Change one input
Choose spot, volatility or time remaining for the horizontal axis. All other market inputs stay fixed.
Black–Scholes & Greeks · BSM-05 · Core
Read a Greek curve
What does the shape add to a single number?
Ask about the shape
Price's local slope is Delta. Delta's local spot slope is Gamma. A single number becomes easier to interpret when you see its neighborhood.
Use the actual state
The marked state is your entered value. The chart domain expands to include it instead of clamping and mislabeling another point.
Time-axis caution
Moving right on a days-remaining chart means a longer option life. It is not a picture of calendar time passing.
Working Greek visualizer
The tool below is live. The written examples that follow retain their fixed fictional inputs.
What you will learn and prerequisites
- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.
Read first: Greeks without intimidation
A curve shows how a sensitivity changes across controlled states. Its horizontal axis is not automatically time; a spot scan contains many hypothetical spot values at the same maturity.
Read axes, fixed inputs and units before assigning an interpretation to the shape.
Understand the mechanism
On a price-versus-spot curve the slope is Delta and the curvature Gamma. On a Delta-versus-spot curve, slope is Gamma. A graph of Vega versus maturity answers a different question again.
Scaling can hide or exaggerate apparent changes. The plotted current marker must represent the actual current input, not a clamped substitute at the chart boundary.
Walk through the process
Choose one varying input and name everything held fixed. Compare the current state with a nearby point, then a larger move. Explain why local approximations degrade.
Keep a table equivalent so exact points and units remain readable without relying on the graphic alone.
Read before applying
All numerical market states are hypothetical. The calculations illustrate a European continuous-yield model, not a quote feed. Financial-model validation, instrument suitability and executable pricing are separate questions.
A worked example
At spot 100 the shared model Delta is 0.527565. At 101 it is 0.582324. Their difference demonstrates that the hedge ratio changes with spot.
The graph scans spot 80–120 at a fixed thirty-day maturity. It is a set of counterfactual states, not a forecast that price travels from left to right. No live chart data are used.
Read a Greek curve—worked comparison
Vertical: Delta (per unit)
Horizontal: Hypothetical spot (USD)
1. Fictional example
Read the graph as a data table
| Hypothetical spot (USD) | Fictional example |
|---|---|
| 80 | 0.00116971 |
| 82 | 0.00347865 |
| 84 | 0.00907127 |
| 86 | 0.0209542 |
| 88 | 0.0432903 |
| 90 | 0.0807229 |
| 92 | 0.137057 |
| 94 | 0.213694 |
| 96 | 0.308523 |
| 98 | 0.415854 |
| 100 | 0.527565 |
| 102 | 0.635006 |
| 104 | 0.730933 |
| 106 | 0.810776 |
| 108 | 0.872975 |
| 110 | 0.918493 |
| 112 | 0.949894 |
| 114 | 0.970379 |
| 116 | 0.983056 |
| 118 | 0.990519 |
| 120 | 0.994708 |
What would invalidate the reading?
A reader treats a scenario scan as a future trajectory or compares axes with different units as though their slopes were identical.
Check your understanding
Try the question before revealing its answer. These are reading checks, not trading certification or a site completion record.
Is the x-axis here a forecast timeline?
Reveal the worked answer
No; it is hypothetical spot at fixed maturity.
The varied input defines the experiment.
What is the critical failure to avoid?
Reveal the worked answer
A reader treats a scenario scan as a future trajectory or compares axes with different units as though their slopes were identical.
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: What does the shape add to a single number? State the observed facts, the assumptions and the failure condition separately.
Try it in the working lab
- In Greek curves plot Delta against spot.
- Move to Gamma using the same state; compare where each changes most.
- Set spot well outside the old default range; confirm the marked input is still the actual value.
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.
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