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Options Education & Tools

Option Greeks
Calculator

Calculate Delta, Gamma, Theta, Vega and Rho instantly using the Black-Scholes model. Interactive charts show exactly how each Greek behaves as market conditions change.

Δ Delta Γ Gamma Θ Theta V Vega ρ Rho

Black-Scholes Greeks Calculator

Live computation  ·  No server needed
Quick Presets
Option Premium
—
ATM
Intrinsic: ₹0
Time Value: ₹0
Δ Delta
—
₹ per ₹1 move
Γ Gamma
—
Δ per ₹1 move
Θ Theta
—
₹ per day
V Vega
—
₹ per 1% IV
ρ Rho
—
₹ per 1% rate

Greeks vs Spot Price

Theta Decay — Option Value vs Days to Expiry

How premium erodes as expiry approaches

Computed for current inputs. Call (teal) and Put (orange) shown simultaneously. Theta acceleration is visible inside 10 days.

Vega Profile — Option Price vs Implied Volatility

How changing IV affects the premium

Greeks Sensitivity — Spot Price Ladder

Current inputs  ·  ±5 strikes around ATM
SpotMoneynessPrice Δ DeltaΓ GammaΘ Theta/dayV Vega
Options Education

The 5 Option Greeks Explained

Understanding what each Greek measures — and how to use it in your trading decisions.

Δ
Delta
Rate of change of option price w.r.t. spot
Delta tells you how much the option's price changes for every ₹1 move in the underlying. A call with Delta 0.5 gains approximately ₹0.50 if the stock moves up ₹1. Delta also approximates the probability the option finishes in-the-money.

Key ranges: Deep ITM calls approach Δ = 1. Deep OTM calls approach Δ = 0. ATM is typically Δ ≈ 0.5. Put deltas are always negative (-1 to 0).
Call: N(d₁)  ·  Put: N(d₁) − 1
Directional risk Hedge ratio ITM probability
Γ
Gamma
Rate of change of Delta w.r.t. spot
Gamma is the acceleration of Delta. If you're long options, Gamma works in your favour — your Delta increases as the market moves your way. Short options traders fear high Gamma because it makes their Delta exposure unpredictable.

Gamma is highest for ATM options near expiry. This is why weekly expiry options are so explosive — high Gamma means small moves create large P&L swings.
φ(d₁) / (S · σ · √T)
Delta convexity Expiry risk Long = positive
Θ
Theta
Time decay — value lost per day
Theta is the daily erosion of option premium due to the passage of time, assuming everything else is constant. Option buyers fight Theta every day — it's the silent cost of holding options.

Theta accelerates sharply inside the last 10–15 days before expiry. ATM options decay fastest. This is why selling weekly options (theta harvesting) is a popular strategy in Indian markets.
≈ −(S · φ(d₁) · σ) / (2√T) − rKe−rTN(d₂)
Time decay Long = negative Accelerates near expiry
V
Vega
Sensitivity to implied volatility changes
Vega measures how much an option's price changes for a 1% change in implied volatility (IV). Long options have positive Vega — rising IV increases their value. Short options have negative Vega.

This is crucial around events like budget, RBI policy, or earnings — IV spikes before the event and collapses after (IV crush), destroying the value of long options even if the move is in your direction.
S · φ(d₁) · √T / 100
IV sensitivity Event risk Long = positive
ρ
Rho
Sensitivity to interest rate changes
Rho measures the sensitivity of an option's price to a 1% change in the risk-free interest rate. Call options have positive Rho (benefit from higher rates); puts have negative Rho.

In Indian markets, Rho is less impactful than the other Greeks for short-dated weekly options. It becomes more meaningful for longer-dated contracts (1–3 months) especially around RBI policy announcements.
Call: K · T · e−rT · N(d₂) / 100
Rate sensitivity Longer-dated RBI policy
Greeks Relationships
How the Greeks interact with each other
Theta–Gamma relationship: Long Gamma = Short Theta. When you own options with high Gamma (fast Delta changes), you pay for it through Theta decay. This is the fundamental tension in options trading.

Vega–Theta relationship: Both are highest for ATM options. High IV inflates both Vega and Theta simultaneously.

Delta neutrality: A portfolio with net Delta ≈ 0 is directionally neutral — but still has Gamma, Theta and Vega exposure.
Long Γ = Short Θ Delta neutral

See live Greeks on real strikes. The TradePulse option chain shows Delta, Gamma, Theta, Vega and Rho for every strike across NIFTY, BANKNIFTY, SENSEX, stocks and MCX commodities.

Open Live Chain →

How to Use Option Greeks in Indian Markets

Option Greeks are the most powerful risk measurement tools available to derivatives traders. Unlike simply buying or selling an option based on market direction, Greeks let you precisely quantify and manage every dimension of risk in your position.

Delta for directional trades

When you buy a NIFTY call because you expect the index to rise, your effective market exposure is not ₹1 per point — it's Delta × Lot Size. A 50-Delta NIFTY call gives you exposure equivalent to holding 0.5 Nifty futures. Delta hedging — keeping your portfolio delta-neutral by offsetting with futures — is the foundation of professional options market-making.

Using Theta for income strategies

The most popular strategy in Indian retail options trading is selling weekly options to collect Theta. Short straddles, short strangles, and iron condors are all fundamentally Theta harvesting strategies. The risk is Gamma — a large unexpected move can wipe out weeks of Theta collection in a single day. Understanding the Theta/Gamma trade-off is essential before selling options around Indian expiry cycles.

Vega and event-driven trading

India's calendar creates predictable Vega opportunities: RBI policy announcements, Union Budget, quarterly results of index heavyweights like Reliance, HDFC Bank, and Infosys all cause IV to spike before the event and collapse after. Experienced traders sell Vega before the event (expecting IV crush) or buy it weeks before when IV is still low (anticipating the pre-event spike).

Gamma scalping around expiry

Weekly NIFTY and BankNIFTY expiries create extreme Gamma conditions on Thursdays. ATM options with 1–2 days to expiry have very high Gamma, meaning tiny moves in the index create large Delta changes. Gamma scalpers continuously delta-hedge to extract value from this volatility. This is an advanced strategy but understanding Gamma is the prerequisite.

Black-Scholes Model — How the Calculator Works

The calculator on this page uses the standard Black-Scholes-Merton (BSM) model, which is the industry-standard framework for pricing European options. While Indian index options are European-style (can only be exercised at expiry), making BSM directly applicable.

The inputs are: spot price (S), strike price (K), time to expiry in years (T = DTE/365), implied volatility (σ), risk-free rate (r), and dividend yield (q). The model computes d₁ and d₂, then uses the cumulative normal distribution N(·) to price the option and derive each Greek analytically.

Note: BSM assumes constant volatility and log-normal returns. Real markets have volatility skew (OTM puts are more expensive than BSM suggests in Indian markets). Use the calculator as a reference, and cross-reference with the live IV from TradePulse's option chain.

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