and IV stay flat, after 1 day, premium ≈ ₹192.

  • After 3 days, decay ≈ 3 × 8 = 24 → premium ≈ ₹176.​

• Bank Nifty Example:

  • Bank Nifty = 48,000

  • 48,000 weekly Put premium = ₹300, Theta = −12.

  • Each day with no move, you lose ~₹12 per lot on time.​

Use:

• Option buyers must demand strong move quickly to beat theta.​

• Option sellers design theta‑positive strategies (spreads, short straddles) to let time decay work in their favour.​

4. Vega – Impact of Volatility Changes

• Nifty Event Example (Budget / RBI):

  • Nifty = 22,000, 22,000 ATM Call = ₹200

  • Vega = 4 (means ₹4 change per 1% IV move).​

  • IV rises from 15% to 20% (change = +5%).

  • Price gain from volatility ≈ 

  • 4×5=20

  • 4×5=20.

  • New premium ≈ ₹220 plus any intrinsic change from price move.​

• Post‑event IV Crush:

  • Same option, IV falls from 20% to 14% (−6%).

  • Price drop from volatility ≈ 

  • 4×−6=−24

  • 4×−6=−24.

  • Even if Nifty moves slightly in your favour, IV crush can reduce premium.​

Use:

• Before big events: Long options (long vega) can benefit from rising IV.​

• After events: Short vega strategies (spreads, short straddles with hedge) try to profit from IV collapse.

5. Rho – Interest Rate Effect (Mostly for Longer Dated)

• Nifty 6‑month Call:

  • Nifty = 22,000, 22,000 6‑month Call premium = ₹800

  • Rho = 0.40 (₹0.40 per 1% rate change).​

  • If interest rates rise 1%, premium ≈ ₹800 + ₹0.40 = ₹800.40 (small effect).​

Use: For weekly and monthly Nifty/Bank Nifty options, rho impact is negligible; more relevant for LEAPS or when building portfolio‑level hedges.

6. Sample Nifty Trade

Assume:

• Nifty = 22,000, buying 22,000 weekly Call at ₹200

• Greeks: Delta = 0.50, Gamma = 0.015, Theta = −8, Vega = 4.​

Scenario A – Strong Up Move, No IV Change

• Nifty goes to 22,100 (+100).

• Price effect ≈ 

• 0.5×100=+50

• 0.5×100=+50 → ₹250

• Delta adjusts by Gamma: new Delta ≈ 

• 0.50+0.015×100=2.0

• 0.50+0.015×100=2.0 (capped near 1 in reality).​

• 1 day passes: Theta ≈ −8 → final ≈ ₹242 (ignoring gamma non‑linearity).​

Scenario B – No Price Move, 2 Days Pass, IV Falls 3%

• Nifty stays at 22,000.

• Time decay: 2 × 8 = 16 → ₹184

• Vega effect: 

• 4×−3=−12

• 4×−3=−12 → final ≈ ₹172.​

This shows how a buyer can lose even without adverse price moves if time and volatility move against the position.​

When to Buy or Sell Options