DP
Optionsbeginner

Time Value

Time value is the part of an option premium above its intrinsic value. It compensates the buyer for the chance that the underlying moves favourably before expiry. Time value grows with time to expiry TT and with volatility σ\sigma, and decays as TT shrinks. The rate of decay is theta, Θ=∂V/∂t\Theta = \partial V / \partial t. At expiry, time value equals zero and the option is worth only its intrinsic value.

Why it matters

Time value is the opportunity premium built into an option. With time on the clock, the underlying might still rally past the strike, or crash below it, so the market pays extra above the current intrinsic value. As days tick by, the set of remaining future paths shrinks. Less time means less room for surprises, which is why an ATM option loses time value fastest near expiry, the well-known theta acceleration pattern in the last few weeks before expiry.

Formulas

Time value identity
Time Value=Premium−Intrinsic Value\text{Time Value} = \text{Premium} - \text{Intrinsic Value}
Always non-negative for a European option before expiry. For American calls on non-dividend stocks it equals premium minus max⁡(S−K,0)\max(S - K, 0).
Theta (per unit time)
Θ=∂V∂t\Theta = \frac{\partial V}{\partial t}
Usually negative for long options, since time value falls as expiry approaches. Quoted per day or per year depending on convention.

Worked examples

Scenario

An ATM call on Wesfarmers with K=K = 50,, S = $50,threemonthstoexpiry,tradesatpremium, three months to expiry, trades at premium C = $3$.

Solution

Intrinsic value =max⁡(50−50,0)== \max(50 - 50, 0) = 0$. Time value =3−0== 3 - 0 = 3$. The entire premium is pure time value because the option is ATM. As expiry nears, this $3 will steadily decay toward zero if Wesfarmers stays near $50.

Scenario

Same option one day before expiry, with S=S = 50$ and premium C=C = 0.20$.

Solution

Time value has shrunk from $3 to $0.20. Theta has stripped most of the premium during the three months. At the moment of expiry, the call settles at $0 unless the stock has moved above the strike. This time decay is the writer's structural source of return when the underlying does not move.

Common mistakes

  • ✗Time value is always positive. It is zero at expiry, and a deep ITM American put can have near-zero time value because early exercise is so attractive that the European-style time-value component is squeezed out.
  • ✗Time value decays linearly. Theta is non-linear and typically accelerates as expiry approaches, especially for ATM options. A weekly option loses time value much faster in its final week than in its first.
  • ✗Time value depends only on time. It also depends on volatility σ\sigma, on SS versus KK, and on interest rates. Two options with identical TT can have very different time value if their underlyings have different implied vols.

Revision bullets

  • •Time value == premium −- intrinsic value
  • •Decays as expiry approaches (theta)
  • •Highest for ATM options
  • •Zero at expiry by definition
  • •Grows with σ\sigma and TT

Quick check

Time value is highest for which type of option?

A 6-month call on a non-dividend stock with S=K=S = K = 100$ trades at $6. Its time value is:

Connected topics

IntrinsicBSM Intro

In learning paths

Options Path

Sources

  1. Hull (2022), §11.3, §19.5
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Develops the time-value concept and the role of theta in option price dynamics.
  2. Black and Scholes (1973)
    Black, Fischer, and Myron Scholes. "The Pricing of Options and Corporate Liabilities." Journal of Political Economy, vol. 81, no. 3, 1973, pp. 637 to 654.
    Underpins the formal link between time, volatility, and option price for European options.
  3. Cboe Options Institute Glossary
    Cboe Global Markets. Options Trading Glossary. Cboe Options Institute, accessed 2026.
    Industry definition of time value, theta, and time decay used by US options market practitioners.
  4. McDonald (2013), §12.3
    McDonald, Robert L. Derivatives Markets. 3rd ed. Pearson, 2013. ISBN 978-0-321-54308-0.
    Detailed treatment of theta, time decay patterns, and how moneyness affects the decay path.
How to cite this page
Dr. Phil's Quant Lab. (2026). Time Value. Derivatives Atlas. https://phucnguyenvan.com/concept/time-value
← Back to the atlasSee in the network →