Question it answers
If spot stays still, how will my convexity change tomorrow?
Black–Scholes & Greeks · BSM-19 · Advanced
Color
What does Color measure, in which units, and what does it not predict?
Why it matters
Gamma can change rapidly close to expiry.
Use
Helpful for planning future hedge intensity.
Naming warning
Higher-order Greek labels vary by platform.
What you will learn and prerequisites
- Explain Color in plain language.
- Reproduce the unit conversion.
- Compare a local estimate with model revaluation.
Color measures how Gamma changes as calendar time passes. It is sometimes called Gamma decay, but decay is a nickname rather than a sign guarantee. Near strike, Gamma can increase as expiry approaches.
The derivative helps plan how tomorrow's hedge instability can differ from today's.
Read the derivative as a sentence
This course uses calendar time, opposite to remaining-maturity differentiation. Divide the annual quantity by 365. Matching call and put Color agree because their Gamma agrees in this model.
A daily estimate on a contract with hours left needs an accepted horizon and boundary handling. It cannot be extrapolated past expiry.
Use it within its scope
Use Color to identify where hedge intensity may concentrate with time. Actual spot movement can carry the option away from the concentration, so an isolated clock experiment is not a complete path forecast.
The model boundary
The smooth formulas require positive spot, strike, volatility and remaining time. Zero time and zero volatility still admit explicit value limits, but smooth Greek availability needs separate rules. No invalid or zero input is silently replaced with a default. Continuous dividends, constant parameters and European exercise are modeling assumptions, not claims about every real option.
One complete numerical experiment
The shared fictional European call uses spot 100, strike 100, 30 calendar days, sigma 25%, continuous rate 4% and yield 1%. Its BSM value is 2.977574155; d1=0.070239317 and d2=-0.001433455. Values are per option unit before contract multiplication.
Raw Color is 0.339716300896. The displayed convention gives 0.000930729591 Gamma change per calendar day. Isolate one calendar day passing while holding every other input fixed.
Starting Gamma is 0.055478868929. The local estimate after the shock is 0.056409598521; a full-model recomputation gives 0.056433480449. Approximation minus recomputation is -0.000023881928. The difference shows the limitation of a local derivative, not a claim that the market must follow either number.
The graph varies only its labeled horizontal input. It is a series of controlled states, not historical observations or a future trajectory. Read its units before interpreting sign or magnitude.
Open the calculation without leaving this lesson
Color across controlled states
Vertical: Gamma change per calendar day
Horizontal: Calendar days remaining
1. Fictional example
Read the graph as a data table
| Calendar days remaining | Fictional example |
|---|---|
| 1 | 0.152452 |
| 2 | 0.0539059 |
| 3 | 0.0293459 |
| 5 | 0.0136417 |
| 7 | 0.00823706 |
| 10 | 0.00482571 |
| 15 | 0.00262822 |
| 20 | 0.00170801 |
| 30 | 0.00093073 |
| 45 | 0.000507445 |
| 60 | 0.000330125 |
| 90 | 0.00018027 |
A correct number can be misread
The stated unit is Gamma change per calendar day. Mixing raw decimal derivatives with point shocks or calendar time with remaining time can magnify or reverse the result.
The controlled comparison also omits live spread, surface dynamics, unsupported exercise effects and execution. A local sensitivity is not a market forecast or a guarantee of realized P/L.
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 displayed Color in this example?
Reveal the worked answer
0.000930729591 Gamma change per calendar day.
Always state the unit.
Does model agreement prove the same live-market change?
Reveal the worked answer
No.
Actual inputs, instrument features and executable quotes can differ.
Translate Color into its specific input, affected quantity and unit before applying it. Revalue when the local approximation no longer fits.
Try it in the working lab
- Record Gamma with 30 days and then 29 days remaining.
- Compare that change with Color/day.
- Distinguish a calendar-time derivative from a time-remaining derivative.
Your live inputs are independent of the fixed worked example above. Return to the “Lesson example” preset to reproduce it.
My reading record
Personal review marks are not quiz passes, course certification or trading approval. Old plugin progress is not overwritten.
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.
Read this lesson as Markdown · Download its JavaScript content module