What each Greek tells you
- Delta – how much the option price moves for a ₹1 move in the underlying. A 0.50 delta call gains about ₹0.50 when spot rises ₹1. It is also a rough probability of expiring in the money.
- Gamma – how fast delta changes. Gamma is highest for at-the-money options close to expiry, which is why expiry-day moves are so violent.
- Theta – time decay per day. Option buyers pay it, option sellers collect it.
- Vega – price change for a 1-point change in implied volatility. Important around results, budgets and elections, when IV rises and then collapses.
- Rho – price change for a 1% change in interest rates. Usually the least important Greek for short-dated options.
The Black-Scholes formula
Call = S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2)Put = K·e^(−rT)·N(−d2) − S·e^(−qT)·N(−d1)d1 = [ln(S/K) + (r − q + σ²/2)·T] ÷ (σ·√T), d2 = d1 − σ·√TS is spot, K strike, T time to expiry in years, σ implied volatility, r the risk-free rate, q the dividend yield and N() the standard normal distribution.
Worked example
Nifty at 25,000, a 25,000 strike expiring in 7 days, IV 13% and a 6% rate gives a call worth about ₹194 and a put about ₹165. Both have delta near ±0.5 and lose roughly ₹11–15 a day to theta. That decay speeds up as expiry gets closer.
Frequently asked questions
Is Black-Scholes accurate for Nifty and Bank Nifty options?
Index options in India are European-style, which is what Black-Scholes assumes, so it is a good fair-value estimate. Market prices still differ because traders price in volatility skew and demand that the model does not capture.
Which volatility should I enter?
Use implied volatility (IV) from your option chain for the same strike and expiry. Using India VIX gives a rough at-the-money estimate for Nifty.
What risk-free rate should I use?
Traders in India typically use the 91-day T-bill yield or the RBI repo rate, around 5.5–7%. The rate has a small effect on short-dated options.
Why is theta shown per day?
Theta is the price an option loses as one calendar day passes, all else equal. Per-day theta is easier to relate to your position than the annual figure the formula produces.
Results are estimates for educational purposes only and are not investment, tax or financial advice. Verify figures with your broker or advisor before acting on them.