# Gamma scalping

**ADV-25 · Advanced Options · Core**

**Lesson question:** Can hedge gains pay for owning convexity?

Original fictional examples; educational writing, not live market data, orders or production approval.

## By the end

- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.

**Prerequisites:** OPT-F01, OPT-F02, OPT-F03, OPT-F04

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.

## Graph: Gamma scalping—worked comparison

**Horizontal:** Hedge / option / costs / total  
**Vertical:** Example P/L (USD)

Fictional data from the written example. The chart organizes the comparison; its shape is not a forecast.

Complete numerical data are embedded in `scripts/advanced-options/ADV-25.js` and displayed as an accessible table in the HTML lesson.

## 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

### What is total P/L given hedge +80, option −60 and costs10?

**Answer:** +10.

**Why:** Count all components exactly once.

### What is the critical failure to avoid?

**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.

**Why:** Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome. **Critical risk check.**

## Takeaway

Return to the question: Can hedge gains pay for owning convexity? State the observed facts, the assumptions and the failure condition separately.

## References and provenance

The cited references support definitions and conventions. The teaching prose, tickets and numerical scenarios are original; they are not attributed as historical market observations.

- [OIC Strategy Reference](https://www.optionseducation.org/strategies/all-strategies-en)

- [OCC Options Disclosure Document](https://www.theocc.com/company-information/documents-and-archives/options-disclosure-document)

- [OIC Greeks](https://www.optionseducation.org/advancedconcepts/understanding-options-greeks)