Apply a market shock, compare full repricing with a local Greek approximation, and inspect what the approximation misses. Black–Scholes, synthetic inputs; no live market data.
Base state stays fixed while you explore.
The curve reprices the base option versus spot. Dots show the actual base and shocked states; a volatility/time shock can move off the curve.
| Spot | Base option price |
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Preparing contributions…
| Component | Currency units | Convention |
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Local expansion at the base state. Cross and higher-order terms are omitted; the residual is approximation error, not a separate trading gain. Large shocks and near-expiry cases can be less accurate.
Invert the price generated above using the same Black–Scholes model. This checks internal consistency; it is not market calibration or independent validation.
—This supplied P&L sample is unrelated to the option. Gains are positive; losses are negative.
—VaR uses ceil(confidence × n) − 1 in sorted losses. ES averages losses at and beyond that observation. A small synthetic sample is illustrative.
Deterministic case v1 · one option unit · annual continuous rates and volatility · calendar-time decay per year.
Build revision: unknown. No production accuracy or latency claim.