Why Option Theta Is a Local Decay Rate

Summary

The note explains why multiplying an option’s current theta by the days remaining can imply more decay than its current time value. It uses a deep in-the-money call as an example: most of its price is intrinsic value, while the quoted time value is small and the current theta is comparatively large.

Theta measures the option’s instantaneous sensitivity to the passage of time, not a fixed daily charge that remains constant through expiry. As expiry approaches in the example, theta moves closer to zero, so the decay rate slows. The example is illustrative rather than a general numerical forecast; actual theta also depends on the option’s pricing inputs and can change as market conditions and the underlying price change.

Key ideas

• Theta is a local estimate of an option’s time decay at the current point, not total time value divided by days remaining.
• Current theta should not be projected unchanged across the option’s entire remaining life.
• In the deep in-the-money example, the decay rate slows and theta approaches zero toward expiry.

Tags

# Why theta multipled by days to expiry exceeds the total time premium of the option


# Why theta multipled by days to expiry exceeds the total time premium of the option












Sometimes, I find an option where the total time value of the option may be 5 cents(rest is intrinsic value) and there are about 15 days to expiry and theta is .08 (8 cents).

How is this possible. If it is decaying 8 cents a day, then in 15 days, it will lose 120 cents of time premium( and that is assuming a linear time decay, which is not true), but time premium is only 5 cents to start with. So total time decay can only be 5 cents. So how can it keep decaying at 8 cents/day for 15 days?

Please look at AAPL 102 call with underlying ~130, and the call is asking 28.05. So time value of this call is ~ 28.05 - (130-102) = 0.05

Theta is 0.0882. There are ~ 15 days to expiry. Today is feb 27

## Answer by onlyvix.blogspot.com (score 2)

https://quant.stackexchange.com/a/16854

It is because theta is not premium / days to expiration. Theta is a "local" decay, measure of current rate of option decay, which is not assumed to stay constant.

In the example you provided, theta will be closer to zero (decay rate will slow down) as you approach expiration.

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