Option Greeks Calculator
Key takeaways
- The option is at or out of the money at this spot, so the whole ₹447.86 model price is time value — and time value decays to ₹0 by expiry.
- Delta 0.557935 — a ₹1 rise in the spot moves the model price up by about ₹0.56, and a ₹1 fall moves it down by about the same.
- Theta −8.521338 — one day passing, everything else unchanged, lowers the model price by about ₹8.52 (1.9% of it a day).
- At 16% implied volatility instead of 15%, the model price would be ₹473.33 — ₹25.47 more for one extra point of IV, close to what Vega (25.462139) measures.
Model price across spot prices
Call model price at 30 days to expiry and 15% implied volatility, under the assumptions listed above — a model output, not a quote. The dot marks the spot price entered.
About the Option Greeks Calculator
The Option Greeks Calculator prices a European call or put with the Black-Scholes model and reports the five headline Greeks — Delta, Gamma, Theta, Vega and Rho — the sensitivities describing how the model price would move if the spot, time, volatility or interest rate each moved a little on its own, everything else held fixed.
Every figure on this page is a MODEL PRICE UNDER STATED ASSUMPTIONS, not a quote and not an expectation of profit. The assumptions are: European exercise (settled only at expiry), volatility constant at the level you enter, a frictionless market with no charges or bid-ask spread, and a dividend yield of zero. Real option prices are set by supply and demand and can and do sit away from the model, particularly close to expiry and during sharp moves. Nothing here says an option is cheap, dear, or worth trading.
Enter the spot price, the strike, the days remaining to expiry, the implied volatility (annualised — the market's own estimate of how much the underlying will swing, which you supply; this page does not derive it from history), the annualised risk-free rate, and Call or Put. Time enters the model as days ÷ 365. "Model price" is the Black-Scholes value. "Delta" is the price change per ₹1 move in the spot (0 to 1 for a call, −1 to 0 for a put). "Gamma" is how much Delta itself moves per ₹1 move in the spot, and is the same for a call and a put at identical inputs. "Theta (per day)" is the price change from one day passing alone. "Vega" is the change per one percentage point of implied volatility. "Rho" is the change per one percentage point of the risk-free rate.
JavaScript, like Dart, has no built-in error function, so the model's N(x) term is built from the standard Abramowitz & Stegun rational approximation to erf, with a maximum absolute error of about 1.5 × 10⁻⁷. At index-level prices that leaves the model price within roughly a thousandth of a rupee of an exact-erf implementation; the same approximation is used in the Android app so both platforms print the same number. At zero days to expiry, or zero implied volatility, the model is degenerate — the term σ√T that d₁ divides by is zero — so all six outputs show an em dash together instead of any of them printing a value that does not exist. At expiry an option is worth its plain intrinsic value, which the Options Profit Calculator computes.
Frequently asked questions
What exactly is the "model price"?
It is the Black-Scholes theoretical value of the option at the inputs you entered, under the assumptions listed above — European exercise, constant volatility, no dividends, no charges. It is what the model says, not what the option trades at, and it is not a forecast that the option will be worth this. Market prices differ from it routinely.
What is the formula?
d₁ = [ln(S/K) + (r + σ²/2)T] ÷ (σ√T) and d₂ = d₁ − σ√T. Call = S·N(d₁) − K·e^(−rT)·N(d₂); Put = K·e^(−rT)·N(−d₂) − S·N(−d₁). S is the spot, K the strike, T the time to expiry in years (days ÷ 365), σ the volatility as a decimal, r the risk-free rate as a decimal, and N(x) the standard normal cumulative distribution.
Where do I get the implied volatility to enter?
From the option chain — most brokers and exchanges publish an IV figure per strike. It is the market's own estimate of future movement, backed out of the traded price, and it is an input to this page rather than something the page can derive. Changing it changes every output, which is exactly what Vega measures.
Why is Theta usually negative, and why is it shown per day?
Because an option loses time value as expiry approaches, all else unchanged. The textbook formula is naturally per year; it is divided by 365 here because decay is read day by day. A deep in-the-money European put is the one common case where Theta can be positive: the discounting of the strike can outweigh the time value left.
Why do all six outputs show an em dash sometimes?
Because the model has no answer at those inputs. At 0 days to expiry, or 0% implied volatility, the quantity σ√T that d₁ divides by is zero. Rather than print six numbers derived from a division by zero, the calculator shows an em dash for all of them. At expiry, use the Options Profit Calculator: an option is then worth exactly its intrinsic value.
How accurate is the approximation used for N(x)?
The Abramowitz & Stegun 7.1.26 approximation has a maximum absolute error of about 1.5 × 10⁻⁷ on erf, which works out at roughly 7.5 × 10⁻⁸ on N(x). On the Greeks that is invisible. On a price it is multiplied by the spot, so at a spot of ₹22,500 the model price sits about 0.0008 of a rupee from an exact-erf computation. Both figures are pinned by tests against an independent implementation.
Do the Greeks predict what the option will do?
No. Each one is a partial derivative of the model price: it says how the MODEL's output changes if one input moves slightly and everything else is held still. Real markets move several inputs at once, and the model's own assumptions — constant volatility above all — do not hold. They describe the model, not the future.
Disclaimer: This calculator is for information and education only. It is not investment advice and not a recommendation or a tip, and it does not predict prices. Trading in shares and derivatives carries a risk of loss: futures and sold options are leveraged, and a loss on them can exceed the margin paid. Brokerage differs by broker, and brokerage, taxes and exchange charges change over time. Option prices and Greeks from a model are theoretical, and traded premiums differ. SEBI’s studies found that 93% of individual traders in equity futures and options made losses between FY22 and FY24, and 87.7% did in FY26. Every figure is computed solely by applying the formula and assumptions stated on this page to the inputs you entered.