Learn the IV crush around events — Stock-Market notes

WHY does IV crush happen?

The key: stock price moving and IV changing are two separate forces on an option. You can be right on direction and still lose money because IV fell more than the move helped you.

WHAT is IV, precisely?

So IV is not observed directly — it's inverted from price: $\text{Market Price} = \text{BS}(\sigma_{\text{IV}}) \quad\Rightarrow\quad \sigma_{\text{IV}} = \text{BS}^{-1}(\text{Market Price})$

HOW an event pumps and dumps IV — derived from Black–Scholes

Take an at-the-money (ATM) call. From Black–Scholes with $r=0$ , $S=K$ (ATM), and small time $T$ , the price simplifies beautifully.

Formula ATM option price ≈ linear in IV

Start from BS call: $C = S\,N(d_1) - K e^{-rT} N(d_2)$ . With $r=0$ , $S=K$ : $d_1 = \dfrac{\sigma\sqrt{T}}{2}$ , $d_2 = -\dfrac{\sigma\sqrt{T}}{2}$ . Then $C = S[N(d_1) - N(d_2)]$ . For small $\sigma\sqrt{T}$ , expand $N(x) \approx \tfrac12 + \tfrac{x}{\sqrt{2\pi}}$ : $N(d_1)-N(d_2) \approx \frac{d_1 - d_2}{\sqrt{2\pi}} = \frac{\sigma\sqrt{T}}{\sqrt{2\pi}}$ $\boxed{\,C_{\text{ATM}} \approx \frac{S\,\sigma\sqrt{T}}{\sqrt{2\pi}} \approx 0.4\, S\,\sigma\sqrt{T}\,}$

Why this matters: Price is directly proportional to $\sigma$ . If IV halves ( $\sigma \to \sigma/2$ ), the ATM option loses half its value — even if $S$ never moved. That's the crush, in one line.

Figure — Learn the IV crush around events

HOW to model the P&L: move vs. crush tug-of-war

Change in option value splits into two pieces (first order): $\Delta C \approx \underbrace{\Delta_{\text{opt}}\,\Delta S}_{\text{direction (delta)}} + \underbrace{\mathcal{V}\,\Delta\sigma}_{\text{IV crush (vega)}}$

where Vega $\mathcal{V} = \dfrac{\partial C}{\partial \sigma}$ . From our ATM formula: $\mathcal{V}_{\text{ATM}} = \frac{\partial}{\partial\sigma}\left(0.4\,S\sigma\sqrt{T}\right) = 0.4\,S\sqrt{T}$

Worked Examples

Worked example Example 1 — Long call, right direction, still lose

Stock $S=\$ 100 $, ATM call,$ T = 1 $day before earnings$ = \tfrac{1}{252} $yr. Pre-event IV$ \sigma_0 = 80% $. Post-event IV$ \sigma_1 = 40%$.

Pre price: $C_0 = 0.4(100)(0.80)\sqrt{1/252} = 0.4\cdot 100 \cdot 0.80 \cdot 0.063 = \$ 2.01 $. *Why this step?* Use the ATM approximation;$ \sqrt{1/252}\approx0.063$.
Stock rises to $\$ 102 $(good, you were long). Delta of ATM$ \approx 0.5 $, so delta gain$ \approx 0.5 \times 2 = $1.00 $. *Why?*$ \Delta C_{\text{dir}} = \Delta \cdot \Delta S = 0.5\cdot 2$.
But IV crushes to 40%. Vega $= 0.4\cdot100\cdot0.063 = 2.52$ ; IV drop $=-0.40$ . Vega loss $= 2.52 \times (-0.40) = -\$ 1.01 $. *Why?*$ \Delta C_{\text{iv}} = \mathcal{V},\Delta\sigma$.
Net: $+1.00 - 1.01 \approx \$ 0$. You called direction correctly and made nothing. That's IV crush.

Worked example Example 2 — Short straddle harvests the crush

Same setup, sell the ATM call + put. Straddle premium $\approx 2C_0 \approx \$ 4.02$.

Expected move (from straddle) $\approx \$ 4 $($ \pm 4% $). *Why?* Straddle price ≈ 0.8·$ S\sigma\sqrt{T}$ = market's priced 1σ move.
Actual move is only $\$ 2 $. Post-event both options reprice at IV = 40%. New straddle value$ \approx 0.8\cdot100\cdot0.40\cdot0.063 + \text{intrinsic} \approx 2.01 + 2.00 = $4.01 $? *Careful:* the ATM formula assumed$ S=K $; after a$ $2 $move one leg has$ $2 $intrinsic. Combined post value$ \approx $3.0 $–$ 3.5$. Why? Crush shrinks extrinsic on both legs; only the ITM leg keeps intrinsic.
Net: collected $4.02, bought back ~$3.2 → ~+$0.8 profit from the crush, despite the stock moving.

Common Mistakes (Steel-manned)

Active Recall

Recall Test yourself (hidden)

Why does IV rise before a scheduled event? → Uncertainty of outcome is priced in.
Why can a correct directional bet still lose? → Vega loss > delta gain.
Which Greek measures crush exposure? → Vega.
Formula for ATM price? → $C\approx 0.4\,S\sigma\sqrt{T}$ .

Recall Feynman: explain to a 12-year-old

Imagine a mystery box that might have candy or nothing. Before opening, kids will pay a lot to guess, because it's exciting and unknown. The moment you open it, everyone knows what's inside — nobody pays for guessing anymore, so the "guessing tickets" become nearly worthless instantly. Options are guessing tickets on a stock. Right before earnings, the box is closed and tickets cost a lot (high IV). After the announcement, the box is open — ticket prices crash. That crash is the "IV crush," and it happens even if the stock itself barely budged.

Connections

Vega — the Greek that quantifies IV crush.
Theta — time decay accelerates into the event too.
Black-Scholes Model — where IV is inverted from price.
The Volatility Smile — event days steepen the smile/term structure.
Expected Move and Straddles — how the market prices the coming jump.
Iron Condor / Iron Fly — defined-risk ways to sell the crush.
Earnings Season — the main habitat of IV crush.

What is IV crush?

The sharp drop in an option's implied volatility (and hence price) right after a scheduled event resolves the uncertainty.

Why does IV rise before earnings?

The market prices in the unknown outcome; more uncertain outcomes demand a fatter premium, i.e. higher IV.

Which Greek measures exposure to an IV crush?

Vega — the sensitivity of option price to changes in implied volatility.

Approximate ATM option price formula?

C \approx 0.4\,S\,\sigma\sqrt{T}

(price is proportional to IV).

Can you be right on direction and still lose on a long option?

Yes — if the vega loss from the IV crush exceeds the delta gain from the move.

How do traders profit from IV crush?

Sell premium (short straddle/strangle, iron condor) before the event and buy it back after IV collapses.

Main risk of shorting IV into earnings?

A larger-than-priced gap move; the crush is a premium paid for taking that gap/tail risk.

What is the "implied move"?

The market's priced expected move, roughly the ATM straddle price; your directional edge must beat it to profit from long options.

Why buy options after earnings if they're cheap?

They're cheap because uncertainty is gone; you now need a genuine directional move without the event tailwind.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, IV crush ka funda simple hai. Kisi bhi bade event se pehle — jaise earnings, FDA decision, ya Fed meeting — market ko pata hai ki stock ek badi jump maar sakta hai, par kis direction mein pata nahi. Is uncertainty ki wajah se option ki implied volatility (IV) bahut upar chadh jaati hai, aur option ka premium fat ho jaata hai. Yaani aap bahut mehnga ticket khareed rahe ho. Jaise hi result aa jaata hai, uncertainty khatam — IV dhadam se neeche gir jaati hai, aur option ka price bhi crash ho jaata hai, chahe stock hila hi na ho. Isi ko "IV crush" kehte hain: pump before, dump after.

Sabse important baat: option pe do alag forces kaam karti hain — ek direction (delta) aur doosri IV change (vega). Bahut log call khareedte hain, stock sahi direction mein bhi chala jaata hai, phir bhi paisa nahi banta ya loss ho jaata hai. Kyunki vega loss (IV girne se) delta gain (move se) ko kha jaata hai. ATM option ke liye ek simple formula yaad rakho: $C \approx 0.4 \times S \times \sigma \times \sqrt{T}$ . Isse saaf dikhta hai ki price seedha IV ( $\sigma$ ) ke proportional hai — IV aadha hua to price bhi aadha, bina stock hile.

Ab isse paisa kaise banega? Jo log samajhdaar hain wo event se pehle premium bechte hain — short straddle, strangle, ya safe tarike se iron condor — aur event ke baad IV crush hone par saste mein wapas khareed lete hain. Difference unka profit. Par yaad rakho, ye free money nahi hai: agar stock market ke expected move se zyada gap kare, to short wale ki lag jaati hai (Example 3 dekho). Isliye IV bechna ek insurance premium jaisa hai — chhote-chhote wins, par kabhi-kabhi ek bada loss. Hamesha risk define karke chalo aur naked short mat maaro binaries mein.

Test yourself — The Greeks

Connections