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Key Takeaways
- Veta is the time sensitivity of vega. This page uses calendar time moving forward.
- Near the money with small carry effects, annual veta is approximately −vega / (2T).
- The full Black-Scholes formula determines the sign and magnitude for each strike and expiration.
- In the example, one day reduces 30-day vega by 1.7% and one-year vega by 0.1%.
- A calendar spread’s net veta is the signed sum of its two legs.
- Specify volatility-point units, time convention, and day count when comparing veta.
What is veta in options?
Veta is the second-order option Greek that measures how vega changes as time passes, with spot, implied volatility, rates, and dividends held fixed. Vega measures premium sensitivity to implied volatility; veta shows how that sensitivity evolves through the holding period. Risk systems also label it vega decay or DvegaDtime.
This page measures calendar time moving forward. Negative veta means vega decreases as the clock advances. Positive veta means it increases. A derivative taken against remaining time uses the opposite sign.
How do you calculate veta?
Black-Scholes vega per one volatility point equals S × exp(−qT) × φ(d1) × √T / 100.
Multiply that vega by q + (r − q)d1/(σ√T) − (1 + d1d2)/(2T) to obtain annual calendar veta in the same volatility-point units. Divide by 365 for the daily sensitivity used here.
Near the money with small carrying-cost effects, −vega/(2T) gives a compact approximation. The full expression determines the sign and magnitude across strikes, maturities, interest rates, and dividends.
The √T term is one part of the result. The dividend factor and density at d1 also change with remaining time. For example, a $100 spot-at-the-money option with ten years remaining, 30% IV, a 10% rate, and zero dividends has positive annual calendar veta of 0.0262 in vega-per-point units. The complete calculation captures that behavior directly.
Formula
Calendar veta = vega × [q + (r − q)d₁/(σ√T) − (1 + d₁d₂)/(2T)].- Vega per volatility point = S × exp(−qT) × φ(d₁) × √T / 100. Using it in this formula gives veta in vega-per-point units per year.
- d₁ = [ln(S/K) + (r − q + σ²/2)T]/(σ√T); d₂ = d₁ − σ√T.
- S is spot, K is strike, T is years remaining, σ is decimal volatility, r is the interest rate, and q is continuous dividend yield.
- Divide annual calendar veta by 365 for a calendar-day sensitivity in this example.
- A derivative with respect to remaining time has the opposite sign.
- With small carry effects near the money, calendar veta is approximately −vega/(2T). The complete formula determines the result across the chain.
Veta example: 30-day vs 365-day options
Two at-the-money calls on a $100 stock, both marked at 30 percent implied volatility with rates and dividends set to zero. One expires in 30 days and one in 365 days. Vega is quoted per share for a one point change in implied volatility, and nothing moves except the calendar.
- 30-day call: vega per point = 0.1143. Annual calendar veta = −0.6938, or −0.0019 per calendar day.
- 365-day call: vega per point = 0.3945. Annual calendar veta = −0.1928, or −0.0005 per calendar day.
- Reprice one day later: the 30-day vega becomes 0.1124 and the 365-day vega becomes 0.3940.
- The actual one-day reductions are 1.7% and 0.1% of starting vega.
- At the 109 strike with 30 days left, vega is 0.0722 and annual calendar veta is −0.8795.
The annual contract starts with 3.45 times the vega. After one day it retains 99.9% of that exposure, while the 30-day contract retains 98.3%. Compare both the amount of vega and its evolution through the planned holding period.
Compare 100 calls on a $100 stock at 30% IV with zero rates and dividends, as the table at the top of the page does. The 30-day call starts with 0.1143 vega per point and an annual calendar veta of −0.6938. One day later its vega is 0.1124, a 1.7% reduction. The 365-day call starts with 0.3945 vega and a veta of −0.1928. One day later it holds 0.3940, a 0.1% reduction.
The annual contract starts with 3.45 times the vega and retains more of it over the next day. Multiply the vega figures by 100 for a standard contract’s dollar response to one IV point.
At the 109 strike in the same 30-day chain, vega is 0.0722 and annual calendar veta is −0.8795. That strike has less vega than the 100 strike but a larger absolute time derivative. Calculate both measures when comparing the chain.
How does veta affect a calendar spread?
Short one of the example’s 30-day calls and buy one of its 365-day calls. The resulting net vega is 0.2802 per point and annual calendar veta is +0.5010.
The front leg contributes positive position veta because it is short. In this structure, that contribution exceeds the long back leg’s negative veta, so net volatility exposure grows as time passes.
Compute the signed sum for each calendar. Strike, expiration, IV, rates, and dividends determine the two legs’ values. A deeply in-the-money front leg with almost no vega creates a different profile from the at-the-money example.
How do traders use veta?
Start with the date of the trade thesis. Reprice the position at that date and compare the surviving vega with the exposure at entry. In the example, moving a 30-day at-the-money contract forward to nine days leaves 54.81% of its initial vega at unchanged inputs.
Compare longer expirations to match the holding period. Track each expiration’s IV separately, then combine the actual price, time, and volatility scenarios. The passage of time changes the Greek; the IV move changes the premium through that evolving sensitivity.
Use theta for value changes from time, vomma for changes in vega from IV, and vanna for changes in delta from IV. This separates the distinct drivers of the position.
In the options profit calculator, the spread between payoffs at a higher and a lower volatility on the thesis date shows how much vega survives, so pick the expiration that keeps the exposure you need.
Limitations of veta
- Reprice at the target date instead of multiplying the daily figure. Veta is a local derivative, and over many days vega changes along a curve.
- Add each expiration’s IV move and the vanna effect to the scenario. Veta holds spot, implied volatility, rates, and dividends fixed, while each expiration’s IV moves separately and a spot move changes vega through vanna.
- Match the convention before you compare. Calendar time and remaining time give opposite signs, and annual versus daily units and volatility-point scaling change the number.
- Use the full formula away from the money. The −vega/(2T) approximation works only near the money with small carry effects; the 109 strike and the ten-year, 10% rate case show the full formula giving a larger absolute value or even a positive sign.
- Pair veta with your IV scenario. Veta tells you how much volatility exposure remains on the date the IV move arrives.
Bottom line
Veta shows how much volatility exposure an option keeps as the calendar advances, which matters to anyone holding vega through a catalyst or a calendar spread. State the time direction and units, compute it from the full formula across the chain, and reprice the position at the thesis date to see the vega that actually survives.
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Sources and Further Reading
How entries are sourced, calculated and updated: editorial methodology.