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Calendar Spreads: Vega, Delta, and Time-Decay Risks

Article Quant Q&A · Author: Distraction Arrestor
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Summary

The document considers a same-strike options calendar spread that sells a nearer-expiry option and buys a later-expiry option, with equal initial premium amounts. It asks whether matching those premiums makes the position neutral to implied volatility or underlying price changes. The response explains that premium equality alone does not establish Greek neutrality: the longer-dated option generally has greater vega, so the spread can retain net volatility exposure.

Time passage can also alter the legs differently. The answer discusses veta, the change in vega over time, and charm, the change in delta over time; their effects depend on moneyness and option details. Delta neutrality is described as an exceptional case requiring closely matched options that are exactly at the money, with expiration as their only difference. The document does not calculate a specific spread’s exposures or worst-case loss, and emphasizes that the underlying product and the position’s net Greeks matter.

Key ideas

  • Equal premiums do not imply a calendar spread is vega neutral.
  • The longer-dated option generally has greater vega than the nearer-dated option.
  • Charm can change the spread’s net delta as time passes, depending on moneyness.
  • Net exposures and favorable or unfavorable effects depend on the specific options and underlying.
  • The response provides qualitative guidance rather than a numerical risk analysis.

Tags

OptionsVolatilityDerivatives pricingRisk management
Full text
# Calendar spread: What are the worst cases?


# Calendar spread: What are the worst cases?












I am looking to solely make use of the theta decay and trying to overcome the effects of delta and Vega.

​​If,

I sell ABC Feb OTM (strike price X) with 3 x 10 = Rs. 30 credit and buy ABC Mar OTM (strike price X) with 1 x 30 = Rs. 30 debit.

- Is Calendar spread Vega neutral?

Now, both the values are simply extrinsic values. How would calendar spread pair react to any change in Implied volatility?

- Is Calendar spread Delta neutral?

This is my biggest concern. I could imagine that when spot price moves, the neutrality may be disturbed, but the sell and buy at same strike price should somehow diminish the losses/profits made on underlying price movements. Will they do it?

- What are the factors that work solely to create losses? What are the factors that can work in both favorable and unfavorable ways?

Thanks.

## Answer by user42108 (score 2)

https://quant.stackexchange.com/a/61352

You should specify the underlying product. I can think of seasonal commodities where an options calendar spread would effectively be on underlyings that are very different. In that case, "What are the factors that work solely to create losses?" could be very different than, say, risks for doing a calendar in something like EURUSD.

## Answer by justasking (score 1)

https://quant.stackexchange.com/a/61347

Theoretically:

- Veta (dVega/dTime), is almost always negative, therefore, all else equal your calendar spread will not be vega neutral, the longer dated option will have higher vega.

- Charm (dDelta/dTime) increases delta with the passage of time for ITM options (to +-1 depending if call/put) and decreases for OTM options (to 0), it has no effect on ATM options. Therefore, all else equal your calendar spread will not be delta neutral unless both options are exactly the same in all ways except expiration and exactly ATM.

- It all depends on the specific parameters of the options you use in your calendar spread, what's favourable and unfavourable for your position depends on the net greeks of the calendar spread overall.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.