Krishna Rungta
Greeks Cheat Sheet 📋
A quick reference to the five Greeks. The example values are for our bought 22,500 CE, per option unit.
| Greek | What it measures | Typical position sign | Our 22,500 CE |
|---|---|---|---|
| Delta Δ | Premium change for a 1-point NIFTY move | Bought call +; bought put −. Selling reverses the sign. | +0.533 |
| Gamma Γ | Delta change for a 1-point NIFTY move | Buyer +; seller − | +0.000763 per point |
| Theta Θ | Premium change as one calendar day passes | Usually buyer −; seller + | −₹12.30 per day |
| Vega ν | Premium change for a 1-percentage-point IV rise | Buyer +; seller − | +₹14.81 per IV point |
| Rho ρ | Premium change for a 1-percentage-point rise in the model rate | Bought call +; bought put −. Selling reverses the sign. | +₹3.22 per rate point |
NIFTY and strike 22,500 · 10 calendar days to expiry · IV 14% · model rate 6% · zero dividends. One NIFTY lot is 65 units. Figures above are rounded per-unit model sensitivities, not guaranteed price changes. Greeks change with market inputs; theta can have exceptions.
You bought a NIFTY call. NIFTY went up. Your call went down. If that has happened to you (or you want to make sure it never does), this article is for you. Nothing was broken and nobody cheated you. An option premium answers to four separate forces at once: where the underlying is, how much time is left, how nervous the market is, and (a little) where interest rates sit. The option Greeks are simply the dials that measure each force. Read the dials and the “mystery” moves stop being mysterious.
Think of a car dashboard. The speedometer tells you how fast you are going (delta), the accelerator pedal changes that speed (gamma), the fuel gauge drops even while you idle at a signal (theta), and the weather outside decides how expensive the trip feels (vega). Rho is the uncle in the back seat commenting on petrol prices: technically relevant, rarely decisive.
By the end you will be able to look at any option chain and say, with numbers, what should happen to a position if NIFTY moves 100 points, if a day passes, or if the market panics before a budget. Every calculator on this page is live. Drag things. Break things. The quiz at the bottom will tell you whether it stuck.
NIFTY is at 22,500 (an illustrative level; the maths works at any level). One NIFTY lot is 65 units on the NSE (since 30 December 2025; it was 75 before that) and NIFTY weekly options expire on Tuesday.
Our option is the 22,500 CE (an at-the-money call) with 10 days to expiry and implied volatility of 14%. The model gives ₹226.8304 per unit, or ₹14,743.97 per lot, with delta +0.532885, gamma 0.000762548 per index point, theta −₹12.2986 per calendar day, vega ₹14.8070 per IV percentage point and rho ₹3.22 per interest-rate percentage point. Calculations use full precision; displayed values are rounded independently, and simpler examples below explicitly use rounded or fixed Greeks.
Prices are from the Black-Scholes model, the same model every calculator on this page uses. Real quotes and sensitivities can differ because the inputs and market conditions differ.
Options in 60 Seconds (So the Greeks Make Sense) ⏱️
A pizza costs ₹100 today. You pay the shop ₹5 for a coupon that says: “next Tuesday, I may buy one pizza for ₹100, no matter what it costs then.” If pizza is ₹150 next Tuesday, your ₹5 coupon is worth ₹50 (you buy at 100, it is worth 150). If pizza is ₹80, you throw the coupon away and lose ₹5. That coupon is a call option. A coupon that lets you sell at a fixed price is a put option.
Swap pizza for NIFTY and the vocabulary is the same:
- Premium: the ₹5. The price of the option. Everything on this page is about what makes the premium move.
- Strike: the ₹100. The fixed price written on the coupon (22,500 in our example).
- Expiry: next Tuesday. After this the coupon is worthless.
- Lot: you cannot buy one unit. NIFTY options trade in lots of 65 units, so a ₹227 option costs ₹227 × 65 = ₹14,755 per lot.
- Buyer vs seller: somebody sells (writes) you that coupon and collects the ₹5. Whatever the buyer gains, the seller loses, and vice versa. Most Greeks simply flip sign between the two.
- ITM / ATM / OTM: a call is in-the-money when NIFTY is above the strike (the coupon is already useful), at-the-money when NIFTY is at the strike, and out-of-the-money when NIFTY is below it (useful only if NIFTY rises). Puts are the mirror image.
- Intrinsic value vs time value: an ITM 22,000 call with NIFTY at 22,500 has ₹500 of real, exercise-today value (intrinsic). Anything you pay above that is time value: the price of hope that things get even better before expiry. Our ATM 22,500 CE at ₹227 is 100% time value.
Four things move a premium: the underlying price, time, implied volatility (how big a move the market is pricing in) and interest rates. Each Greek answers one question: “if this one thing changes by one unit and nothing else changes, what happens to my premium?” That “nothing else changes” clause is important, and we will come back to it when we put the Greeks together.
Meet the Greeks: Your Option’s Dashboard 🎛️
Here is the cast, with the numbers for our 22,500 CE. Do not memorise formulas yet. Learn the story each one tells: what changes, which dial reacts, who benefits.
Explore the five Greeks
Watch each sensitivity, then open its extra tips.
Our example: 22,500 CE · 10 calendar days · option IV 14%.
Your device requests reduced motion, so the illustrations are still. Every explanation and example remains available.
Delta
“If NIFTY moves one point, how much does my option premium move?”
NIFTY +100 points → about +₹53.29 per unit, or +₹3,463.75 per lot.Starting-delta estimate only; gamma changes delta during the move.
- Range
- Long calls: 0 to +1
Long puts: −1 to 0 - Buyer / seller
- Direction depends on call versus put; selling reverses that option’s delta.
Moneyness, probability and a useful tip
- Typical call deltas: ATM about 0.50; deep ITM often 0.90 or higher; far OTM can be around 0.10 or lower. These are examples, not fixed cutoffs.
- Delta is a rough moneyness indicator. In our zero-dividend model, call delta is N(d1); risk-neutral ITM probability is N(d2). Neither is a realised trading win rate.
- One lot’s starting delta exposure is about +34.64 NIFTY-equivalent units. A long put has negative delta; a short call also has negative delta.
Gamma
“How fast does my delta change as NIFTY moves?”
NIFTY +100 points: delta goes from 0.5329 to 0.6079 in the model.Full model comparison at fixed time and IV. Initial linear delta change ≈ +0.0763.
- Sign
- Positive for an individual long vanilla option; negative for a short one.
- Largest near
- At-the-money, close to expiry; 0DTE delta can change rapidly.
Expiry-day spikes and reversal risk
Gamma is often concentrated near the strike as expiry approaches. This is why small underlying moves can rapidly change the sensitivity of a short-dated option.
It can amplify the change in premium relative to a fixed-delta estimate, but no fixed “10×” return follows from gamma. A reversal can erase a long call’s gains, and an option can lose its entire premium. A portfolio’s net gamma depends on all its legs.
Reprice after a large move: gamma changes too. Never force an invalid linear delta estimate back into range by simply capping it at 1.
Theta
“How much can the premium change just because time passes?”
About −₹799.41 per lot per calendar day at this snapshot.Instantaneous daily rate. Repricing 10 → 9 days gives a loss of about ₹12.57 per unit.
- Typical signs
- Buyer: negative
Seller: positive - Shape
- For short-dated ATM options, decay generally steepens near expiry, especially in the final week.
Time decay, sellers and the final week
Time usually works against a long option’s time value and in favour of the corresponding short option, with all other inputs fixed. Positive theta is not guaranteed daily profit: a price move or IV rise can outweigh it.
Theta’s sign can differ for some options and portfolios. The model uses calendar time, but a market price change over a weekend is not simply a guaranteed multiple of Friday’s theta.
A daily theta rate near expiry is not an amount you can lose in every remaining hour. Time value cannot decay below the remaining premium.
Vega
“If this option’s IV rises one percentage point, how much does its premium change?”
IV 14% → 15%: estimated premium change +₹14.81 per unit, or +₹962.46 per lot.One IV point means one percentage point. The option’s own IV is used, not India VIX.
- Sign
- Positive for a long vanilla option; negative for the corresponding short.
- Largest near
- At-the-money, with more time remaining, all else equal.
Before events, after events and IV crush
IV can rise before budgets, company results or policy decisions as uncertainty increases, and can fall after the event. For NIFTY, use a market-wide event; company earnings are a stock example.
An option’s IV falling from 24% to 14% is a drop of 10 percentage points, or about 42% relative to its starting IV. A 30–60% relative IV decline is an illustrative possibility, not a standard event outcome or a fixed premium loss.
You can be right on the underlying’s direction and still lose if an IV decline and time decay outweigh the directional gain. Higher IV alone does not make selling profitable.
Rho
“If the model’s interest rate changes one percentage point, how much does my premium change?”
Estimated change: +₹209.48 per lot for a one-percentage-point rate rise, about 1.4% of the option premium.Other inputs fixed. A rate cut reverses the estimated sign.
- Sign
- Long call: positive · long put: negative. Selling reverses the sign.
- Matters more
- For longer-dated options; often a smaller exposure for weeklies.
When should I pay attention to rho?
Rho is usually less prominent than delta, gamma, theta and vega for short-dated options, but it is not zero. It becomes more important over longer maturities.
A central-bank policy announcement does not necessarily change a model’s risk-free rate input one-for-one. Use the relevant rate assumption, and assess its effect with the other Greeks.
Illustrative European Black-Scholes examples. Rupee sensitivities are per unit unless a lot is specified; one NIFTY lot is 65 units. Figures are rounded independently from full-precision calculations. Animations explain the concepts; their shapes and timing are not forecasts or market data. Each Pause control keeps its own state when you scroll away and return.
Four of these matter every day; rho mostly matters for options that expire months away. We will take them in the order most traders feel them: delta (direction), gamma (acceleration), theta (time), vega (fear), then a short word on rho. After that comes the part most guides skip: how they act together.
Delta (Δ): The Speedometer 🚗
What delta tells you
Delta is how many rupees the premium moves when NIFTY moves one point. Our 22,500 CE has a delta of 0.53. NIFTY rises 100 points; the premium rises about 0.53 × 100 = ₹53 per unit, so ₹53 × 65 = ₹3,445 per lot. NIFTY falls 100 points; the premium drops by roughly the same amount.
A useful way to say the same thing: delta is the fraction of the underlying’s move that your option “copies”. A 0.53-delta call copies about half of every NIFTY move. Multiply by the lot and you get your equivalent exposure: 0.53 × 65 ≈ 34.5 NIFTY units. Owning that one lot of calls feels, for small moves, like owning 34.5 units of NIFTY, for a fraction of the money.
Calls have positive delta, puts have negative delta
The 22,500 PE (the put at the same strike) has a delta of −0.47. NIFTY rises 100; the put loses about ₹47 per unit. NIFTY falls 100; the put gains ₹47.
The sign matters
Same option. Opposite position.
Change the trade and NIFTY move. This isolates delta using the rounded +0.53 call delta and −0.47 put delta from the text.
Selling flips the position delta. The option gets more expensive to buy back, so the seller loses.
A first-order estimate with delta held fixed. Gamma, time, IV, rates and trading costs are excluded. Selling reverses the position exposure; it does not reverse the option’s quoted premium move.
A neat check for any strike: call delta − put delta = 1 (0.53 − (−0.47) = 1.00). That is put-call parity doing its job.
| Moneyness (10 days left) | Call delta | Put delta | What it feels like |
|---|---|---|---|
| Deep ITM (22,500 strike, NIFTY at 23,500) | ≈ 0.97 | ≈ −0.03 | The call moves almost one-for-one with NIFTY, like a cheaper future |
| ATM (NIFTY at 22,500) | ≈ 0.53 | ≈ −0.47 | Copies about half the move; maximum uncertainty about where it ends |
| OTM (NIFTY at 22,000) | ≈ 0.19 | ≈ −0.81 | The call barely reacts; it needs a big rally before it starts “working” |
| Far OTM (NIFTY at 21,500) | ≈ 0.03 | ≈ −0.97 | The call is a lottery ticket: cheap because it almost never pays |
Try it: move NIFTY and watch the premium
🚗 Try it: move NIFTY, watch the premium
Δ +0.50 call · Δ −0.50 put · lot = 65Delta is held at exactly 0.50 here so the rule of thumb is visible: premium change ≈ delta × points moved. In real life delta drifts as NIFTY moves. That drift is gamma, coming up next.
Delta changes with moneyness
Delta is not a fixed property of an option. It depends on where NIFTY is relative to the strike, and it traces an S-shaped curve: near zero far out-of-the-money, around 0.5 at-the-money, near 1 deep in-the-money. That curve explains a classic beginner disappointment: the ₹55 OTM call that barely moved when NIFTY rallied 100 points. With a delta of 0.19 it was only ever going to capture ₹19 of that move.
Delta by moneyness: the S-curve
Delta as a rough probability
Absolute delta is sometimes used as a rough indicator of moneyness probability. In this zero-dividend Black-Scholes model, call delta is N(d1), while the risk-neutral probability of expiring in the money is N(d2). For the master call they are 53.29% and 52.37%, respectively. Neither is the real-world probability of a profitable trade. Premium, costs, exits and loss size matter: a 0.15–0.20 delta does not establish an 80–85% trading win rate.
Delta works identically, per $1 of stock move and per share. A standard US equity contract covers 100 shares, so a 0.50-delta call gains about $50 per contract when the stock rises $1. Index options such as SPX use a $100 multiplier, so SPX up 10 points × 0.50 delta × $100 = $500 per contract.
Gamma (Γ): The Accelerator 🚀
What gamma tells you
Gamma is how much delta changes when NIFTY moves one point. It is the speed of the speed. Our 22,500 CE has a gamma of 0.0008 per point. NIFTY rises 100 points; delta climbs from 0.53 to about 0.61. Rise another 100 and delta is 0.68. Each additional 100 points earns you more than the previous 100, because the option is turning into a higher-delta option as it goes.
That is why a delta-only estimate undershoots on the way up and overshoots on the way down. For a +300 move, delta alone predicts 0.53 × 300 = ₹160; add the gamma term ½ × 0.0008 × 300² = ₹36 and you get ₹196, which is within a few rupees of the fully repriced model change (₹193). For a −300 move the same gamma term softens the loss: ₹160 predicted, ₹126 actual. Owning options means your profits accelerate when you are right and your losses decelerate when you are wrong. That asymmetry is what the premium pays for.
A note on scale, because this trips people up: gamma on NIFTY is a small number (0.0004 to 0.005) because it is per index point and NIFTY has five digits. On a ₹2,000 stock the same option might show gamma of 0.01 per rupee. Never compare raw gammas across underlyings; compare “how much does delta change on a 1% move” instead.
Why expiry day is wild
Gamma is highest at-the-money and it grows as expiry approaches. With 30 days left, a 100-point move nudges our ATM delta by 0.04. With one day left it jumps by 0.24. In the final afternoon it can swing by 0.5 on the same move: a ₹33 option becomes ₹105 if NIFTY rallies 100 points, or ₹5 if it drops 100. That is the “zero to hero” expiry-day story, and its quieter twin, “hero to zero”.
Gamma spikes at-the-money as expiry approaches
Try it: how fast does delta change?
🚀 Try it: how fast does delta change?
ATM 22,500 CE · IV 14% · lot = 65Plenty of time left: gamma is gentle, delta drifts slowly.
Long gamma vs short gamma
Buyers are long gamma: the market moving, in either direction, bends the position in their favour. Sellers are short gamma: the same move bends the position against them, and the bend gets sharper the closer the option is to the strike and to expiry. This is why an option seller who is comfortably ahead at 1 pm on expiry Tuesday can be badly behind by 3 pm. Gamma is the price sellers pay for theta, which is up next.
One more thing the textbooks gloss over. You will see examples like “delta 0.5 plus gamma 0.05 times a ₹10 move = delta 1.0”. In reality gamma itself shrinks as the option goes deep in-the-money, so delta glides toward 1 and never crosses it. Delta is bounded between 0 and 1 (or −1 and 0 for puts) no matter how big the move. If your arithmetic takes delta past 1, you have stretched a straight-line estimate too far.
Theta (Θ): The Melting Ice Cube 🧊
What theta tells you
Theta is how many rupees the premium loses per day if nothing else changes. Our 22,500 CE has a theta of −₹12.3. Tomorrow, with NIFTY exactly where it is and IV unchanged, the ₹227 option is worth about ₹215. Per lot that is −₹800 a day for doing nothing. Buyers pay theta. Sellers collect it: the person who sold you that call shows +₹12.3 of theta and earns ₹800 a day for the same nothing.
Why does an option lose value just because the clock moved? Because time value is the price of possibility. Ten days gives NIFTY plenty of room to rally above 22,500; one day gives it very little. Less possibility, lower price. The intrinsic part (if any) does not decay; only the time value does.
Theta is not a straight line
Here is how our ATM call melts if NIFTY never moves:
| Days left | 14 | 10 | 7 | 5 | 3 | 1 | Last 6 hours |
|---|---|---|---|---|---|---|---|
| ATM 22,500 CE value | ₹273 | ₹227 | ₹187 | ₹156 | ₹120 | ₹68 | ₹33 |
| Instantaneous theta (₹ per calendar day) | −₹11 | −₹12 | −₹14 | −₹17 | −₹21 | −₹35 | −₹68 |
Theta accelerates. In this model, repricing from 10 to 9 days reduces the premium by ₹12.57, while the starting theta is −₹12.30 per calendar day. With six hours left, premium is ₹33.35 and instantaneous theta is −₹67.63 per day: only the remaining ₹33.35 can disappear by expiry if NIFTY stays at the strike. A daily rate is not a six-hour loss. Drag the slider below to compare the curve with the current rate.
🧊 Try it: watch the ice cube melt
ATM 22,500 CE bought with 14 days left · IV 14% · lot = 65Time value is not a straight line. It melts slowly at first, then collapses in the final few days. The OTM option has nothing but time value, so it goes to zero.
In this short-dated example, near-the-money options have substantial time value and large negative theta. Theta also depends on rates, dividends and moneyness; a deep-ITM European put can have positive theta. An OTM option can lose its entire remaining premium.
The weekend trap
This model uses calendar time, so a weekend reduces the time remaining. Friday-to-Monday market prices also reflect spot, the option’s IV, liquidity and how participants price non-trading days. The observed change is not guaranteed to equal Friday’s theta multiplied by three. The same distinction applies to exchange holidays.
How many points per day do you need just to break even?
At this snapshot, −Θ/Δ ≈ 23.08 NIFTY points per calendar day offsets the call’s theta in a first-order estimate with IV and rates fixed. It is not a guaranteed breakeven move or a constant daily target. With spot and IV held fixed, the ratio becomes about 27.15 with seven days remaining, 40.28 with three days and 68.09 with one day. Recalculate after changes and use full model repricing for a finite scenario; include costs separately.
Theta is quoted in dollars per day per share (multiply by 100 per contract). SPX and the big ETFs have expirations every trading day, so “0DTE” options exist on any day you like; their theta and gamma are the extreme end of everything in this section.
Vega (ν): The Fear Thermometer 🌡️
What vega tells you
Vega is how many rupees the premium changes when the option’s own implied volatility (IV) moves by one percentage point. IV is inferred from that option’s market price using a pricing model. Different strikes and expiries can have different IVs. India VIX is a separate, annualised 30-calendar-day volatility measure derived from a range of NIFTY option prices; its change cannot automatically be substituted for this option’s IV change.
Our 22,500 CE has a vega of ₹14.8. If IV climbs from 14% to 17% with NIFTY unmoved, the premium rises about 3 × 14.8 = ₹44 per unit, or ₹2,900 per lot, for a market that did nothing. If IV falls three points, the same ₹2,900 vanishes. Vega is not a Greek letter, by the way; the name stuck anyway.
Try it: turn the fear dial
🌡️ Try it: turn the fear dial
ATM 22,500 CE · 10 days to expiry · lot = 65NIFTY has not moved at all in this widget. Only the market’s nervousness changed, and the premium changed with it. That is vega.
IV crush: right on direction, still lost money
IV behaves like a balloon around scheduled events. It inflates in the days before (uncertainty is high, everyone wants protection or a punt) and pops the moment the news is out (uncertainty is gone). The pop is called IV crush, and it is the most expensive lesson in options.
In a hypothetical NIFTY scenario before a scheduled market-wide event, such as a policy announcement, you buy our 22,500 CE with five days left and IV pumped up to 24%. It costs about ₹261. Assume one calendar day passes, NIFTY rallies 100 points and this option’s IV falls to 14%. The assumed IV decline is illustrative, not a forecast. The call is now worth ₹197. You were right on direction and lost ₹64 per unit, ₹4,180 per lot. Delta gave you ₹52; vega took away ₹105; theta took another ₹27 overnight. Play with the sliders and find out how big the move had to be to beat the crush.
💥 IV crush simulator: right on direction, still lost?
Hypothetical NIFTY policy-event scenario · buy ATM 22,500 CE with 5 days left · lot = 65Right on direction, still lost ₹4,180 per lot. Vega took ₹105 per unit while delta only gave +₹52. That is IV crush.
Bars show what each Greek contributed, estimated from the Greeks at the moment you bought. The P&L figures use full repricing.
Vega loves time
All else equal, longer-dated near-the-money options generally have more vega: our 30-day ATM call has about ₹25 per IV percentage point, the ten-day call about ₹15 and the one-day call under ₹5. Vega usually decreases as expiry approaches, while short-dated gamma and theta can become large. Higher IV means more movement is priced in; buying low IV or selling high IV is not inherently an edge. Outcomes depend on realised moves, changes in IV, event risk, hedging and costs.
Why different strikes have different IVs: smile and skew
The IV inferred from an option’s market quote can differ by strike and expiry. The cross-strike pattern is often called a volatility smile or skew. This lab applies one IV at a time to explain sensitivities; it is not a calibrated market volatility surface. Its single-IV examples are a teaching simplification. Compare actual strikes and expiries using their own quoted or inferred IVs.
VIX is the S&P 500 version of India VIX. Single-stock earnings are where IV crush bites hardest: in a hypothetical stock example, IV could fall from 90% to 45% after results. The effect on a call depends on its own vega, time remaining and the price move; no fixed percentage premium loss follows from that IV change alone. Vega is quoted per 1 vol point per share.
Rho (ρ): The Boring Uncle 👴
Rho is how much the premium changes when the model’s interest rate moves by one percentage point. Calls have positive rho and puts negative rho under these assumptions. For the master ten-day call, rho is about ₹3.22 per unit per rate percentage point, or ₹209.48 per lot. A one-percentage-point change in the model rate changes its premium by about 1.4% in a first-order estimate. Rho is often relatively small for weekly options, but it is not identically zero.
Rho generally matters more for longer-dated options. Our one-year 22,500 call has model rho of about ₹135.62 per rate percentage point on a premium of about ₹1,984.28. A 0.5-percentage-point change in the risk-free rate therefore has an estimated effect of about ₹67.81 per unit, with other inputs fixed. A policy-rate announcement need not translate one-for-one into the risk-free input used by a pricing model.
Compare maturities
Turn the interest-rate dial
NIFTY and strike 22,500 · option IV 14% · zero dividends. Each comparison starts at a model interest rate of 6%.
A longer maturity usually makes this example more sensitive to the model’s rate input. Calls and puts respond in opposite directions.
Only the model rate changes; spot, remaining time and IV stay fixed in each comparison. A policy announcement can also change other inputs. Values are model estimates before costs.
How the Greeks Work Together (This Is the Part That Matters) 🤝
Each Greek was explained with “if nothing else changes”. In a real day everything changes at once: NIFTY moves, a day passes and IV shifts, and your P&L is the sum of what each Greek did. Keep this one line in your head and you can explain almost any option P&L you will ever see:
Change in premium ≈ Δ × move + ½ Γ × move² + Θ × days + ν × IV change
All terms are premium changes per unit; multiply by 65 for one lot. IV and rate changes are in percentage points. Add rho × rate change when relevant: short-dated rho is often smaller, not zero.
The first term estimates direction. The gamma term captures local curvature: it is positive for an individual long vanilla option and negative for a short one. Theta estimates the effect of elapsed calendar time; for long options it is usually negative, with exceptions for some inputs and portfolios. Vega estimates the effect of the option’s own IV change. This Taylor expansion is a local P&L estimate, not an exact decomposition of every market move.
Try it: why did my P&L change?
🧮 Why did my P&L change? The attribution machine
You own the ATM 22,500 CE (10 days, IV 14%, ₹227) · lot = 65Push NIFTY to +500 and the gap grows: the Greeks are a snapshot taken at the start, and a big move takes you far from that snapshot.
Worked example: Riya’s three-Greek trade
Build the explanation
Follow Riya’s P&L, one Greek at a time
One next-morning scenario: NIFTY +50 points, 1 calendar day passes, option IV 14% → 16%. Reveal the arithmetic, then compare it with full repricing.
Start with the paid premium
Riya pays ₹226.83 per unit. The next-morning scenario is NIFTY +50 points, 9 days left and IV 16%.
The steps show terms in a starting-Greeks approximation, not sequential market prices. The original calculation below remains available in full.
Riya buys our 22,500 CE at the model price of ₹226.8304. By the next morning NIFTY is up 50 points, nine days remain, and the IV of her 22,500 CE has risen from 14% to 16%. Using the full-precision starting Greeks, with rates unchanged:
- Delta: 0.532885 × 50 ≈ +₹26.64
- Gamma: ½ × 0.000762548 × 50² ≈ +₹0.95 (small on a small move)
- Theta: −₹12.2986 × 1 calendar day ≈ −₹12.30
- Vega: ₹14.8070 × (+2 percentage points) ≈ +₹29.61
- Total: Greek estimate ≈ +₹44.91 per unit (about +₹2,919.34 per lot). Full model repricing gives a premium of ₹269.67, a gain of ₹42.84 per unit, or ₹2,784.67 per lot. The residual reflects changing sensitivities and higher-order effects.
Notice what actually paid: the IV rise contributed more than the NIFTY move. Had the option’s own IV fallen from 14% to 12% instead, the vega loss (−₹29.6) would have wiped out the entire delta gain before theta even sent its bill, and Riya would have been down about ₹14 per unit. Same trade, same correct view on direction, opposite result. Now flip to the seller. Arjun sold the slightly out-of-the-money 22,900 CE at ₹76 (delta 0.25, theta −₹9, so +₹9 for him). NIFTY rises 100 in a day: delta costs him ₹25, theta pays him ₹9, net −₹17 per unit. If NIFTY instead rockets 400 points, the call’s delta climbs from 0.25 to 0.53 on the way and he is down about ₹140 per unit, ₹9,200 per lot, on a trade that was collecting ₹600 a day. That is gamma arriving to collect the rent theta promised.
The tug-of-war: who helps and who hurts
The multi-Greek showdown
Same market change. Who benefits?
Think of four forces pulling on one position. Choose a buyer or seller, then change the scenario. The cards show which forces help, which hurt, and whether they add up to a gain.
Starting point: NIFTY and strike 22,500 · 10 calendar days left · option IV 14% · model rate 6% · zero dividends.
Choose what changes
Build your own scenario
Try “All four pull”, then flip buyer and seller.
Current scenario: Buy 22,500 CE · NIFTY +100 pts · 1 calendar day passes · IV 14% → 12%
Δ Delta · direction
Helps this scenarioPositive position delta helps when NIFTY rises.
Why this contribution?
Position delta × NIFTY move. Selling reverses the position delta; the option’s own quoted price still moves the same way.
+0.532885 × (+100) = +₹53.29 per unit.
Γ Gamma · curvature
Helps this scenarioPositive gamma adds to the delta-only estimate for either direction of move.
Why this contribution?
½ × position gamma × NIFTY move². For a long option this term is positive on a rise or fall. It may soften a loss without making the total position profitable.
½ × (+0.000762548) × 10,000 = +₹3.81 per unit.
Θ Theta · time
Hurts this scenarioTime decay contributes a loss to this bought position. Other effects can outweigh it.
Why this contribution?
Position theta × calendar days passing. This is a local estimate using the starting theta; the daily rate itself changes as expiry approaches.
−₹12.2986 × 1 = −₹12.30 per unit.
ν Vega · volatility
Hurts this scenarioPositive position vega hurts when the option’s own IV falls.
Why this contribution?
Position vega × IV change in percentage points. Moving from 14% to 12% is −2 percentage points. This is the option’s IV, not the separate India VIX index.
+₹14.8070 × (−2.0) = −₹29.61 per unit.
Each card’s bar extends left for a negative contribution and right for a positive one. All four bars use the same scale.
Which side wins this scenario?
All amounts per unit.
Delta and Gamma help. Theta and Vega hurt. The net model result is about +₹17.5 per unit. One helpful Greek does not guarantee a profitable position.
Greeks are starting sensitivities. The four-card sum is a local approximation; full repricing uses all the changed inputs together. The residual captures changing sensitivities and higher-order effects. Rates are held fixed, so there is no rho contribution. Model estimates exclude trading costs and are not executable quotes. Displayed values are rounded independently.
View all position signs
| Greek | Long call (buyer) | Long put (buyer) | Short call (seller) | Short put (seller) |
|---|---|---|---|---|
| Delta (direction) | + wants NIFTY up | − wants NIFTY down | − benefits from NIFTY falling | + benefits from NIFTY rising |
| Gamma (acceleration) | + positive curvature | + positive curvature | − negative curvature | − negative curvature |
| Theta (time) | − time decay hurts here | − time decay hurts here | + time decay helps here | + time decay helps here |
| Vega (fear) | + wants IV up | + wants IV up | − wants IV down | − wants IV down |
For the individual vanilla options in this example, buying gives positive gamma and vega; selling reverses both. Theta is negative for these bought options and positive for their sold counterparts. Other inputs can produce theta exceptions, and multi-leg portfolios need net sensitivities. A Greek’s sign describes exposure, not a guaranteed profit.
Delta-neutral: when direction stops mattering (and gamma sneaks back in)
A desk seeking to reduce directional exposure can hedge its net delta toward zero. That reduces first-order sensitivity at the current inputs; gamma, IV, time, trading costs and hedge changes still affect P&L. You can build one: long one lot of NIFTY futures is +65 delta units; each 22,500 PE lot adds about −30 (65 × −0.47); two put lots gets you close to zero.
⚖️ Delta-neutral hedge builder
You are long 1 lot of NIFTY futures (+65 delta units) · hedge with 22,500 PE, 10 days, IV 14%Roughly delta-neutral: a 100-point move barely changes your P&L.
The beam represents net delta: level means futures and put exposures approximately balance. A tilt indicates directional exposure; read the signed net-delta value above for its direction and size.
Gamma pushed the puts’ delta toward −1 as NIFTY fell, so the hedge grew too big: you are now net short 15 units. Rebalance by selling some puts or buying futures. This position is long gamma. Rebalancing results depend on the price path, time decay, spreads and trading costs.
The catch is the second slider. As NIFTY falls, the puts’ delta heads toward −1 and the hedge becomes too big; as NIFTY rises it shrinks and the hedge becomes too small. Gamma keeps un-neutralising a neutral book, so the desk re-hedges all day. For a long-gamma position, re-hedging tends to sell after rises and buy after falls; for short gamma the pattern reverses. Whether gamma scalping produces a net profit depends on realised moves, time decay, IV changes and trading costs. This is also the mechanism behind the famous “gamma squeeze”: dealers short lots of calls must buy more and more stock as it rises, which pushes it higher still.
Every strategy is a bundle of Greeks
Once you can read the four dials, every options strategy stops being a name to memorise and becomes a Greek profile you can reason about. Click through the six below: the chart shows the payoff at expiry (solid) and today (dashed), and the stats show the net Greeks of the whole position.
🧩 Every strategy is a bundle of Greeks
NIFTY 22,500 · 10 days to expiry · IV 14% · lot = 65Long call
Buy 22,500 CE
You expect a quick move up. Delta works for you, gamma speeds you up, but theta bleeds every day and an IV drop hurts.
Dashed line = what the position is worth today if NIFTY jumped there instantly. Solid line = at expiry. The space between them is time value that theta will transfer from buyers to sellers.
Advanced: Greek combinations
Two Greeks can work together while another works against you. Explore both option legs together, then compare their starting sensitivities with the full model result.
Delta–Gamma combo
A long straddle buys a call and a put at the same strike. Positive gamma makes net delta rise as NIFTY rises and fall as NIFTY falls. Time decay and falling IV can still outweigh that benefit.
Buy 22,500 CE + 22,500 PE · same expiry · 65 units of each leg.
Start: NIFTY 22,500 · 10 calendar days left · IV 14%.
Adjust the market inputs
Choose a scenario or play the guided example.
NIFTY 22,500 (+0) · 10 days left · IV 14% → 14%
NIFTY-equivalent units
NIFTY-equivalent units
No inputs changed, so the model P&L is zero.
Premium paid: ₹27,086 for 65 CE + 65 PE.
See the contribution breakdown
- Δ Direction
- +₹0.00
- Γ Curvature
- +₹0.00
- Θ Time
- +₹0.00
- ν IV change
- +₹0.00
- Starting-Greeks total
- +₹0.00
- Full model − estimate
- +₹0.00
The four contributions use starting Greeks. Their sum is an approximation; the full model reprices both legs together. The residual captures changing sensitivities and higher-order effects.
Delta-neutral is temporary. An ATM long straddle is not automatically exactly delta-neutral. A hedge can offset its current delta; gamma changes the hedge needed as NIFTY moves. This example is unhedged. Positive gamma alone does not guarantee profit.
Vega–Theta combo
A short straddle sells a call and a put at the same strike. After an event, falling IV and passing time can both help. Compare a small move with a large move to see why that does not guarantee profit.
Sell 22,500 CE + 22,500 PE · same expiry · 65 units of each leg.
Start: NIFTY 22,500 · 5 calendar days left · IV 24%.
Adjust the market inputs
Choose a scenario or play the guided example.
NIFTY 22,600 (+100) · 4 days left · IV 24% → 14%
starting-Greeks estimate
starting-Greeks estimate
Falling IV helps this short-vega position. Elapsed time adds a positive starting-theta contribution. The combined model result is a gain in this scenario. Time and volatility estimates alone do not determine profit.
Premium received: ₹32,778 for 65 CE + 65 PE.
See the contribution breakdown
- Δ Direction
- −₹224.52
- Γ Curvature
- −₹409.91
- Θ Time
- +₹3,277.67
- ν IV change
- +₹13,644.80
- Starting-Greeks total
- +₹16,288.05
- Full model − estimate
- −₹1,668.49
The four contributions use starting Greeks. Their sum is an approximation; the full model reprices both legs together. The residual captures changing sensitivities and higher-order effects.
High IV is not a guaranteed edge. A post-event IV drop may help, but short gamma leaves the position exposed to large moves. A short straddle has uncapped upside loss and substantial downside risk. This is a hypothetical event, not a historical Budget-day result.
Both examples use the article’s European Black-Scholes model, a 6% rate, zero dividends and a constant IV across the two legs at each snapshot. One straddle here is one 65-unit call lot plus one 65-unit put lot; add the two premiums, then multiply by 65. All P&L excludes costs and is a scenario estimate. The strategy profile above has its own 10-day, 14%-IV starting assumptions. Long-straddle reference · Short-straddle reference.
| Strategy | Delta | Gamma | Theta | Vega | Use it when |
|---|---|---|---|---|---|
| Long call / long put | + / − | + | − | + | You expect a big, fast move in one direction |
| Bull call spread / bear put spread | + / − | small | small | ≈ 0 | Moderate view; you want a cheaper, defined-risk entry |
| Long straddle | ≈ 0 | + | − − | + | Big move expected, direction unknown (and IV is not already sky-high) |
| Short straddle | ≈ 0 | − − | + + | − | Range-bound view; professionals only, because losses are uncapped |
| Iron condor | ≈ 0 | − | + | − | Range-bound view with wings that cap the loss |
| Covered call (stock illustration: shares + short call) | + (reduced) | − | + | − | Own the underlying shares and sell calls against the covered quantity; upside is capped. NIFTY is an index, not directly held shares; futures and ETFs need separate treatment. |
The Greeks lie (a little)
Three caveats help you interpret the dashboard. First, Greeks are a snapshot: delta, gamma, theta and vega change with spot, time and IV. Second, they are local: accuracy depends on the size of the changes, moneyness and time remaining; no fixed 100-point or 500-point move is always safe to approximate. The residual between the starting-Greeks estimate and full model repricing includes changing sensitivities, higher-order and cross effects. Third, they come from a model. Black-Scholes assumes continuous prices and a constant volatility input. Overnight, NIFTY can gap across several strikes before you can adjust a hedge, and a stop order does not guarantee an execution price. Platforms can use different dividend assumptions, spot or futures inputs, IVs and time conventions. Full model repricing is a scenario estimate, not a promise of market liquidity or an executable quote; neither calculation includes bid–ask spreads, fees or model mismatch.
Where to Actually See the Greeks 📱
The NSE option chain shows you strikes, premiums, open interest and IV, but not the Greeks themselves. Most broker apps and analytics platforms (Sensibull, Opstra, Quantsapp and the strategy builders inside the big discount brokers) show live delta, gamma, theta and vega for every strike and for a whole multi-leg position. Three habits worth forming:
- Look at the net Greeks of the whole position, not leg by leg. A spread’s vega can be close to zero even though each leg has a large vega.
- Note the Greeks at entry in a journal, then compare with what actually happened. The attribution formula turns every trade into a lesson.
- Paper-trade for a month before you use real money. Simulators are free; theta is not.
7 Classic Mistakes (and the Greek Behind Each) 🚫
Open a mistake to see which Greek explains it.
1. Buying cheap, far-OTM options.
Low price means low delta: the option copies almost none of the move, and theta eats the rest. (Delta, theta)
2. Being right too slowly.
A snapshot suggested about 23 points a day to offset theta, but that first-order estimate changes with delta, time and IV. (−Theta ÷ delta)
3. Buying into a known event.
You paid peak IV; the news popped the balloon. (Vega, IV crush)
4. Selling naked options for “easy money”.
Theta paid ₹600 a day until one 400-point day took back a month. (Short gamma)
5. Treating the Greeks as fixed.
The delta you hedged at 9:20 was gone by noon. (Gamma)
6. Ignoring the lot.
“Only ₹12 of theta” is ₹800 a day per lot and ₹8,000 a day on ten lots. (Position sizing)
7. Trading expiry afternoon without understanding gamma.
It is a casino with a very fast wheel, in both directions. (Gamma, theta)
Set a loss budget appropriate to your finances, strategy, liquidity and total portfolio exposure. There is no universally suitable percentage. A long option can lose its entire premium. Calculate contractual spread payoff limits and costs; a naked short call has no finite maximum loss. Stress scenarios and stop orders do not cap that loss.
Write down the position’s payoff risks in rupees and the Greeks at entry. Distinguish a contractual maximum loss from a stress estimate, and identify any exposure without a finite loss limit.
Consider how a defined-risk spread changes the whole position. Bought wings can cap the contractual payoff loss, but spreads still carry execution, liquidity and market risk.
Keep a journal: reason for the trade, Greeks at entry, what happened, which Greek explained it, lesson. Thirty entries will teach you more than any book.
Glossary 🔤
All 14 terms shown.
| Term | Plain-English version |
|---|---|
| Premium | The price of the option, per unit. Multiply by the lot for the real cost. |
| Strike | The fixed price written on the contract. |
| Expiry | The contract’s last day. NIFTY weeklies expire on Tuesday; monthlies on the last Tuesday of the month. |
| CE / PE | Call option / put option, in NSE notation (22,500 CE = the 22,500 call). |
| ITM / ATM / OTM | In, at or out of the money: already useful / at the line / not useful yet. |
| Intrinsic value | What the option is worth if exercised right now (never below zero). |
| Time value | Everything you pay above intrinsic value: the price of possibility. This is what theta eats. |
| Lot | The minimum trading quantity. 65 units for NIFTY options on the NSE (from 30 December 2025). |
| Implied volatility (IV) | The volatility input inferred from an individual option’s price. It can vary by strike and expiry; India VIX is a separate 30-day index measure. |
| Long / short | Bought / sold. “Long gamma” means your position gains from big moves. |
| Margin | The deposit sellers must keep with the exchange because their loss is not capped. |
| Delta-neutral | A position whose net delta is about zero, so small moves in the underlying barely change its value. |
| IV crush | The sharp drop in implied volatility (and option prices) after a scheduled event. |
| 0DTE | Zero days to expiry: trading options on their expiry day. |
Frequently Asked Questions
What are the option Greeks in simple terms?
The Greeks estimate how an option’s model price responds to changes in its inputs: delta to the underlying, gamma to the resulting change in delta, theta to elapsed time, vega to the option’s own implied volatility and rho to the interest-rate input. They do not predict NIFTY’s direction or an executable future price. Treat them as local sensitivities that need updating as conditions change.
Which Greek should a beginner learn first?
Delta, then theta. Delta explains most of the day-to-day movement and the “why did my cheap option not move?” problem. Theta explains why being right slowly still loses money. Vega becomes important the first time you trade around a budget, results or an RBI decision; gamma the first time you hold anything into expiry day. Rho can wait until you trade options that expire months away.
Is delta the probability that an option expires in the money?
Absolute delta is sometimes used as a rough indicator of moneyness probability. In this zero-dividend Black-Scholes model, call delta is N(d1), while the risk-neutral probability of expiring in the money is N(d2). For the master call they are 53.29% and 52.37%, respectively. Neither is the real-world probability of a profitable trade. Premium, costs, exits and loss size matter: a 0.15–0.20 delta does not establish an 80–85% trading win rate.
Why did my option lose value when NIFTY moved in my favour?
A favourable underlying move may be too small to offset time decay, the option’s own IV may fall, or its delta may be small. The ratio −theta ÷ delta is only a changing first-order estimate of the move needed to offset theta with other inputs fixed. The attribution widget compares a starting-Greeks estimate with full model repricing; neither is an executable market quote.
What delta should I buy, and what delta should I sell?
There is no universally suitable delta to buy or sell. A higher-absolute-delta option usually follows more of the underlying’s local move and has a different premium and risk profile. A lower delta does not establish a trading win rate or limit loss size. Select strikes in the context of expiry, IV, liquidity, the full strategy and your loss budget. Spreads can define payoff limits, but they do not guarantee a profit.
Does theta decay over the weekend?
This model uses calendar time, so a weekend reduces the time remaining. Friday-to-Monday market prices also reflect spot, the option’s IV, liquidity and how participants price non-trading days. The observed change is not guaranteed to equal Friday’s theta multiplied by three. The same distinction applies to exchange holidays.
What is IV crush and how do I avoid it?
IV crush is a sharp decline in an option’s own implied volatility, often after a scheduled event. It can reduce the time-value component even when the underlying moves in the buyer’s favour. An event does not guarantee an IV drop, and avoiding it is not assured by any one trade. Spreads may reduce net vega, but their exposures vary with spot and time. Selling higher IV also carries movement and loss risk. Compare full-model scenarios and include costs rather than relying on a universal rule.
What does negative gamma mean?
Negative gamma means the position’s delta becomes more negative as the underlying rises and more positive as it falls. An individual short vanilla option has negative gamma, so adverse moves can accelerate losses. A multi-leg portfolio’s net gamma is the signed sum across its positions; selling one option does not determine the whole portfolio’s exposure. Theta is often positive for short options, but its sign and P&L depend on the inputs and the rest of the position.
Do the Greeks change during the trading day?
Constantly. Delta changes with every tick (that is gamma), theta grows as expiry approaches, vega moves with time and moneyness, and all of them shift when implied volatility changes. Treat the Greeks as a snapshot that needs refreshing after any meaningful move, and remember that two platforms can show slightly different values for the same option because they feed the model slightly different inputs.
Are the Greeks the same for US options?
The definitions are identical; only the units change. US equity options cover 100 shares per contract, so delta, theta and vega are usually quoted per share and multiplied by 100 for a contract. SPX index options use a $100 multiplier and have daily expirations. VIX plays the role of India VIX. The behaviour, including IV crush around earnings and gamma on expiry day, is the same everywhere.
Can I calculate the Greeks myself?
Yes. The expandable Python snippet and the browser calculators use European Black-Scholes with zero dividend yield. Inputs are spot, strike, calendar days to expiry, the option’s IV and an interest rate. Broker values can differ because of dividends, futures-based inputs, IV conventions and day counts. These model estimates do not establish the price at which you can trade.
Test Yourself: The Greeks Quiz Arena 🏆
Three tiers, from warm-up to detective work: 52 questions in total. The hypothetical arithmetic exercises use the supplied fixed or rounded Greeks unless a case explicitly asks for full model repricing. They are not all repricings of the master example. Score is per tier; you can reset and retry any time.
Tier 1: Quick-fire MCQs ⚡
⚡ Tier 1: Quick-fire
0 / 0 correct · 17 to goOne Greek at a time. Pick an answer; the explanation appears immediately.
Question 1
You buy a call with delta 0.70. The underlying rises ₹20. Roughly how much does the premium change?
- A) ₹14
- B) ₹7
- C) ₹20
- D) ₹0.70
Show answer
A. Delta × move = 0.70 × 20 = ₹14. Delta tells you what fraction of the move your option captures.
Question 2
You sold an option that shows theta of −12. If nothing else changes, what is your P&L from time decay tomorrow?
- A) −₹12 per unit
- B) ₹0.12 per unit
- C) +₹12 per unit
- D) Nothing until expiry
Show answer
C. Theta is negative for the buyer and positive for the seller. The ₹12 the buyer loses is the ₹12 you collect.
Question 3
Implied volatility rises by 3 points. Your option has vega of 0.25. Change in the option price?
- A) ₹0.75
- B) ₹0.25
- C) ₹2.50
- D) ₹7.50
Show answer
A. Vega × IV change = 0.25 × 3 = ₹0.75 (a US-style per-share vega; multiply by 100 for a contract).
Question 4
Stock illustration in per-share units: you own 2 shares (delta +1 each). Puts on the stock have delta −0.50. How many puts make you delta-neutral?
- A) 3 puts
- B) 4 puts
- C) 2 puts
- D) 5 puts
Show answer
B. Shares give +2 delta. Each put is −0.5, so you need 2 ÷ 0.5 = 4 puts to reach zero. (Per-share units; scale by the lot in real markets.)
Question 5
Who benefits from time passing, if nothing else changes?
- A) The option seller
- B) Nobody
- C) Both equally
- D) The option buyer
Show answer
A. Time value melts, and it melts out of the buyer’s pocket into the seller’s. That transfer is theta.
Question 6
Which option has the highest gamma?
- A) Deep in-the-money, 1 day left
- B) Far out-of-the-money, 30 days left
- C) At-the-money, 1 day left
- D) Deep in-the-money, 30 days left
Show answer
C. Gamma peaks at-the-money and grows as expiry approaches. Deep ITM options already behave like the underlying (delta ≈ 1), so their delta has nowhere to go.
Question 7
Being short gamma means…
- A) You have no directional risk
- B) Your losses accelerate when the market moves against you
- C) Your delta never changes
- D) Your profits accelerate when you are right
Show answer
B. For an individual short vanilla option, negative gamma makes delta move against the position as the underlying moves. A portfolio’s net gamma depends on all its legs; positive theta does not guarantee a profit.
Question 8
A call trades at ₹45 with delta 0.60. The stock rises ₹20. New option price (delta only)?
- A) ₹65
- B) ₹33
- C) ₹57
- D) ₹47
Show answer
C. 20 × 0.60 = ₹12 gain, so 45 + 12 = ₹57. ₹65 forgets to multiply by delta; ₹47 uses delta 0.10; ₹33 moves the wrong way.
Question 9
An ATM call costs ₹50 with vega 8. Results are tomorrow and IV jumps from 20% to 28% while the stock sits still. New price?
- A) ₹14
- B) ₹400
- C) ₹114
- D) ₹58
Show answer
C. Use the change in IV: 28 − 20 = 8 points × vega 8 = +₹64, so ₹114. ₹58 used the level instead of the change; ₹400 multiplied the price by vega; ₹14 subtracted.
Question 10
An ATM call has delta 0.50 and gamma 0.01 per ₹1. The stock rises ₹20. New delta?
- A) 0.50
- B) 0.30
- C) 0.51
- D) 0.70
Show answer
D. Delta change = gamma × move = 0.01 × 20 = 0.20, so 0.50 + 0.20 = 0.70. (0.51 applied gamma to a ₹1 move only; 0.30 went the wrong way.)
Question 11
It is Friday, 3:25 pm, and your weekly call is up 50%. If you hold through the weekend, which Greek works against you while the market is shut?
- A) Rho
- B) Gamma
- C) Theta
- D) Delta
Show answer
C. The model uses calendar time: remaining time falls over the weekend. The observed market-price change also depends on spot, IV and how non-trading days are priced.
Question 12
NIFTY closes at 22,495 on expiry day. You hold the 22,500 CE. What is it worth at settlement?
- A) ₹20
- B) ₹5
- C) Your premium is refunded
- D) ₹0
Show answer
D. A call expiring below its strike has zero intrinsic value, however close it got. “Nearly in-the-money” pays nothing.
Question 13
The 22,500 CE has delta +0.53. What is the delta of the 22,500 PE (same expiry)?
- A) −0.53
- B) −0.47
- C) 0
- D) +0.47
Show answer
B. Call delta − put delta = 1 for the same strike and expiry, so the put is 0.53 − 1 = −0.47.
Question 14
What are the signs of rho?
- A) Both negative
- B) Calls negative, puts positive
- C) Calls positive, puts negative
- D) Both positive
Show answer
C. Higher rates make calls slightly dearer (positive rho) and puts slightly cheaper (negative rho). For weekly options the amounts are tiny either way.
Question 15
Which option has the most vega?
- A) 30-day ATM call
- B) 1-day far-OTM call
- C) 1-day ATM call
- D) They are all the same
Show answer
A. Vega grows with time to expiry and is highest at-the-money. Our 30-day ATM call has vega of about ₹25; the 1-day call under ₹5.
Question 16
Your call has theta −12 and delta 0.50. Using a first-order estimate with IV and rates fixed, about how many NIFTY points per calendar day offset this theta?
- A) 6
- B) 48
- C) 24
- D) 12
Show answer
C. Using the supplied fixed Greeks, −theta ÷ delta = 12 ÷ 0.5 = 24 points per calendar day. This is a first-order estimate with IV and rates fixed, not a guaranteed or constant breakeven move.
Question 17
Theta is −12 per unit and the NIFTY lot is 65. What does one flat day cost a buyer of one lot?
- A) ₹7,800
- B) ₹780
- C) ₹65
- D) ₹12
Show answer
B. 12 × 65 = ₹780 per lot per day. Always multiply a per-unit Greek by the lot before deciding whether it is “small”.
Need a hint?
Your answers stay available while this page is open. Restart resets this tier’s answers and score.
Tier 2: Case files 🔍
Step-by-Step Q&A Arena
0 / 0 correct · 24 to goHypothetical cases, one step at a time. Use the supplied fixed Greeks unless full model repricing is specified.
Riya buys a NIFTY 22,500 CE for ₹227. Delta = 0.50, theta = −12, vega = 15. NIFTY is at 22,500 and this option’s IV is 13%.
Step 1 of 4
NIFTY rises to 22,550. Using delta only, what is the option’s new price?
- A) ₹239.50
- B) ₹252
- C) ₹227
- D) ₹277
Show answer
B. 0.50 × 50 = ₹25 gain, so ₹227 + ₹25 = ₹252.
Step 2 of 4
One day passes and NIFTY stays at 22,550. Now apply theta. New price?
- A) ₹252
- B) ₹264
- C) ₹227
- D) ₹240
Show answer
D. Theta is a cost to the buyer: ₹252 − ₹12 = ₹240.
Step 3 of 4
The option’s own IV rises from 13% to 15%. Apply the supplied vega. New price?
- A) ₹240
- B) ₹210
- C) ₹255
- D) ₹270
Show answer
D. Vega 15 per point × 2 points = +₹30, so ₹240 + ₹30 = ₹270.
Step 4 of 4
What is Riya’s total P&L on one lot of 65?
- A) +₹2,795
- B) +₹1,625
- C) −₹780
- D) +₹43
Show answer
A. Bought at ₹227, now ₹270: +₹43 per unit × 65 = +₹2,795. Three Greeks, one real trade.
Arjun sells a NIFTY 22,900 CE for ₹76. Delta = 0.25, theta = −9 (so +9 for him), gamma = 0.0006 per point.
Step 1 of 4
NIFTY rises 100 points. What happens to the option price (delta only), and to Arjun?
- A) No change
- B) Price +₹25; Arjun loses ₹25
- C) Price −₹25; Arjun gains ₹25
- D) Price +₹76
Show answer
B. 0.25 × 100 = +₹25 on the option. Arjun sold it, so a dearer option is his loss.
Step 2 of 4
One day passes with NIFTY flat. Arjun’s P&L from theta?
- A) +₹76
- B) −₹9
- C) ₹0
- D) +₹9
Show answer
D. Sellers collect theta: +₹9 per unit, about +₹585 per lot.
Step 3 of 4
Net result for Arjun after one day in which NIFTY rose 100?
- A) +₹25
- B) +₹16
- C) −₹16
- D) −₹9
Show answer
C. Lost ₹25 to delta, collected ₹9 of theta: −₹16 per unit. Delta hurt more than theta helped.
Step 4 of 4
NIFTY keeps rallying to 22,900, the strike. Delta has climbed from 0.25 to about 0.55. Why is Arjun in trouble?
- A) His theta increases
- B) Nothing changes; delta is fixed
- C) His vega turns positive
- D) His losses accelerate as delta grows: he is short gamma
Show answer
D. Gamma is the seller’s nightmare. As NIFTY approaches the strike, the option’s delta rises and every further point costs Arjun more than the last.
Hypothetical arithmetic exercise: RBI policy is at 10 am. You buy a 22,500 CE at ₹180: delta 0.50, vega 10, IV 22%. After the announcement NIFTY is +80 and IV has fallen to 14%.
Step 1 of 4
Delta gain per unit?
- A) ₹80
- B) ₹40
- C) ₹160
- D) ₹8
Show answer
B. 0.50 × 80 = ₹40.
Step 2 of 4
What is the change in IV, in points?
- A) −14
- B) −22
- C) −8
- D) +8
Show answer
C. After − before = 14 − 22 = −8 points.
Step 3 of 4
Vega effect per unit?
- A) +₹80
- B) −₹8
- C) −₹80
- D) −₹140
Show answer
C. Vega × IV change = 10 × (−8) = −₹80.
Step 4 of 4
Net P&L per lot of 65 (ignore theta)?
- A) −₹40
- B) +₹5,200
- C) −₹2,600
- D) +₹2,600
Show answer
C. (+40 − 80) × 65 = −₹2,600. Right on direction, still lost: on event days vega beats delta.
Hypothetical full-model example: NIFTY and strike are 22,500; IV is 14%, annual rate 6%, dividend yield zero, and 150 calendar minutes remain (T = 150 ÷ 1,440 ÷ 365). The 22,500 CE has model premium ₹21.4224, delta 0.50336 and gamma 0.0074966 per index point. Ten minutes later NIFTY is 22,540 and 140 minutes remain; IV and rate are unchanged. Use full model repricing, not a capped linear estimate.
Step 1 of 4
How should you obtain the new delta?
- A) Cap the old linear estimate at 1
- B) Keep delta fixed
- C) Reprice with the new spot and remaining time
- D) Allow delta above 1
Show answer
C. Reprice with NIFTY 22,540 and 140 minutes remaining. Gamma changes during the move; capping an invalid linear estimate does not recover the correct delta.
Step 2 of 4
What is the fully repriced delta?
- A) 0.45
- B) 1.00
- C) About 0.784
- D) 1.05
Show answer
C. The same Black-Scholes model gives delta 0.78392. It remains between 0 and 1 without imposing an artificial cap.
Step 3 of 4
What is the fully repriced premium per unit?
- A) About ₹46.72
- B) ₹59
- C) ₹30
- D) ₹61
Show answer
A. Full model repricing gives ₹46.7172 per unit. Subtracting the original ₹21.4224 gives a gain of ₹25.2947 per unit, or ₹1,644.16 for a lot of 65, before costs.
Step 4 of 4
What is the approximate return on the premium before costs?
- A) 97%
- B) About 118%
- C) 45%
- D) 0%
Show answer
B. Using unrounded model prices: (46.7171501 − 21.4224466) ÷ 21.4224466 × 100 ≈ 118.1%. This hypothetical outcome is not a promised expiry-day return.
Hypothetical arithmetic exercise: buy one lot of a 22,500 CE at ₹130 on Monday at 10 am; its expiry is the following week’s Tuesday. Use fixed delta 0.50, theta −₹10 per calendar day and vega ₹8 per IV percentage point. By Tuesday at 10 am NIFTY is +60 and the option’s IV is unchanged. Ignore gamma, changing Greeks and costs.
Step 1 of 4
Delta effect per unit?
- A) +₹30
- B) +₹15
- C) +₹6
- D) +₹60
Show answer
A. 0.50 × 60 = +₹30.
Step 2 of 4
Theta effect for the one day held?
- A) −₹10
- B) −₹20
- C) ₹0
- D) +₹10
Show answer
A. Using the supplied fixed theta for one calendar day gives an estimated −₹10 per unit.
Step 3 of 4
New premium?
- A) ₹120
- B) ₹140
- C) ₹160
- D) ₹150
Show answer
D. 130 + 30 − 10 = ₹150.
Step 4 of 4
Profit on the lot of 65?
- A) +₹1,950
- B) +₹2,600
- C) +₹1,300
- D) +₹650
Show answer
C. (150 − 130) × 65 = +₹1,300. One-third of the ₹30 delta gain was offset by the ₹10 theta estimate.
You run a market-making book. A client buys 10 lots of the 22,500 CE from you (650 units). The call’s delta is 0.60.
Step 1 of 4
What is your net delta after the trade?
- A) +390 units
- B) −650 units
- C) −390 units (short 650 × 0.60)
- D) 0
Show answer
C. You sold 650 call deltas at 0.60: 650 × 0.60 = 390, and the sign is negative because you lose if NIFTY rises.
Step 2 of 4
How do you get to delta-neutral?
- A) Buy 6 lots of NIFTY futures (+390)
- B) Sell 6 lots of futures
- C) Do nothing
- D) Buy 10 lots of futures
Show answer
A. Six futures lots × 65 = +390 delta units. −390 + 390 = 0.
Step 3 of 4
Next day NIFTY rallies and gamma lifts the call’s delta from 0.60 to 0.75, so your short calls are now −487.5 units. What do you do?
- A) Buy 487.5 more units
- B) Nothing; the hedge is permanent
- C) Sell 98 units
- D) Buy about 98 more units (roughly 1.5 lots)
Show answer
D. You need +487.5 and hold +390: buy the difference, about 98 units. Gamma keeps changing the hedge you need.
Step 4 of 4
What is this continuous rebalancing called?
- A) Buy and hold
- B) Averaging down
- C) Dynamic delta hedging
- D) Scalping
Show answer
C. Dynamic delta hedging is how option desks survive. When they are short gamma it costs money; theta is their compensation.
Need a hint?
Previous steps in this mission
Your answers stay available while this page is open. Restart resets this tier’s answers and score.
Tier 3: Greek Detective 🕵️
🕵️ Tier 3: Greek Detective
0 / 0 correct · 11 to goSomething happened to a position. Which Greek did it?
Case 1 of 11
NIFTY closed exactly where it opened, but your call lost ₹8.
- A) Theta
- B) Gamma
- C) Vega
- D) Delta
Show answer
A. No move, no news: time decay (theta) is the culprit.
Case 2 of 11
NIFTY did not move, but your put’s own IV rose from 12% to 18% and its premium jumped 40%.
- A) Rho
- B) Delta
- C) Vega
- D) Theta
Show answer
C. Price flat, fear up: vega inflated the balloon.
Case 3 of 11
NIFTY rose 50 points and your 0.50-delta call rose ₹25.
- A) Vega
- B) Gamma
- C) Theta
- D) Delta
Show answer
D. Textbook delta: 0.5 × 50 = 25.
Case 4 of 11
On expiry day a 30-point move turned your ₹10 option into ₹35.
- A) Delta
- B) Gamma
- C) Rho
- D) Vega
Show answer
B. Delta alone cannot explain a 250% move. Gamma pushed delta toward 1 within minutes.
Case 5 of 11
Right after the Budget speech NIFTY rose 120 points, but your call price fell.
- A) Theta
- B) Vega
- C) Delta
- D) Gamma
Show answer
B. IV crush: the vega loss outweighed the delta gain.
Case 6 of 11
RBI raised the repo rate by 0.25% and your one-week option barely changed.
- A) Theta
- B) Rho
- C) Vega
- D) Delta
Show answer
B. Rho is the Greek that reacts to rates, and for short-dated options it is so small you can ignore it. Which is exactly what you observed.
Case 7 of 11
Your short strangle was delta-neutral at 9:15. By 1 pm, after a 200-point rally, you are heavily short delta.
- A) Vega
- B) Rho
- C) Gamma
- D) Theta
Show answer
C. Short options have negative gamma: the position’s delta moves against you as the market moves.
Case 8 of 11
Your iron condor made ₹1,200 over a week in which NIFTY went nowhere.
- A) Gamma
- B) Delta
- C) Theta
- D) Rho
Show answer
C. A range-bound week is exactly what a condor is paid for. Theta, collected daily, is the income.
Case 9 of 11
You hold a one-year 22,500 call. The risk-free rate used in the model fell by 0.5 percentage points, NIFTY and the option’s own IV did not move, and the premium dropped about ₹70.
- A) Theta
- B) Vega
- C) Gamma
- D) Rho
Show answer
D. On a long-dated call, rho is large enough to notice: about ₹135.62 per rate percentage point, so about ₹67.81 for a half-percentage-point cut in the model rate.
Case 10 of 11
You bought a straddle before results. NIFTY moved 150 points, yet the straddle lost money.
- A) Gamma
- B) Rho
- C) Delta
- D) Vega
Show answer
D. The move was real but IV collapsed after the event. A straddle is long vega twice over, so the crush hit both legs.
Case 11 of 11
Your deep in-the-money call moved almost exactly one-for-one with NIFTY all day.
- A) Theta
- B) Vega
- C) Rho
- D) Delta
Show answer
D. Deep ITM calls have delta near 1: they behave like a future with a smaller ticket size.
Need a hint?
Your answers stay available while this page is open. Restart resets this tier’s answers and score.
This article is education, not investment advice, and the calculators are illustrative models, not quotes. Options can lose their entire premium, and selling options can lose far more than the premium collected. SEBI’s July 2025 study found that 91% of individual traders in equity F&O lost money in FY25, with aggregate net losses above ₹1 lakh crore. Learn the Greeks, size positions small, prefer defined-risk structures, and paper-trade before using real capital. Trading F&O in India requires an adult (18+) demat and trading account.
References
- NSE circular FAOP70616: revision in lot size of index derivative contracts (NIFTY lot 75 → 65 from 30 Dec 2025)
- Zerodha Market Intel: Revision in lot size of index derivative contracts from December 30, 2025
- Business Standard: NSE bids adieu to Thursday expiry as dates swap come into effect (NIFTY weekly expiry moves to Tuesday)
- Business Standard: Net losses of individual traders in F&O widened in FY25 (SEBI study, July 2025: 91% of individual traders lost money)
- Black, F. and Scholes, M. (1973), “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy 81(3)
- Hull, J. C., Options, Futures, and Other Derivatives (Pearson), chapter on the Greek letters
