Intrinsic vs Extrinsic Value of Options: Time Value and Decay

An option's price splits into two parts. Intrinsic value is what the option would be worth if exercised right now; extrinsic value, also called time value, is everything else in the price. Intrinsic value depends only on the share price and the strike, while extrinsic value shrinks as expiration approaches and is zero at expiration.

Intrinsic Value Formula

With S the share price and K the strike:

Call intrinsic value = max(S − K, 0)
Put intrinsic value = max(K − S, 0)

Only in-the-money options have intrinsic value. At-the-money and out-of-the-money options have none.

Extrinsic (Time) Value Formula

Extrinsic value = option price − intrinsic value

For an at-the-money or out-of-the-money option, the whole price is extrinsic value.

Illustrative example: a stock trades at $105. A $100 call priced at $6.20 has $5.00 of intrinsic value and $1.20 of extrinsic value. A $110 call priced at $1.40 has no intrinsic value, so all $1.40 is extrinsic.

What Determines Extrinsic Value

Extrinsic value is the price of the possibility that the option becomes worth more before it expires. It grows with:

Time to expiration: more time leaves more room for the share price to move.
Implied volatility: a larger expected range of movement is worth more.
Closeness to the money: extrinsic value is largest at the money and smaller for options deep in or far out of the money.

Interest rates and expected dividends play a smaller part.

For an at-the-money option, a common approximation from the Black–Scholes model is:

At-the-money option price ≈ 0.4 × S × σ × √t

where σ is implied volatility and t is time to expiry in years.

How Time Value Decays Toward Expiration

Because at-the-money extrinsic value scales with the square root of time, it does not fall in a straight line. It falls slowly when expiration is far away and faster as expiration approaches.

Illustrative example: a $100 stock with 20% implied volatility. A 30-day at-the-money call is worth about $2.29, all extrinsic. With the same volatility and price, a 7-day call is worth about $1.10. Less than a quarter of the time remains, but about half of the extrinsic value does. The remaining value then falls to zero over the final week.

The daily rate of this decay is theta. For options far out of the money, extrinsic value is small to begin with and can approach zero well before expiration. For options deep in the money, the price moves toward pure intrinsic value.

At expiration, extrinsic value is zero: an option is worth exactly its intrinsic value, and an out-of-the-money option expires worthless.

Can Extrinsic Value Be Negative?

For American-style options, which can be exercised at any time, a price far below intrinsic value would rarely persist. A quoted price slightly below intrinsic value can reflect a wide bid-ask spread, a stale quote, or a deep in-the-money option whose time value is close to zero. European-style options, which cannot be exercised early, can trade below intrinsic value, for example deep in-the-money puts when interest rates are high.

Where Extrinsic Value Shows Up In Vyreon's Measures

The at-the-money straddle behind the expected move is almost entirely extrinsic value.
IV crush after earnings is a fall in extrinsic value as implied volatility drops.
Covered call and cash-secured put yield uses premiums at the money and out of the money, where premium is all or mostly extrinsic value.

What It Does Not Tell You

Whether an option is cheap or expensive. That depends on implied volatility relative to what the share price later does, which is unknown in advance.
How decay will actually unfold: the approximation assumes constant volatility.

Sources

John C. Hull, Options, Futures, and Other Derivatives (Pearson, many editions): intrinsic and time value, and price bounds for American and European options.
Robert C. Merton, "Theory of Rational Option Pricing", Bell Journal of Economics and Management Science (1973): price bounds and when early exercise can be optimal.
Menachem Brenner and Marti G. Subrahmanyam, "A Simple Formula to Compute the Implied Standard Deviation", Financial Analysts Journal (1988): the at-the-money approximation, call ≈ 0.4 × S × σ × √t, so a straddle ≈ 0.8 × S × σ × √t.