What is vega?

Formula

From the Black-Scholes-Merton model, vega is the derivative of the option price with respect to volatility:

Where:

• S = underlying spot price
• φ(d1) = standard normal probability density at d1
• d1 = (ln(S/K) + (r + ½σ²)×T) / (σ√T)
• T = time to expiration in years
• The × 0.01 converts from "per unit sigma" to "per 1 vol point" (1%)

Vega is the same for calls and puts at the same strike, expiration, and IV (put-call parity guarantees this). Vega is always positive for a long option position — buying options is a bet on higher IV, selling is a bet on lower IV.

Worked example

SPY spot = $520, ATM $520 strike, 30 DTE, ATM IV = 15.2%, risk-free rate = 4.5%. Compute vega for a single call:

Interpretation: if IV moves from 15.2% to 16.2% (a +1 vol point spike), this option's theoretical price rises by ~$0.71 per share, or $71 per contract (100 shares). If IV crushes to 14.2%, price falls by ~$0.71.

Portfolio vega example

Consider a short iron condor on SPY: sell 1 × 505 put + sell 1 × 535 call + buy 1 × 500 put + buy 1 × 540 call, all 30 DTE.

• Short 505 put vega ≈ +$0.68/share → leg vega = −$68 per contract (short position sign flip)
• Short 535 call vega ≈ +$0.61/share → leg vega = −$61
• Long 500 put vega ≈ +$0.55/share → leg vega = +$55
• Long 540 call vega ≈ +$0.50/share → leg vega = +$50

Interpretation: this iron condor loses $24 for every +1 vol point IV spike (bad if IV expands from 15% to 20%: expected loss = ~$120) and gains $24 for every −1 vol point IV crush (good if IV compresses back to 10%: expected gain = ~$120). This is why iron condors and other short-vol structures are called "vega-negative."

Long-vega vs short-vega positions

Why vol-shifted P&L matters (Bloomberg OVME's moat feature)

Traditional payoff diagrams and P&L tables (including those on OptionStrat and most retail platforms) hold IV flat when computing cell values at each price × date point. This is materially misleading for any strategy with non-trivial vega:

• Calendars and diagonals have net-vega concentrated in the back-month leg. A flat-IV P&L table under-represents the exposure to IV shifts.
• Iron condors that look "safe" at flat IV can look dramatically worse after a vol spike, because both credit-selling wings gain in value.
• Pre-earnings strategies have a foreknown IV crush baked into the tail dates. Flat-IV assumption inflates expected P&L on both sides of the payoff.

Bloomberg's OVME (Option Value & Model Evaluator) function has a scenario tab that shocks IV across all legs and recomputes the P&L grid. This is the "vol-shifted P&L overlay" — the ability to answer "what does my P&L look like if IV crushes 5 points overnight?" or "if a vol spike hits, how much do I lose?"

The OptionIncomeTools payout table (in the covered-call, cash-secured-put, Black-Scholes, and double-calendar calculators) implements this exact feature with an IV shock slider (±20 vol points) and preset buttons. Slide the shock left to see the crush scenario; slide right to see the spike scenario. The vega decomposition panel below the grid always shows portfolio vega + the expected P&L delta for ±5 and ±10 point shocks.

Common misconceptions

"Vega tells me how much the option will move"

No. Vega tells you how much the option will move for a given change in IV. If IV doesn't change, vega is irrelevant. Vega is a sensitivity, not a forecast.

"Higher vega means more risk"

Depends on direction. Higher positive vega means more upside if IV rises AND more downside if IV crushes. Higher negative vega means more upside if IV crushes AND more downside if IV rises. The absolute value is a measure of vega exposure; the sign tells you the direction of that exposure.

"Vega is constant"

No. Vega changes with spot, strike, time, and IV itself. Deep ITM and deep OTM options have lower vega than ATM options because they're closer to intrinsic value (their price is dominated by moneyness, not volatility). Vega decays toward zero as expiration approaches.

"I don't need to think about vega for covered calls"

You do, actually. A covered call is short-vega. When IV crushes (typical post-earnings), your short call gains value faster than the model predicts — that's your vega tailwind. When IV spikes (typical pre-earnings or during volatility events), you take a vega hit. Understanding this decides whether to write CCs before or after earnings.

How OptionIncomeTools uses vega

The site computes vega using the closed-form BSM formula (Vega = S × φ(d1) × √T × 0.01) with these implementation notes:

• Portfolio vega is exposed in the payout-table module: sum of leg vegas with sign per leg direction (long adds, short subtracts).
• Vol-shifted P&L overlay is available on covered-call, cash-secured-put, and Black-Scholes calculators via the IV shock slider. Preset buttons snap to -20, -10, -5, 0, +5, +10, +20 vol points.
• Sensitivity panel shows the dollar P&L delta at ±5 and ±10 vol shifts, updated live as the strategy inputs change.
• Constant-maturity vega is not tracked historically; only the current-snapshot vega is displayed.

Related terms

• Expected Move — the market-implied ±1σ price envelope, derived from IV. When IV shifts, expected move shifts, and vega P&L follows.
• IV Rank — vol regime normalization. Short-vega positions favor high IVR entries; long-vega positions favor low IVR entries.
• Implied volatility (pillar guide) — deep dive on IV and how it's computed.
• Greeks pillar guide — complete Greeks primer including delta, gamma, theta, rho.
• Covered Call Calculator — shows the vol-shifted P&L overlay on the payout table.
• Cash-Secured Put Calculator — same treatment.
• Black-Scholes Calculator — single-option vega calculation with Greeks decomposition.