Should smooth Gamma at exact expiry and strike be labeled an ordinary finite value?
Reveal the worked answer
No.
The payoff kink requires explicit boundary treatment.
Dealer Logic · DL-11 · Core
Expiration and concentrated Gamma
Why is the near-strike region special near expiry?
What you will learn and prerequisites
- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.
Read first: Why dealers hedge
As time runs down, finishing in or out of the money becomes increasingly sensitive to small price changes near the strike. The hedge ratio can change rapidly there. Far from the strike, the same option may instead become almost stock-like or nearly irrelevant.
Understand the mechanism
ATM Gamma can rise as remaining time approaches zero in the smooth model. At exact expiry the payoff has a kink at strike; the ordinary smooth Gamma is not a normal finite number there.
Expiring inventory can disappear, be exercised or be replaced. Tomorrow's book is not simply today's book with a clock moved forward.
Walk through the process
Separate mathematical concentration from settlement operations. Identify exercise style, settlement method and the consequences of short options near strike. Decide whether the hedge can be managed under realistic liquidity.
Gross 0DTE activity is not proof of net dealer short Gamma. Offsetting flows can leave a different retained inventory.
Evidence boundary
The arithmetic is original conditional teaching material, not a measurement of current dealer positions. The cited Cboe research is historical product-specific evidence, not a live inventory feed. Model outputs should remain distinguishable from observed market facts.
A worked example
Hold S=K=100 and sigma=25%, with zero rate and yield. Calculate Gamma at 30, 10, 3 and 1 day. The graph increases toward shorter time near this strike.
It deliberately stops above zero. A zero-time value is intrinsic, but the smooth derivative formulas need explicit boundary handling rather than an undisclosed tiny-time substitution.
Expiration and concentrated Gamma—worked comparison
Vertical: ATM Gamma per USD
Horizontal: Calendar days remaining
1. Fictional example
Read the graph as a data table
| Calendar days remaining | Fictional example |
|---|---|
| 1 | 0.304865 |
| 3 | 0.176006 |
| 5 | 0.136328 |
| 10 | 0.0963881 |
| 20 | 0.0681421 |
| 30 | 0.0556259 |
What would invalidate the reading?
Keeping yesterday's Delta near expiry can leave a rapidly changing exposure. Flooring exact zero time silently can also create misleading boundary outputs.
Check your understanding
Try the question before revealing its answer. These are reading checks, not trading certification or a site completion record.
What is the critical failure to avoid?
Reveal the worked answer
Keeping yesterday's Delta near expiry can leave a rapidly changing exposure. Flooring exact zero time silently can also create misleading boundary outputs.
Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome.
Return to the question: Why is the near-strike region special near expiry? State the observed facts, the assumptions and the failure condition separately.
Sources, assumptions and downloadable script
External references support definitions and conventions. Worked scenarios and prose are original. No current quotes or dealer inventory are claimed.
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