Option Greeks - sangramnayak1/derivative_market_backtest GitHub Wiki

Option Greeks – The 5 Key Metrics

1. Delta (Ξ”) – Directional sensitivity

Meaning: How much the option price changes if the underlying (NIFTY/BANKNIFTY) moves by 1 point.

Example:

NIFTY = 20,000

Call option Delta β‰ˆ 0.5

If NIFTY goes up +100 points, the option price increases by 100 Γ— 0.5 = 50 points.

Rule of Thumb:

Calls: Delta between 0 and 1.

Puts: Delta between 0 and -1.

ATM options β†’ Ξ” ~ 0.5

Deep ITM β†’ Ξ” ~ 1

Deep OTM β†’ Ξ” ~ 0

2. Gamma (Ξ“) – Acceleration of Delta

Meaning: How much Delta itself changes if the underlying moves 1 point.

Example:

A NIFTY Call has Delta = 0.5, Gamma = 0.002.

If NIFTY goes up 100 points, New Delta = 0.5 + (100 Γ— 0.002) = 0.7.

Now the option behaves more like the underlying.

Think of Gamma as "steering sensitivity" – higher Gamma means your Delta moves faster.

3. Theta (Θ) – Time decay

Meaning: How much the option loses in value each day due to time passing.

Example:

A BankNifty option premium = β‚Ή200, Theta = -5.

If the market doesn’t move at all, tomorrow the option is worth β‚Ή195 (β‚Ή5 lost just due to time).

Rule of Thumb:

Short sellers love Theta (they earn from decay).

Buyers hate Theta (their option bleeds every day).

4. Vega (Ξ½) – Volatility sensitivity

Meaning: How much the option price changes if Implied Volatility (IV) changes by 1%.

Example:

NIFTY Call = β‚Ή150, Vega = 8.

If IV rises by 5%, option price increases by β‚Ή8 Γ— 5 = β‚Ή40 β†’ new price β‚Ή190.

When events like RBI policy, Elections, or Budget approach β†’ IV rises β†’ options get expensive.

5. Rho (ρ) – Interest rate sensitivity

Meaning: Change in option price if interest rate changes by 1%.

Example:

NIFTY Call Rho = 0.5.

If interest rate rises by 1%, Call increases by 0.5.

Usually small in Indian markets β†’ traders mostly ignore Rho.

πŸ“Š Practical Scenario: BANKNIFTY Weekly Options

Let’s say BankNifty = 45,000, and you buy an ATM 45,000 CE at β‚Ή200. Greeks might look like this:

Greek Value Meaning
Delta 0.5 If BN moves +100, option +50
Gamma 0.004 For 100-point move, Delta jumps from 0.5 β†’ 0.9
Theta -10 You lose β‚Ή10 per lot per day if price doesn’t move
Vega 6 If IV rises 2%, option gains β‚Ή12
Rho 0.1 Almost negligible

πŸ“Š Summary Table

Greek Measures Positive for Impact before Expiry
Delta Price change with stock move Calls ATM β‰ˆ 0.5, ITM β†’ 1, OTM β†’ 0
Gamma Change in Delta Both Highest at ATM, spikes near expiry
Theta Time decay per day Sellers Accelerates near expiry
Vega Volatility sensitivity Buyers Higher for longer expiries
Rho Interest rate sensitivity Calls Minor for short options
Symbol Expiry Strike Spot CE_LTP PE_LTP IV_CE IV_PE Delta_CE Delta_PE Gamma Theta_CE Theta_PE Vega
BANKNIFTY 04-Sep-2025 44500 44610 225.5 230.1 15.2 15.8 0.48 -0.52 0.0012 -15.3 -14.8 22.4
BANKNIFTY 04-Sep-2025 44600 44610 190.3 260.7 15.0 16.1 0.45 -0.55 0.0011 -14.7 -15.0 21.9

Key Insights

  • Delta + Gamma β†’ Directional risk
  • Theta β†’ Time decay risk (always hurts buyers)
  • Vega β†’ Volatility risk
  • Rho β†’ Minor, usually ignored in short-dated trading
  • Before expiry: Gamma & Theta dominate.

πŸ‘‰ Interpretation:

If BN rallies fast β†’ Delta + Gamma make you profit quickly. If BN stays sideways β†’ Theta decay eats your premium. If news increases IV β†’ Vega boosts your option price even without index moving.

πŸ† Golden Rules for Traders

Intraday traders focus on Delta + Gamma. Positional sellers rely on Theta (decay works in their favor). Event traders (Budget, Elections) focus on Vega (IV spikes). Rho is mostly ignored for NIFTY/BANKNIFTY.

Visual chart (Delta/Gamma/Theta curves vs strike) to know how Greeks behave before expiry

CALL Option Greeks

PUT Option Greeks

Put Option Greeks Conceptual Definition

πŸ“Š Long Put Greeks Exposure (Buyer vs Seller)

Greek Buyer of Put (Long Put) Seller of Put (Short Put) Interpretation
Delta (Ξ”) Negative (β‰ˆ –0.50 at ATM) Positive (β‰ˆ +0.50 at ATM) Buyer gains if underlying falls; seller gains if underlying rises.
Gamma (Ξ“) Positive (β‰ˆ +0.02) Negative (β‰ˆ –0.02) Buyer’s Delta becomes more favorable with bigger moves (convexity). Seller’s Delta worsens (concavity).
Theta (Θ) Negative (β‰ˆ –0.05/day) Positive (β‰ˆ +0.05/day) Buyer loses daily to time decay. Seller earns from time decay.
Vega (Ξ½) Positive (β‰ˆ +0.12 per 1% IV) Negative (β‰ˆ –0.12 per 1% IV) Buyer benefits if IV rises (volatility expansion). Seller suffers if IV rises.
Rho (ρ) Negative (β‰ˆ –0.02 per 1% rate) Positive (β‰ˆ +0.02 per 1% rate) Buyer loses slightly if interest rates rise. Seller benefits slightly.

Examples:

1️⃣ Buyer (Long Put)

Spot @ Expiry Payoff = max(K – S, 0) P&L = Payoff – Premium
90 (fall) 10 +6.5 (WIN)
95 (mild fall) 5 +1.5 (WIN)
100 (ATM) 0 –3.5 (LOSS)
105 (rise) 0 –3.5 (LOSS)
110 (big rise) 0 –3.5 (LOSS)

πŸ‘‰ Buyer has limited loss (–3.5) but unlimited profit potential as spot falls.

2️⃣ Seller (Short Put)

Spot @ Expiry Obligation = –max(K – S, 0) P&L = Premium – Obligation
90 (fall) –10 –6.5 (LOSS)
95 (mild fall) –5 –1.5 (LOSS)
100 (ATM) 0 +3.5 (WIN)
105 (rise) 0 +3.5 (WIN)
110 (big rise) 0 +3.5 (WIN)

πŸ‘‰ Seller has limited gain (+3.5) but unlimited downside risk if spot crashes.

3️⃣ Effect of Time Decay (Theta)

  • 10 days to expiry β†’ Premium β‰ˆ β‚Ή3.50
  • 5 days to expiry β†’ Premium β‰ˆ β‚Ή2.20 (loses value fast)
  • At expiry β†’ Premium = intrinsic only

For Buyer:

  • Waiting hurts if spot doesn’t fall (premium decays).
  • Fast move down is needed to win.

For Seller:

  • Waiting helps (collects Theta).
  • Sideways/rising market is perfect.

4️⃣ Effect of Volatility (Vega)

  • At 20% IV β†’ Premium β‰ˆ β‚Ή3.50
  • At 30% IV β†’ Premium β‰ˆ β‚Ή5.00

For Buyer:

  • Higher IV β†’ Premium costlier, but if already holding β†’ option value rises.

For Seller:

  • Higher IV β†’ more risk, mark-to-market loss (must buy back costlier).

βœ… Summary Matrix

Factor Long Put (Buyer) Short Put (Seller)
Spot ↓ (down) Big Profits Big Losses
Spot ↑ (up) Small Loss (premium) Small Gain (premium)
Time Decay Hurts (–Theta) Helps (+Theta)
Volatility ↑ Helps (+Vega) Hurts (–Vega)
Max Loss Premium Paid (β‚Ή3.5) Unlimited (huge if spot crashes)
Max Gain Huge (spot β†’ 0) Limited (β‚Ή3.5)

πŸ“Š ATM Put Greeks & P&L Sensitivity Assumptions

  • Strike = 100
  • Spot = 100 initially
  • IV = 20%
  • Risk-free = 0
  • Lot size = 1
  • Premium at entry β‰ˆ β‚Ή3.50

We’ll track Delta, Theta, Vega and P&L at different spot levels & days-to-expiry.

1️⃣ 10 Days to Expiry (Fresh Trade)

Spot Premium (approx) Delta Theta (per day) Vega Buyer P&L Seller P&L
90 10.20 –0.85 –0.25 +0.20 +6.7 βœ… –6.7 ❌
95 5.40 –0.60 –0.18 +0.15 +1.9 βœ… –1.9 ❌
100 3.50 –0.50 –0.12 +0.12 0 0
105 2.20 –0.30 –0.08 +0.08 –1.3 ❌ +1.3 βœ…
110 1.40 –0.15 –0.04 +0.05 –2.1 ❌ +2.1 βœ…

πŸ”Ή Buyer: Needs quick move down (Delta β‰ˆ –0.5, Vega helps). πŸ”Ή Seller: Happy if sideways/up, collects Theta.

2️⃣ 5 Days to Expiry (Theta Accelerates)

Spot Premium Delta Theta Vega Buyer P&L Seller P&L
90 10.00 –0.90 –0.45 +0.12 +6.5 βœ… –6.5 ❌
95 5.00 –0.65 –0.30 +0.09 +1.5 βœ… –1.5 ❌
100 2.20 –0.50 –0.25 +0.07 –1.3 ❌ +1.3 βœ…
105 0.80 –0.20 –0.15 +0.03 –2.7 ❌ +2.7 βœ…
110 0.20 –0.05 –0.08 +0.01 –3.3 ❌ +3.3 βœ…

πŸ”Ή Time decay really hurts buyer if spot stays flat. πŸ”Ή Seller’s P&L accelerates (Theta crush).

3️⃣ Expiry Day (Only Intrinsic Value Left)

Spot Premium Delta Theta Vega Buyer P&L Seller P&L
90 10.00 –1.0 0 0 +6.5 βœ… –6.5 ❌
95 5.00 –1.0 0 0 +1.5 βœ… –1.5 ❌
100 0.00 0 0 0 –3.5 ❌ +3.5 βœ…
105 0.00 0 0 0 –3.5 ❌ +3.5 βœ…
110 0.00 0 0 0 –3.5 ❌ +3.5 βœ…

πŸ”Ή Buyer’s time value = 0 β†’ only intrinsic matters. πŸ”Ή Seller wins max premium if spot β‰₯ strike.

Key Takeaways

  • Delta β†’ moves toward –1 if spot drops ITM, 0 if OTM.
  • Theta β†’ explodes near expiry; buyer bleeds if spot doesn’t move.
  • Vega β†’ only matters when time > 0; vanishes at expiry.
  • Buyer β†’ asymmetric bet: small fixed loss, big potential win.
  • Seller β†’ insurance provider: small fixed gain, big potential loss.

Practical takeaways for traders

  • Long put = negative Delta (benefit from falls), positive Vega (benefit from IV spikes), negative Theta (loses with time).
  • Sellers of puts have the opposite exposures: they collect Theta (time decay), are short Vega (hurt by IV rises), and short Delta (hurt if market falls).
  • Gamma matters for big moves: buyers of options get convexity (benefit grows faster as the underlying moves), sellers have to manage gamma risk.
  • For intraday traders: Delta & Gamma dominate immediate P&L.
  • For event trades (earnings, RBI), Vega matters: IV moves can change option prices even with small underlying moves.
  • Use Greeks together: e.g., if you buy a put before an event you want: (a) enough Delta/Gamma to profit from expected move, and/or (b) positive Vega if you expect IV to rise. But you must pay Theta.

Popular Option Strategies:

  • Long Straddle
  • Short Straddle
  • Long Strangle
  • Short Strangle
  • Bull Call Spread
  • Bear Put Spread
  • Iron Condor
  • Covered Call
Option Instrument Strike Price Option Instrument Strike Price Option Instrument Reward Risk
CALL 24750 217.75 PUT 24700 168.00 Buy 0.6 0.3
CALL 24800 194.85 PUT 24750 193.00 Sell 0.75 0.75
Strategy Instrument Type Strike Price Qty P Margin Profit P Exit L Margin Loss SL Exit Margin Week View At Support Support Strike
Bull Put Spread PUT Buy 24700 168.00 75 100.8 7,560.00 294.00 50.4 3,780.00 117.60 54,140.00 Bullish
PUT Sell 24750 193.00 75 144.75 10,856.25 48.25 144.75 10,856.25 337.75
Bull Call Spread CALL Buy 24750 217.75 75 130.65 9,798.75 381.06 65.325 4,899.38 152.43 54,366.00 Bearish
CALL Sell 24800 194.85 75 146.13 10,960.31 48.71 146.13 10,960.31 340.99
Call Back Spread CALL Sell 24750 217.75 75 130.65 12,248.44 54.44 65.325 12,248.44 381.06 67,037.00
CALL Buy 24800 194.85 150 146.13 17,536.50 340.99 146.13 8,768.25 136.40
Call Front Spread CALL Buy 24750 217.75 75 130.65 9,798.75 381.06 65.32 4,899.38 152.43 2,65,981.00
CALL Sell 24800 194.85 150 146.13 21,920.63 48.71 146.13 21,920.63 340.99
Bear Call Spread CALL Sell 24750 217.75 75 163.31 12,248.44 54.44 163.31 12,248.44 381.06 54,366.00
CALL Buy 24800 194.85 75 116.91 8,768.25 340.99 58.45 4,384.13 136.40
Bear Put Spread PUT Sell 24700 168.00 75 126 9,450.00 42.00 126 9,450.00 294.00 54,140.00
PUT Buy 24750 193.00 75 115.8 8,685.00 337.75 57.9 4,342.50 135.10
Put Back Spread PUT Buy 24700 168.00 150 126 15,120.00 294.00 126 7,560.00 117.60 67,037.00
PUT Sell 24750 193.00 75 115.8 10,856.25 48.25 57.9 10,856.25 337.75
Put Front Spread PUT Sell 24700 168.00 150 126 18,900.00 42.00 126 18,900.00 294.00 2,55,481.00
PUT Buy 24750 193.00 75 115.80 8,685.00 337.75 57.9 4,342.50 135.10