Model and input conventions
The local approximation is signed option units multiplied by delta times the price change, plus one half gamma times the squared price change. Fixed total costs are deducted afterward. Enter a 5% underlying shock as 5, and enter delta and gamma for one underlying unit of the option. Use negative option quantity for a short position; do not apply the short sign to both quantity and the supplied long-option Greeks.
Worked numerical example
With spot 100, a +5% shock, ten long underlying units of options, delta 0.50 and gamma 0.02, the price change is 5. The delta contribution is 25 and the gamma contribution is 2.50. After a fixed cost of 1, the approximate net result is 26.50. For the same long position and a −5% shock, the gamma contribution remains positive while the delta contribution reverses sign.
Read the scenario table
Each row decomposes a different underlying move into delta P&L, gamma P&L and total approximate net P&L. This helps compare asymmetric outcomes for up and down moves of the same size. The original user shock is included alongside standard illustrative scenarios. If the gamma contribution dominates the delta contribution, compare against a full pricing model before interpreting the approximation economically.
Where the model stops
The formula freezes the initial Greeks and excludes theta, vega, rate changes and volatility-surface movement. Large shocks or a nearby expiry can make a second-order expansion misleading, including implied option values outside valid bounds. The approximate post-shock delta is also a local expansion rather than a fresh derivative of a repriced option. None of these outputs estimate the probability of the entered shock.