🔡 Module 2: Greeks & Time

Option Greeks, theta decay and second-order Greeks

1. The Option Greeks

The Greeks measure the sensitivities of an option to various market parameters. Every options strategy has a characteristic Greeks profile.

The Greeks — 1st & 2nd Order on One Page Cheatsheet

All 9 Greeks (Delta, Vega, Theta, Rho + Gamma, Vanna, Charm, Volga, Color) with formula, intuition, practical rule of thumb and Greeks profiles of typical strategies.

🖨️ As Cheatsheet

Option Sensitivities · The Greek Pantheon

The Five Greeks

Every option premium reacts to several market factors simultaneously. The Greeks measure these sensitivities — and every strategy has its characteristic Greek profile.

ΔDelta

Price Sensitivity

How much does the option premium change when the underlying moves $1? Deep-ITM call has Delta ≈ +1.0, ATM ≈ +0.5, OTM ≈ +0.1. Puts mirror into negative.

Delta Hedging Market makers neutralise delta through offsetting trades in the underlying — a position with Delta 50 is hedged by shorting 50 shares.

ΓGamma

Rate of Change of Delta

How quickly does delta jump when the underlying moves? High gamma = delta changes quickly and unpredictably.

⚠ Gamma Risk ATM options close to expiry have extreme gamma — delta can jump from 0.50 to 0.95. Short-gamma sellers are maximally exposed here.

ΘTheta

Time Value Decay

Daily value loss through passage of time. Negative for buyers (cost per day), positive for sellers (premium income per day).

Decay accelerates In the final 30 days before expiry, theta becomes non-linearly stronger. That's why sellers typically prefer tenors of 30–45 DTE.

VVega

Volatility Sensitivity

Price change per +1% implied volatility. Long vega benefits from rising IV (buyer), short vega from falling IV (seller).

IV-Crush Edge After earnings, IV often collapses by 30–60% → short-vega strategies like iron condor or short strangle draw their edge from exactly this.

ρRho

Interest Rate Sensitivity

Price change per +1% interest rate change. Negligible for short-dated options — noticeable for LEAPS and long-dated positions.

Carry-Cost Effect Rising rates increase call premiums and decrease put premiums — especially relevant for positions with > 12 months to expiry.

Delta Detail: ≈ +1.0 → Deep-ITM call (like 100 shares), ≈ +0.5 → ATM call (50% chance ITM at expiry), ≈ +0.1 → OTM call (10% chance), ≈ −0.5 → ATM put.

Greeks Profiles of Typical Strategies

Strategy	Delta	Gamma	Theta	Vega
Iron Condor	≈0	Short	Long ✅	Short
Long Straddle	≈0	Long	Short ❌	Long
Covered Call	~0.5	Short	Long ✅	Short
Long Call	0–1	Long	Short ❌	Long

📊 Greeks Visualiser

Move the sliders to see how Delta, Theta and Vega of an ATM call option change across the price range. The curves are normalised to their maximum values per Greek — the live values on the right show the actual at-the-money Greeks at S = K.

Strike $100 Days until Expiry 30 DTE Implied Volatility 30%

DeltaPrice reaction per $1 underlying ThetaTime value decay per day (shown positive) VegaReaction to 1% IV change ATMStrike = Underlying

🧮 Margin Calculator

This is how much capital you tie up depending on leverage and position size. For stock options the multiplier is 100 (1 contract = 100 shares).

Leverage (1:X)

Number of Contracts / Shares

Price per Unit ($)

Multiplier (100 for stock options)

Total Position Value — Size × Price × Multiplier

Required Margin — Total Value ÷ Leverage

💡 In sTraderZ.com you can see the Greeks for your open positions under Open Positions → Select Position → Greeks.

2. Theta Decay — Time Value Erosion

When you buy an option, you pay two things: the intrinsic value (how much the option would be worth if it expired immediately) and the time value — a premium for the time remaining during which the price can still move in your favour.

The time value melts every day — this melting is called Theta Decay. The Greek Θ (Theta) measures how much an option loses in value each day purely through the passage of time. The critical point: the decay is not linear. It accelerates massively in the last 30 to 45 days before expiry.

⚡ Theta Acceleration (Theta Cliff): At 90 DTE an ATM option might lose $0.04 per day. At 30 DTE it's $0.10/day. At 7 DTE a single quiet trading day can destroy the same amount as two quiet weeks at 90 DTE. This acceleration is the main reason why sellers love the final 30 DTE — and buyers fear it.

💡 In sTraderZ.com you can see Theta for your open positions under Open Positions → Greeks.

3. Second-Order Greeks — When Delta-Neutral Still Explodes

The first-order Greeks — Delta, Vega, Theta, Rho — tell you how your option price changes when a single variable changes. But they tell you nothing about how the Greeks themselves change. That is exactly what the second-order Greeks do. They are the second derivative of the option price — the sensitivity of the sensitivity.

This sounds academic. In reality, they are the reason so many professionals blow up despite perfect delta hedges. Three of them together lost over $100 billion this way.

💡 For most retail traders it's enough to: always keep an eye on Gamma (especially for short strategies and < 30 DTE), watch Vanna before major news events (vol spikes rotate delta), and track Charm in the final expiry week. Volga and Color are specialist tools — useful, but not daily.

The Most Important Rule

When someone tells you: "My position is delta-neutral, therefore safe" — ask them about their gamma. Ask them about their vanna. Ask them about their vega. If they can't answer any of these three questions, their position is not safe. It just hasn't blown up yet.