Convert IV changes into percentage points
OIC defines vega using a one-percentage-point change in implied volatility. A mathematical derivative with respect to decimal volatility has a different scale: divide that derivative by 100 to quote vega per IV point. Read the data provider convention before combining values. An option premium quoted per share also differs from a dollar value per contract.
- These are hypothetical first-order estimates using a fixed $0.20 vega and a 100-share multiplier, with no change in spot, time, rates or dividends.
- For three short contracts, signed quantity is -3. The +1-point scenario produces about -$60 for that position. A positive long-option vega becomes negative exposure when sold.
- Check contract specifications for the actual premium multiplier and deliverable. Do not automatically use 100 for adjusted equity contracts, index options or futures options, or multiply twice if the displayed Greek is already per contract.
| IV scenario from 30% | Decimal change | IV-point change | One long contract estimate |
|---|
| Increase by 1 point to 31% | 0.01 | +1.0 | $0.20 × 1 × 100 = +$20 |
| Increase by 1% relative to 30.3% | 0.003 | +0.3 | $0.20 × 0.3 × 100 = +$6 |
| Decrease by 5 points to 25% | -0.05 | -5.0 | $0.20 × (-5) × 100 = -$100 |
| Increase by 10% relative to 33% | 0.03 | +3.0 | $0.20 × 3 × 100 = +$60 |
Calculate vega from a stated pricing model
For a European option under the Black-Scholes-Merton model, let S be spot, K strike, T remaining years, σ annualized decimal volatility, r the continuous annual risk-free rate, and q the continuous annual dividend yield. Define d1 = [ln(S/K) + (r - q + σ²/2)T] / (σ√T). Vega per share per IV point is v = S exp(-qT) φ(d1) √T / 100, where φ(x) = exp(-x²/2) / √(2π). The same formula applies to a call and put with matching inputs.
- To reproduce prices below, set d2 = d1 - σ√T and C = S exp(-qT) N(d1) - K exp(-rT) N(d2), where N is the standard normal cumulative distribution. Recalculate C at each scenario volatility rather than extending a fixed vega indefinitely.
- Require positive spot, strike, volatility and remaining time for these expressions. At expiry, value is the payoff and volatility no longer changes it. Handle zero volatility with a model limit rather than dividing by zero.
- These examples assume European exercise and constant rates, dividend yield and scenario volatility. American early exercise, discrete cash dividends, settlement terms and market spreads require additional treatment. A model price is not an executable quote.
Remaining time changes the dollar sensitivity
Hold S = K = $100, σ = 30%, r = q = 0 and use T = calendar days / 365. The following theoretical call vegas isolate remaining time. All figures are per IV point; each contract here has a multiplier of 100. The 365-day value is about 3.45 times the 30-day value under these particular assumptions.
- The square-root-of-time factor helps explain the difference, but d1 changes too. Do not scale every contract by √T without recalculating the full formula.
- This is a controlled comparison, not a claim that every farther expiry has higher vega than every nearer expiry. Moneyness, dividends and the IV surface differ across real contracts.
- Higher vega does not imply a larger likely loss: the magnitude and direction of each expiry's IV shock also matter. Event-driven near-term IV can move much more than longer-term IV.
| Remaining days | Vega per share | Vega per contract |
|---|
| 7 | $0.055236 | $5.5236 |
| 30 | $0.114267 | $11.4267 |
| 90 | $0.197551 | $19.7551 |
| 365 | $0.394479 | $39.4479 |
Sum signed dollar vegas across legs
For leg i, let nᵢ be signed contract quantity, mᵢ its premium multiplier, vᵢ its per-share vega per IV point, and ΔIVᵢ its change in percentage points. The first-order position change is Σ(nᵢ × mᵢ × vᵢ × ΔIVᵢ). Only for a common point shock h can this be written as net dollar vega × h, with net dollar vega = Σ(nᵢ × mᵢ × vᵢ).
- Each leg uses its own IV and remaining time. No historical-volatility input is substituted. The net model value is 200 × C(A) - 300 × C(B), not a recorded entry debit or a realized P&L.
- A +1-point parallel shock means A moves to 31% and B to 36%. A +1% relative shock means A moves to 30.3% and B to 35.35%; it is not a common point shock.
- A small or zero net vega can hide large opposing exposures across expiries. This ratio position also has other risks; the vega calculation does not establish a hedge or a suitable trade.
| Hypothetical call leg | Quantity / multiplier | Baseline premium | Vega / share / point | Signed dollar vega |
|---|
| A: K $100, 90 days, IV 30% | +2 / 100 | $5.937515 | $0.197551 | +$39.510285 |
| B: K $105, 30 days, IV 35% | -3 / 100 | $2.076416 | $0.104000 | -$31.199940 |
| Combined position | S $100, r = q = 0 | Net model value $564.578124 | Different expiries and strikes | +$8.310346 per parallel IV point |
Compare linear exposure with full scenario repricing
Keep spot at $100 and freeze time, rates and dividends at the baseline above. Full model repricing means calculating both call prices again at the stated IVs, then taking 200 × [C(A,new) - C(A,old)] - 300 × [C(B,new) - C(B,old)]. These are hypothetical changes from baseline model value before costs, not observed market returns. Calculations use unrounded values.
- The final row changes the IV term structure: A gains about $79.02 in the linear calculation while the short B leg gains about $93.60. Applying the $8.31 net vega to one common shift would miss this scenario.
- The up and down 10-point repricings are asymmetric because vega itself changes with volatility. Volatility curvature is often called vomma or volga; it is different from gamma.
- If spot or time also changes, recalculate all inputs for every surviving leg. Once an expiry is crossed, use its settlement payoff and subsequent cash treatment. Do not feed negative remaining time into the formula.
| Scenario: A / B IV | Point shifts A / B | Linear value change | Full model value change |
|---|
| 31% / 36% | +1 / +1 | +$8.31 | +$8.21 |
| 40% / 45% | +10 / +10 | +$83.10 | +$74.49 |
| 20% / 25% | -10 / -10 | -$83.10 | -$97.59 |
| 32% / 32% | +2 / -3 | +$172.62 | +$171.59 |
Keep gamma and historical volatility separate
Vega is sensitivity to implied volatility. Gamma is the change in delta per unit move in the underlying price, or the second derivative of option value with respect to spot. A gamma term such as ½ × Γ × (ΔS)² describes spot curvature. It does not correct the error from a large IV shock. When spot and IV move together, cross-effects also make a sum of isolated first-order estimates incomplete.
- Historical volatility describes observed underlying returns over a chosen window. Contract IV is inferred from an option price under a pricing model. The two measures can be compared, but historical volatility does not supply the missing IV for each strike and expiry.
- Missing, stale or implausible IV or vega means the position estimate is incomplete. Preserve that missing status; do not convert it to zero exposure. A wide bid-ask spread can also make a single implied-volatility estimate unstable.
- An IV decline can reduce a long option's value even if spot is unchanged. That isolated sensitivity does not predict the total result after time decay, spot movement, fees and execution.
Verify the contract and scenario inputs in TradingView
TradingView documents IV and vega fields in its options chain and time/IV changes in its Strategy Builder what-if scenarios. Record the underlying contract, strike, call or put, expiry, quote time, premium units and each leg's starting IV. Futures options require the correct underlying futures expiry as well.
- For an IV-only comparison, keep the scenario time shift at zero and evaluate the same underlying price. Record every leg's resulting IV before comparing a curve with a vega estimate.
- The what-if documentation labels IV shift in percent but does not explicitly resolve relative percent versus percentage points. Do not infer the meaning of "+10%" from its label alone: 30% to 33% and 30% to 40% are different tests. If resulting IVs cannot be verified, use explicit calculator inputs for the numerical comparison.
- In Pineify AI Stocks & Options Picker, Options Chain offers expiration selection, strike rows, IV and bid/ask fields, plus an expanded row with available vega and other Greeks. Match the exact contract and verify the provider's unit convention before scaling those values.
- For explicit scenarios, the Black-Scholes Option Calculator accepts spot, strike, time, volatility, rate and dividend yield. Reprice each leg separately and apply quantities and multipliers yourself. This is a theoretical model workflow, not an automatic historical multi-leg backtest.
