What Is Veta?
Veta (also called DvegaDtime) is the second-order cross derivative of option value with respect to volatility and time (partial2 V / partial sigma partial t). Equivalently, veta measures how vega itself decays as expiration approaches. Veta is the structural exposure traded by calendar spreads and the analytical Greek behind term-structure trading.
What Is Veta in Options?
Veta tells you how vega changes per day as time passes. A long 60-day ATM call with vega $0.79 and veta -$0.012 per day sees its vega drop to $0.778 tomorrow. Across the option's life, veta accumulates - vega progressively shrinks toward zero as expiration approaches because the time component scaling vega (sqrt(T)) drives toward zero.
Two intuitions for veta. First, veta is "vega decay" - the time component of how vega itself moves. Second, veta is the analytical foundation of the vega term structure: long-dated vega is much larger than short-dated vega, and veta describes the rate of decay along the term-structure curve.
Worked Example
SPY at $500, two ATM calls: one at 60-DTE (vega $0.79), one at 7-DTE (vega $0.27). Computing daily veta for each:
- 60-DTE vega = $0.79; veta approximately -$0.0066 per day
- 7-DTE vega = $0.27; veta approximately -$0.019 per day
The shorter-tenor option has much faster vega decay per day in absolute terms. Across a calendar-spread position (long 60-DTE, short 7-DTE), the net veta is positive: $0.019 - $0.0066 = $0.012 per day - meaning the position gains daily vega-bias as the front leg decays faster than the back leg.
How Pricing Models Compute Veta
- Black-Scholes: closed-form veta. Approximate form: veta = vega × (rho contribution + d1×d2 term + 1/(2T)).
- Heston (stochastic volatility): veta computed by Fourier inversion of cross-derivative of pricing formula. Heston veta accounts for variance mean-reversion explicitly.
- SABR: veta is computed via the BS formula at SABR-implied vol with time-bumping; SABR is per-expiration so cross-expiration veta interpretation is approximate.
- Local volatility (Dupire): veta computed by re-pricing under bumped IV surface with time-stepping.
Veta and Calendar Spreads
Calendar spreads (sell short-dated, buy long-dated, same strike) are the canonical veta-isolating trade. The structure is built to be approximately vega-neutral in absolute terms but to capture differential vega decay across the two legs - which is exactly veta.
Three operational consequences. First, calendars profit from positive aggregate veta when vol surfaces are flat-to-rising. Second, the breakeven of a calendar trade is described by the veta vs IV-shift trade-off: a static surface produces veta P&L; a vol-regime expansion produces vega P&L. Third, term-structure trading (straddles at one expiration vs straddles at another) is essentially aggregate-veta arbitrage.
Veta in Pre-Event Windows
Pre-earnings option chains have inverted term structure: front-week IV is elevated (event premium) while back-month IV reflects normal regime. Veta in this regime is asymmetric: the front-week's veta accelerates the decay through IV crush on event day, while the back-month decays at normal rate. Calendar spreads positioned for the event window explicitly capture this asymmetric veta.
Special Cases
- Long-dated ATM: veta is small in absolute terms. Vega evolves slowly.
- Short-dated ATM: veta is large. Vega decays rapidly.
- Pre-earnings front-week: veta is anomalously large (IV crush priced in).
- Far OTM/ITM: veta is small. Vega is small to begin with.
Related Greeks
Veta is the cross-Greek of vega and time. Its second-order siblings are vanna (vega cross spot) and vomma (vega cross vol). The third-order extension DcharmDvol is the cross of charm and vol.
Related Concepts
Vega · Theta · Vomma · Term Structure · IV Crush · Heston · All 17 Greeks
References & Further Reading
- Hull, J. (2018). Options, Futures, and Other Derivatives, 10th ed. Pearson.
- Sinclair, E. (2010). Option Trading. Wiley.
This page is part of the 17 Greeks reference covering every options Greek with formula, intuition, worked example, and how each pricing model computes it. Browse the full documentation.