Start small
Try spot +0.25, no IV change and no time passing. Then increase the spot move and compare the approximation error.
Black–Scholes & Greeks · BSM-06 · Core
Approximation versus repricing
Why must both methods receive the same scenario?
Change volatility separately
Reset the spot shock to zero, then change IV by one percentage point. Only after that combine spot and IV.
Use identical shocks
Both methods receive the accepted input changes. A request for 30 days passing on a 7-day option is rejected, not quietly floored in just one method.
Interpret the gap
The gap is approximation error within the same model. Even perfect model agreement does not prove an executable live-market result.
Working scenario lab
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 Greek approximation estimates local P/L; full repricing evaluates the same accepted new state under the model. Their difference is informative only when the input shocks, dates and units match.
Comparing different applied scenarios produces a software inconsistency disguised as model error.
Understand the mechanism
A common approximation includes Delta dS + 0.5 Gamma dS² + Theta dt + Vega dSigma + Rho dr + Epsilon dq. Here dt is positive elapsed calendar years. Additional cross terms are omitted, so combined large moves can diverge.
Full repricing is still exact only within its stated model and numerical accuracy, not exact future market P/L.
Walk through the process
Validate requested shocks first. Reject invalid resulting spot or negative volatility, or explicitly report a shared adjusted scenario. If elapsed time reaches expiry, use exact intrinsic for value and stop beyond the contract's life.
Apply the same validated state to the approximation and repricer. State which terms are included.
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
Starting at the common call, apply spot +0.50, IV +1 point and one calendar day elapsed. Delta contribution is 0.263782308; Gamma 0.006934859; Theta -0.051508870; Vega 0.113997676 per unit.
Estimated new value is 3.310780128; BSM revaluation at S=100.50, sigma=.26 and T=29/365 gives 3.308087339. Estimate minus revaluation is +0.002692789. The graph uses dollars per unit for every contribution.
A request for ten elapsed days on a seven-day option must be rejected or explicitly limited to seven for both methods. Charging ten days of Theta while pricing seven is not an honest approximation comparison.
Open the calculation without leaving this lesson
Approximation versus repricing—worked comparison
Vertical: Model P/L per option unit (USD)
Horizontal: Delta / Gamma / Theta / Vega contribution
1. Fictional example
Read the graph as a data table
| Delta / Gamma / Theta / Vega contribution | Fictional example |
|---|---|
| 1 | 0.263782 |
| 2 | 0.00693486 |
| 3 | -0.0515089 |
| 4 | 0.113998 |
What would invalidate the reading?
Different scenario clamps or time horizons can make the error meaningless. Large shocks also require more than a low-order Taylor expansion.
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 essential comparison requirement?
Reveal the worked answer
Both methods use the same accepted shocks and model conventions.
The remaining difference can then be studied as approximation error.
What is the critical failure to avoid?
Reveal the worked answer
Different scenario clamps or time horizons can make the error meaningless. Large shocks also require more than a low-order Taylor expansion.
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 must both methods receive the same scenario? State the observed facts, the assumptions and the failure condition separately.
Try it in the working lab
- Set spot change +0.25, IV/time/rate/yield changes zero.
- Compare local estimate and full-model repricing.
- Increase the spot shock, then add +1 IV point and inspect Vanna/Vomma contributions.
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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