Why does an option's time value decay accelerate as expiration approaches?

Time value decay (also called theta decay) is one of the most important practical concepts in options. The acceleration near expiration is driven by probability mathematics and has real consequences for traders.

Why Time Has Value

An option's time value reflects the probability that the underlying asset's price will move favorably before expiration. More time = more chances for favorable moves = higher time value.

Why Decay Accelerates: The Square Root of Time

Option pricing models (like Black-Scholes-Merton) show that time value is roughly proportional to the square root of time remaining, not time itself.

Time Value is proportional to sigma x sqrt(T)

This means:

• 12 months to expiry: proportional to sqrt(12) = 3.46
• 6 months to expiry: proportional to sqrt(6) = 2.45 (lost 29% of time value by losing 50% of time)
• 3 months to expiry: proportional to sqrt(3) = 1.73 (lost 50% of value)
• 1 month to expiry: proportional to sqrt(1) = 1.00 (lost 71% of value)
• 1 week to expiry: proportional to sqrt(0.25) = 0.50 (lost 86%)

Numerical Example — Novara Technologies ATM Call

Novara trades at $100. ATM call (K = $100), sigma = 30%, risk-free = 4%:

The last month alone destroys $3.05 of the remaining $4.10 in value — that's 74% of what's left, gone in 30 days.

Practical Implications:

1. Option sellers love theta decay — Selling options with 30-45 days to expiry captures the steepest part of the decay curve.
2. Option buyers face a headwind — Long options need the underlying to move quickly enough to overcome accelerating time decay.
3. ATM options decay fastest — They have the most time value to lose. Deep ITM options (mostly intrinsic value) and far OTM options (small premium) experience less absolute decay.

Theta (The Greek):

Theta measures the daily time decay in dollar terms. For our Novara call:

• At 6 months: Theta = -$0.023/day
• At 1 month: Theta = -$0.051/day
• At 1 week: Theta = -$0.098/day

Theta roughly doubles every time the remaining time is cut by 75%.

Exam Tip: CFA Level I may give you option premiums at different points in time and ask which period saw the greatest time decay. The answer is always the period closest to expiration.

Practice time value calculations in our CFA Derivatives question bank.