Option premium sensitivity tool

Quick answer: The premium sensitivity tool prices an option under Black–Scholes and decomposes what moves it: delta for a move in the underlying, gamma for the change in delta, vega for a one-point change in implied volatility, and theta for one calendar day of decay.

How this calculator works

Premium is mostly volatility, for an out-of-the-money option

An in-the-money option has intrinsic value that no change in volatility can touch. An at-the-money option's premium is very nearly a straight line in implied volatility: double the IV and you roughly double the price. An out-of-the-money option has NO intrinsic value at all — its entire price is a bet on volatility. Buying out-of-the-money options is therefore not primarily a directional trade; it is a volatility trade wearing directional clothing, and it is the most common way to be right about direction and still lose money.

Vega grows with √T; gamma shrinks with it

A 120-day at-the-money option carries roughly four times the vega of a 7-day one, because vega scales with the square root of time to expiry. Gamma does the opposite, scaling with one over that square root. So a bet on the LEVEL of implied volatility is a long-dated trade, and a bet on realised MOVEMENT is a short-dated one. Saying you are 'long volatility' without saying which of these you mean is not a statement.

Theta is the rent on gamma

Theta and gamma are two descriptions of the same trade: θ ≈ −½ Γ S² σ². Every rupee of decay a seller collects is convexity they are short, and the rent rises exactly when the risk does. Raise implied volatility from 10% to 30% on a 30-day at-the-money NIFTY call and its theta rises from about ₹6.90 a day to about ₹15.81 — which looks like a better deal for a seller until you notice that the underlying is now expected to move proportionally further every day too, so the gamma losses that theta is compensating for have grown in the same proportion.

The Greeks are derivatives, and derivatives are local

Delta tells you the effect of a small move. It is wrong for a large one, and gamma is the first correction to that wrongness. Vega tells you the effect of a one-point change in implied volatility, assuming every other strike's implied volatility stays put — which the skew guarantees it will not. Every number this tool produces is a first-order statement about a world that is not first-order.

Using it, step by step

1. Enter spot, strike, implied volatility, calendar days and the option type.
2. Read the premium, then read the Greeks beneath it. All are per unit of the underlying.
3. Multiply by the lot size to get rupees per lot. The tool does this for you.
4. Look at the premium at IV plus and minus five points. That is what an IV crush or an IV expansion actually costs, with everything else held still.
5. Now change the days to expiry to 5 and watch vega collapse while gamma explodes. That single experiment explains most of what happens on a NIFTY weekly expiry day.

Worked example

Assumptions and limitations

• Black–Scholes–Merton for a European option, zero dividend yield. Correct for NIFTY and BANKNIFTY index options; an approximation only for Indian single-stock options, which are American-style and physically settled.
• Volatility is assumed constant across strike and time. The skew and the term structure both say otherwise, so the vega reported here assumes a parallel shift of the whole surface, which never happens.
• The Greeks are first derivatives. They describe SMALL changes. For a large move in the underlying, delta plus gamma is still only a second-order approximation.
• Theta is per calendar day and assumes the underlying does not move. On any real day, delta and gamma effects are typically larger than theta and swamp it.
• Vega is per one percentage point of implied volatility, the trading convention. Some sources quote it per one full unit (100 points), which is a factor of 100 different.

Common mistakes

• Reading theta as guaranteed daily income. Theta is never free money — it is the rent the market pays you for holding an inventory of risk, and the rent rises exactly when the risk does.
• Assuming a rise in implied volatility will make a long option profitable. On a short-dated option vega is small and theta is not, so a genuine IV rise can be entirely consumed by decay.
• Using vega to size a position across two underlyings. A book that is 'vega neutral' across NIFTY and BANKNIFTY is not hedged, because their implied volatilities do not move one for one.
• Applying the Greeks to a large move. Delta is a local statement; on a 3% gap it is simply wrong, and gamma only partly repairs it.
• Forgetting that all figures are per unit. Multiply by 75 for NIFTY or 30 for BANKNIFTY before deciding anything looks small.

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Last reviewed 10 July 2026. Educational content only — not investment advice.