Option Premium Calculator

Estimate the theoretical fair value of a CE or PE using the Black-Scholes model — plus the Greeks that explain how the premium will behave.

Option parameters

India 1-year G-Sec yield is a common proxy (about 6%–7%).

Result

Theoretical premium
₹167.14
Intrinsic value ₹0.00
Time value ₹167.14
Delta 0.5332
Gamma 0.00104
Theta (per day) ₹-13.01
Vega (per 1% IV) ₹12.66
Black-Scholes assumes European exercise and constant volatility, so market premiums will differ — especially for weekly index options where volatility is not constant. Use this as a fair-value reference, not a trading signal.

What the Black-Scholes calculator tells you

The Black-Scholes model estimates what an option should be worth given the index level, strike, time left, volatility and interest rates. Comparing that to the market premium tells you whether an option is trading rich or cheap relative to your volatility input.

Reading the Greeks

  • Delta — how much the premium moves per ₹1 move in the index. A 0.52 delta gains about ₹52 on a 100-point move for a 75-lot.
  • Gamma — how fast delta changes. Gamma rises near expiry and near the money.
  • Theta — premium lost to time decay each day, all else equal.
  • Vega — premium change per 1 percentage point change in implied volatility.

Worked example

Spot 23,000, strike 23,000, 7 days to expiry, IV 12%, rate 6.5%: the call and the put both price near their ATM fair value, with delta around 0.5 and theta bleeding a portion of the premium each day. Watch how the premium falls as you reduce days to expiry — that is time decay in action.

Related reading

Common questions

Why is the model premium different from my broker's price?
The model uses your volatility and rate inputs. The market's premium reflects its own volatility expectations, supply and demand, and event risk. Differences are expected — that gap is what you analyse.
Does this work for weekly index options?
It can be used as a reference, but weekly options are American-style in practice (early exercise is possible but rare for index options) and their volatility skew is significant. Treat the output as an approximation.
How do I choose an implied volatility input?
Use the IV the market is currently quoting for a comparable strike and expiry if your platform shows it. For Bank Nifty and Nifty, weekday IV often sits in the low-to-mid teens in calm markets and rises ahead of events.
What risk-free rate should I use?
The India 1-year government securities yield is a reasonable proxy, currently around 6%–7%. Small changes in the rate have a limited effect on short-dated options.

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