Why Longer-Dated Options Usually Have Greater Vega

Summary

This explanation gives an intuitive account of why a longer-dated option can have greater sensitivity to implied volatility than a short-dated option. It compares two far out-of-the-money calls with the same strike and underlying price, one expiring the next day and the other in two months. If implied volatility rises while spot stays unchanged, the near-term option has little time to benefit from a wider range of possible price moves, while the later option has more time for those moves to occur.

The answer also supplies a standard vega expression involving spot, the square root of time to expiry, and the normal density evaluated at d1. The example is qualitative and does not prove that every back-month option has higher vega: vega also depends on moneyness, underlying price, and other contract inputs. The intuition is most directly applicable when comparing otherwise similar options and considering a volatility change with spot held fixed.

Key ideas

• A volatility increase can matter more to an option with more time remaining because there is longer for price movement to occur.
• The example compares equally struck, far out-of-the-money calls while holding spot constant.
• The answer presents vega as depending on spot, time to expiry, and the normal density at d1.
• Time to expiry alone does not guarantee higher vega across options with different inputs.

Tags

# Why vega increases further out in time


# Why vega increases further out in time












Why do back months options have a higher vega than front month options? If possible , kindly explain on an intuitive level without a lot of math.

## Answer by jaamor (score 3, accepted)

https://quant.stackexchange.com/a/16802

### Intuitive, no math explanation:

Imagine two call options, option A expiring tomorrow and option B expiring in two months. Both of the options are way out of the money and have the same strike price.

Due to some event the implied volatility of the stock spikes. Let's assume stock price stays the same. Does the chances of option A expiring in the money change much? NO, there is not enough time for the volatility to be realized. However, option B is now more valuable as there is "realistic" chances that it will expire in the money.

Check out this link for more information.

### Math explanation for other users:

$$ \nu = S \sqrt{T} \phi (d_1) $$

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.