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Option Premium Calculator
Calculate option premiums using the Black-Scholes model and analyze the Greeks for better trading decisions.
Option Parameters
Premium Breakdown
Greeks Analysis
Profit & Loss at Expiry
Option Details
Market Parameters
How Option Premium is Calculated
This calculator prices call and put options using the Black-Scholes model, which combines the spot price, strike price, time remaining to expiry, expected volatility and the risk-free interest rate into a theoretical fair value for the option.
Premium = S × N(d1) − K × e^(−r×T) × N(d2)
Formula Used (Put Option): Premium = K × e^(−r×T) × N(−d2) − S × N(−d1)
where d1 = [ln(S/K) + (r + σ²/2)×T] / (σ×√T), d2 = d1 − σ×√T, S = spot price, K = strike price, T = time to expiry (in years), σ = annual volatility, r = risk-free rate, and N() is the cumulative standard normal distribution function.
Premium = Intrinsic Value + Time Value, where Intrinsic Value is the payoff if exercised today and Time Value reflects the remaining chance of further favourable price movement before expiry.
Understanding the Greeks
Delta (Δ)
Measures how much the option price changes for a ₹1 change in the underlying price. Call options have positive delta (0 to 1), put options have negative delta (-1 to 0).
Gamma (Γ)
Measures how much delta changes for a ₹1 change in the underlying price. Higher gamma means delta is more sensitive to price movements.
Theta (Θ)
Measures time decay - how much the option loses value each day. Usually negative for long options, representing daily value loss.
Vega (ν)
Measures sensitivity to volatility changes. A 1% increase in implied volatility will change the option price by the vega amount.
Important Notes:
- • This calculator uses the Black-Scholes model which assumes constant volatility and interest rates
- • Real option prices may differ due to market factors like liquidity, demand/supply, and dividends
- • Greeks change as market conditions change - they are not constant
- • American options (which can be exercised early) may have different values than European options
- • Consider transaction costs, bid-ask spreads, and brokerage when trading options
- • Options are leveraged instruments with potential for 100% loss of premium paid
- • This calculator is for educational purposes only and not financial advice
Option Premium Calculator FAQs
What is the Black-Scholes model used in this calculator?
The Black-Scholes model is a widely used mathematical formula for pricing European-style options. It estimates a theoretical 'fair value' premium using the spot price, strike price, time to expiry, volatility and the risk-free interest rate, assuming constant volatility and no dividends during the option's life.
What do the option Greeks (Delta, Gamma, Theta, Vega) tell me?
Delta shows how much the premium moves per ₹1 change in the underlying, Gamma shows how fast Delta itself changes, Theta shows the daily time decay in the option's value, and Vega shows sensitivity to a 1% change in implied volatility. Together they help traders understand and manage the risk of an options position.
Why might the actual market premium differ from the calculated premium?
Real market premiums are driven by live supply and demand, bid-ask spreads, dividends, interest rate expectations and the fact that Indian index/stock options can behave differently near expiry due to liquidity. The Black-Scholes premium is a theoretical fair value estimate, not a guaranteed market price.
What does it mean if an option is In-the-Money, At-the-Money or Out-of-the-Money?
In-the-Money (ITM) means the option has intrinsic value if exercised today, At-the-Money (ATM) means the strike is approximately equal to the spot price, and Out-of-the-Money (OTM) means the option currently has no intrinsic value — its entire premium is time value that decays as expiry approaches.
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