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How Near-At-the-Money Option Time Value Decays Toward Expiration

Article Quant Q&A · Author: Distraction Arrestor
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Summary

The note explains why a near-the-money option can lose value more rapidly as expiration approaches. With volatility held constant and the underlying price assumed to stay near the strike, it approximates the option’s value as proportional to volatility times the square root of remaining time. This implies an accelerating decline in time value as the remaining term shrinks.

The explanation is a simplified approximation, not a universal schedule of percentage losses by month. It does not establish how decay differs for out-of-the-money or in-the-money options, and it assumes the underlying price does not move much. Changes in implied volatility or the option’s moneyness can therefore make actual theta behavior differ from this picture.

Key ideas

  • Near-the-money option value is approximated as proportional to volatility and the square root of remaining time.
  • Under stable volatility and little underlying-price movement, time value falls faster as expiration nears.
  • The square-root approximation does not provide a fixed monthly percentage-loss schedule.
  • Moneyness changes and volatility movements can alter realized option decay.

Tags

OptionsDerivatives pricingVolatility
Full text
# Rate of Options decay


# Rate of Options decay












I know "Time decay accelerates on nearing expiry". But I want to know the rate of acceleration.

- How curvy is the theta curve? Answers could be like,

> Provided IV is stable, in a 3-month contract, Month 1: time value losses 10% Month 2: time value losses 30% Month 3: time value losses 60%

- Does theta work following a standard curve every time? Or it has other factors to affect?

- It works same for all OTM, ATM and ITM? I read OTM options decelerate last month. Is that true?

## Answer by nbbo2 (score 2)

https://quant.stackexchange.com/a/25156

The value of a call option that is near ATM can be approximated as $C(S,T)≈ 0.4 \sigma \sqrt T$. Therefore, under the unrealistic assumption that S does not change very much (i.e. the option stays near the money) the value decays as the square root of the remaining time.

In words, yes it does speed up considerably as you get close to expiration.

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.