What is total P/L given hedge +80, option −60 and costs10?
Reveal the worked answer
+10.
Count all components exactly once.
Advanced Options · ADV-25 · Core
Gamma scalping
Can hedge gains pay for owning convexity?
What you will learn and prerequisites
- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.
Read first: Read a contract and its premium, Rights, obligations and expiration, Defined payoff risk is not margin, Read the whole multi-leg ticket
Gamma scalping combines a long-Gamma position with changing Delta hedges. The hedge sells some underlying after rises and buys some after declines under positive Gamma. Those adjustments can realize trading gains, but the option cost, time decay and execution must also be counted.
It is a volatility and path-dependent process, not free income.
Understand the mechanism
Locally dH≈−Gamma×dS. Repeated hedging attempts to reduce direction while exposing the relationship between movement and option cost. Discrete hedging, jumps, bid/ask costs and changing Greeks alter the textbook picture.
Do not report hedge gains alone as the whole strategy return. Nor should modeled option P/L be double-counted with a decomposition already including those gains.
Walk through the process
Choose a hedge rule before the path is known, track actual fills and reprice the option at the same timestamps. Include funding, fees and inventory. Compare a quiet path that pays Theta but supplies little hedge opportunity.
This material is advanced practice, not a claim that a retail account can harvest every oscillation.
Model and implementation boundary
These are complete fictional reading examples, not live opportunities. Terminal identities assume the stated common settlement. Multi-expiry values require a surviving-leg model. Costs, assignment and financing can alter realized outcomes; a mathematical bound alone does not guarantee the same operational loss path.
A worked example
In a fictional simplified book, Gamma is locally 20 share-equivalents per dollar. Spot 100→102 increases Delta by 40, so the incremental hedge sells 40 at 102. A return to 100 reverses the Delta change and buys 40 back, earning 80.
If the option's net same-endpoint change over the interval is −60 and hedge costs are 10, total is +10. The assumed option change must be independently valued; it is not guaranteed. The chart separates hedge, option and cost components.
Gamma scalping—worked comparison
Vertical: Example P/L (USD)
Horizontal: Hedge / option / costs / total
1. Fictional example
Read the graph as a data table
| Hedge / option / costs / total | Fictional example |
|---|---|
| 1 | 80 |
| 2 | -60 |
| 3 | -10 |
| 4 | 10 |
What would invalidate the reading?
A quiet or trending path, changing Gamma, jumps or costs can defeat the example. Counting hedge gains without option carry creates an illusory profitable strategy.
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
A quiet or trending path, changing Gamma, jumps or costs can defeat the example. Counting hedge gains without option carry creates an illusory profitable strategy.
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: Can hedge gains pay for owning convexity? 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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