Free lesson · Volatility

Vega requires a volatility-unit convention

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An option’s response to an implied-volatility change is often quoted per one volatility point, although mathematical derivatives usually use a full decimal unit.

A rise from 20% to 21% is .01 in decimal volatility and one volatility point. Mixing those conventions can exaggerate sensitivity by a factor of 100. State whether Greeks cover one underlying unit or one exchange contract.

Vega is a local partial derivative that holds spot and other inputs fixed. A market smile may move differently at each strike and maturity, so a single parallel shock is only one scenario.

Apply it in a strategy

• Freeze inputs at the stated decision time and record their units.
• Reconcile option-risk reports, hedge quantities and surface scenarios.
• Recompute the example, then change the material assumption and explain the difference.

Research deliverable

Vega requires a volatility-unit convention: produce the worked calculation, a timestamped input record and a written decision addressing this limitation: Parallel, small volatility moves are an approximation; large skew or spot changes require full repricing.

These are synthetic mechanics examples, not historical performance or paper replications. Module evidence and research boundaries record the 12 September 2026 review.

# Python 3.10+; standard library and NumPy only.
# Synthetic teaching inputs; conventions and units are defined in the notation above.
def vega_change(vega_per_decimal,vol_before,vol_after):
    if min(vol_before,vol_after)<0: raise ValueError('Nonnegative volatilities required')
    return vega_per_decimal*(vol_after-vol_before),.01*vega_per_decimal

change,per_point=vega_change(40,.2,.23)
assert abs(change-1.2)<1e-12 and per_point==.4
print(change,per_point)