Delta & Gamma

The risk I'm carrying right now can itself change — so I should always ask not just 'how exposed am I?' but 'how quickly could that exposure grow?'

• Explain what Delta measures: how much an option's price is expected to move for a ₹1 move in the underlying stock, right now.
• Explain what Gamma measures: how much Delta itself changes for a ₹1 move in the underlying.
• Calculate an option's approximate new price and new Delta after a price move, using Delta + (Gamma × price move).
• Recognize that Delta is a snapshot tied to the current price, not a fixed number that holds regardless of what the stock does next.

Delta tells you how much an option's price is expected to move for every ₹1 move in the underlying stock — right now, at this exact price. If Delta is 0.50, a ₹1 rise in the stock means roughly a ₹0.50 rise in the option. That sounds simple and final. It isn't.

The moment the stock price moves, Delta itself moves. It doesn't stay at 0.50 forever — it recalculates itself as the stock keeps changing. So a Delta you looked up an hour ago may already be out of date.

Gamma is what tells you how fast Delta is shifting. If Delta is the option's current "speed" relative to the stock, Gamma is how quickly that speed itself is changing. A small Gamma means Delta barely moves — you can trust the number a bit longer. A larger Gamma means Delta can swing meaningfully after even a small stock move.

Gamma is what tells you how quickly your exposure can grow.

Here's the formula that ties them together: new Delta ≈ old Delta + (Gamma × price move). Take the example: a stock trades at ₹1,000, its call option has a Delta of 0.50 and a Gamma of 0.03. If the stock rises ₹5, the option's price rises by about Delta × ₹5 = 0.50 × 5 = ₹2.50. But the story doesn't end there — the option's new Delta is now approximately 0.50 + (0.03 × 5) = 0.50 + 0.15 = 0.65.

Notice what just happened: the option didn't just gain ₹2.50 in value. It also became more sensitive to the next ₹1 move than it was a moment ago. That's the part a Delta-only view would miss entirely.

This is why reading Delta alone gives a false sense that your exposure is fixed. Gamma is what tells you how quickly that exposure can grow.

Once you see Gamma this way, the two Greeks stop feeling like two separate facts to memorize — they become one continuous story: Delta is where your sensitivity stands right now, and Gamma is how fast that standing is about to change.

Rohan holds one call option on a stock trading at ₹1,000. He checked the option's Delta this morning: 0.50. Its Gamma: 0.03. He treats the 0.50 as "how much I gain per ₹1 move" and moves on with his day.

By afternoon, the stock has climbed to ₹1,005 — a ₹5 move. Using Delta × ₹5, Rohan's option has gained about 0.50 × 5 = ₹2.50 in value. That part matches what he expected.

But here's what he almost missed: his Delta isn't 0.50 anymore. Using old Delta + (Gamma × price move), the new Delta is 0.50 + (0.03 × 5) = 0.65. His option is now nearly two-thirds as sensitive to the stock as the stock is to itself, up from half.

This matters for what Rohan does next. If the stock rises another ₹5, he won't gain another ₹2.50 — he'll gain closer to ₹3.25, because his Delta is now 0.65, not 0.50. If he's deciding whether to hold, sell part of the position, or hedge it, using the morning's 0.50 figure would understate how exposed he now is. The number he quoted himself at 9 a.m. quietly stopped being true by 2 p.m. — and Gamma is exactly what told him by how much.

Point: Delta gives the immediate price sensitivity and Gamma gives the rate at which that sensitivity itself shifts; using them together (Delta + Gamma × move) lets a learner re-estimate exposure after a move instead of assuming the original Delta still holds.

• Treating Delta as a fixed number that stays true for as long as you hold the option. — Delta is usually first shown as a single quoted figure, like 0.50, without ever showing what happens to it after the stock actually moves. Fix: Remember Delta is only accurate at the current stock price. Once the price moves, recalculate using Delta + (Gamma × price move) instead of reusing the old number.
• Thinking Gamma is a separate, optional Greek that only advanced traders need to worry about. — Delta is taught first and feels complete on its own, so Gamma seems like an extra add-on rather than part of the same idea. Fix: See Gamma as simply the rate of change of Delta — not a new topic, but the missing half of understanding Delta properly.
• Assuming a high Delta or Gamma automatically means the position is dangerous, and a low one means it's safe. — It feels natural to assume bigger numbers mean bigger danger, especially without other context. Fix: Ask what the number means for your specific position size and goal, rather than judging danger from the size of Delta or Gamma alone.

• Delta tells you how sensitive an option's price is to the underlying stock, right now.
• Gamma tells you how fast that sensitivity itself is changing.
• New Delta ≈ old Delta + (Gamma × price move) — use this to re-estimate exposure after any price move.
• A Delta you saw earlier may already be out of date; check Gamma to know how quickly it could have shifted.
• Neither number is a forecast — both describe sensitivity at a moment in time, not a guarantee of what happens next.

Q1. What does an option's Delta tell you?

• How much the option's price is expected to move for a ₹1 move in the underlying stock, right now
• How much profit the option will make by expiry
• The exact future price of the underlying stock
• How many days are left until the option expires Answer: How much the option's price is expected to move for a ₹1 move in the underlying stock, right now — Delta is a snapshot of directional sensitivity — it shows how much the option's price should move for every ₹1 move in the stock, at the current price.

Q2. Gamma measures how fast an option's price rises over time. Answer: False — Gamma does not measure price rising over time — it measures how much Delta itself changes for every ₹1 move in the underlying stock.

Q3. Why can't you fully trust a Delta number you looked up yesterday to still describe today's risk?

• Because Delta itself changes as the stock price moves, and Gamma tells you how much it could have shifted
• Because Delta only applies to stocks, not options
• Because Delta resets to zero every day automatically
• Because Delta is only accurate on days the market is closed Answer: Because Delta itself changes as the stock price moves, and Gamma tells you how much it could have shifted — Delta is tied to the current stock price. Once the price moves, Delta moves too — Gamma tells you the rate at which that shift happens.

Q4. A stock trades at ₹1,000. Its call option has a Delta of 0.50 and a Gamma of 0.03. If the stock rises by ₹5, what is the option's new approximate Delta? Answer: 0.65 — New Delta ≈ old Delta + (Gamma × price move) = 0.50 + (0.03 × 5) = 0.65. The option has become more sensitive to further price moves.

Q5. A trader checks an option's Delta in the morning (0.40) and doesn't check it again all day, assuming: "Delta is Delta, it won't have changed by the time I need to act." Is it safe to assume Delta hasn't changed without checking Gamma? Reveal: Weak: yes, Delta is Delta, no need to recheck. Strong: whether Delta has meaningfully shifted depends on Gamma and how much the stock has moved since morning — a large Gamma means Delta could have changed a lot; assuming it's unchanged without checking Gamma skips exactly what this unit teaches.