Delta hedging works because you can trade along the way. Every hedging argument, and every option model built on one, assumes the stock moves in small steps and you can rebalance at each one. Some of the most expensive things that happen to an options position break that assumption. This lesson is about the risks that a perfect hedge does not remove.
Gaps and jumps
A stock that closes at $200 and opens at $184 never traded at $196, $192 or $188. A short gamma position that was delta neutral at the close is suddenly very long delta at the open, with no chance to have sold stock on the way down. The gamma cost is about half of gamma times the move squared: with a gamma of 0.040 and a $16 gap, that is 0.5 times 0.040 times 256, or $5.12 a share, $512 per contract, all of it landing before you could act. The same move spread over a week would have been hedged in pieces at a fraction of the cost. Jumps are the reason short gamma positions earn theta: the daily income is payment for being on the wrong side of the gap.
The chart shows the shape of that risk for a short strangle on a $100 stock: sell the $90 put and the $110 call, 30 days out. The green line is the P&L one day later against wherever the stock opens. Near $100 the day's theta is a small gain. A few dollars away the line bends down, and past a strike it falls almost dollar for dollar.
Sold at 30 days and 30% volatility; the green line starts one day later. A gap puts you anywhere on it at once. Push volatility up to add the vol spike that usually comes with a gap.
A gap lands you anywhere on that line in one step. The Greeks at $100 describe only the flat middle; the losses live out on the slopes, which is why a desk stress tests the book.
How often the strikes are breached
A short strangle is a bet that the stock stays between its strikes. How often it does not depends on implied volatility and time. The distribution below is the range of prices at expiry that a 30% implied volatility implies for a $100 stock over 30 days. With those inputs the one-standard-deviation band runs from about $92 to $109, so the $90 and $110 strikes sit just outside it.
The range of prices at expiry implied by the volatility, with the 1 and 2 standard deviation bands shaded. A $90/$110 strangle's strikes sit just outside the darker band at 30% volatility; raise volatility and the band swallows them.
Outside one standard deviation is not the same as safe. The model puts about a 24% chance on this strangle finishing past one of its strikes: roughly 11% below $90 and 13% above $110. Real stocks have fatter tails than the model, so the true figure for big moves is usually higher. The next chart shows the chance of a breach at expiry as the time left grows; drag volatility and watch it climb.
The model's chance that the stock finishes past either strike, against days to expiry. At 30 days and 30% volatility it is about one in four. Raise volatility and watch it climb; the model's thin tails mean the real figure is usually higher.
Earnings: the jump the model can see coming
Earnings are a scheduled jump. The market knows the date, so options that expire after the report carry extra implied volatility to pay for it. The Terminal reports this as the implied earnings move: the size of the move, in percent, that the options are pricing for the announcement, shown as an expected absolute move so it reads against the average of past reports beside it. A model that treats the stock as moving smoothly sees the high implied volatility and prices the options accordingly, but it has no idea that most of that volatility arrives in one overnight step. If you are short options through the report, the implied earnings move is the size of the gap you have agreed to absorb.
Pin risk
On expiration afternoon, with the stock sitting on a strike you are short, you cannot know whether you will be assigned, so you cannot know what to hedge, and no Greek measures that. Module 13 will cover exercise, assignment and pin risk in full.
Liquidity
A hedge is only as good as the price you can trade at, and bid-ask spreads widen exactly when a fast market forces you to adjust. Module 13 will cover orders, fills and the spread.
Where the market can accelerate
Market makers hedge their own books too, and where their gamma is short that hedging chases the market and speeds moves up. The next lesson shows how the Terminal estimates dealer gamma from open interest and where its Gamma Flip, Call Wall and Put Wall sit.
The maths: what a stress test adds beyond the Greeks
The Greeks feed a Taylor estimate, dV ≈ Δ·dS + ½·Γ·dS² + ν·dσ + θ·dt, which is accurate for small moves and drifts for big ones. A stress test skips the estimate: it sets the stock, the volatility and the date to the shocked values and reprices every leg with the full model, dV = V(S + dS, σ + dσ, t + dt) - V(S, σ, t). Nothing is assumed about the Greeks staying put.
Take the short $90/$110 strangle above, sold for about $1.06 a share at 30 days and 30% volatility. Its net Greeks at $100 are delta -0.0565, gamma -0.0471, theta +0.059. The stock gaps to $80 overnight. The Taylor estimate is -0.0565 x -20 + ½ x -0.0471 x 400 + 0.059 = 1.13 - 9.42 + 0.06 = -8.23 a share. A full reprice at $80 with 29 days left says -8.95, about $72 a contract worse. On a gap to $92 the two agree within a few cents. The error grows with the jump, which is where the money is, and a stress test prices the vol rise that comes with the gap in the same step. The Greeks tell you how a position feels today; the stress test tells you what the bad day costs.
Your turn
Open IV Intelligence on NVDA and read the implied earnings move, then check on Price Context how many days away the report is. Compare the count with the expirations on the chain to see which contracts carry the jump.