Intrinsic Value (Options)

Intrinsic value, in options, is the amount an option would be worth if it were exercised immediately. For a call option it is the amount by which the price of the underlying exceeds the strike price. For a put option it is the amount by which the strike exceeds the underlying price. If the difference is negative, the intrinsic value is zero, because the holder is never obliged to exercise.

The term has a different meaning in share valuation, where it refers to an estimate of what a business is really worth. In options it is a simple arithmetic quantity that needs no model. It is one of the two parts of the option premium. The other is time value, the extra amount buyers pay for what may happen before expiry.

For a call, the calculation is:

For a put, it is:

• $S$ is the current price of the underlying asset.
• $K$ is the strike price of the option.
• $\max$ means the larger of the two values in the brackets.

Suppose a share trades at 108. A call with a strike of 100 has an intrinsic value of $108 - 100 = 8$. If that call is priced at 11.50, the remaining 3.50 is time value. A put with a strike of 100 on the same share has an intrinsic value of zero, since $100 - 108$ is negative, and whatever it costs is all time value. Equity options usually cover 100 shares, so an intrinsic value of 8 per share is 800 per contract.

Whether an option has intrinsic value defines its moneyness. An in-the-money option has positive intrinsic value. An at-the-money option, with the strike equal or very close to the underlying price, has none or almost none. An out-of-the-money option has none, and its whole price is time value. The general entry on in-the-money and out-of-the-money covers these states.

The split matters for how an option behaves. The price of a deep in-the-money option is mostly intrinsic value and moves almost one-for-one with the underlying, with a delta near 1. An out-of-the-money option responds more to changes in volatility and to the passage of time, because those are the only things giving it value.

Time value shrinks as expiry approaches and is zero at the end. At option expiry an option is worth exactly its intrinsic value, which is why the option payoff formulas have the same form as the formulas above. An option with no intrinsic value at that point expires worthless. Clearing houses normally exercise expiring options automatically when they are in the money by more than a small threshold, so holders do not lose value by oversight.

An American option, which can be exercised at any time, should not trade below its intrinsic value. If it did, a trader could buy the option, exercise it at once and sell the underlying for a riskless profit, and this arbitrage would push the price back up. In practice the bid for a deep in-the-money option can sit slightly under intrinsic value because of the bid-ask spread and trading costs.

A European option, which can be exercised only at expiry, is different. A deep in-the-money European put can trade below its intrinsic value, because the holder must wait to receive the strike price and loses the interest on it in the meantime. A European call on a share that will pay a large dividend before expiry can do the same, since the option holder does not receive the dividend. For this reason some texts define intrinsic value against the forward price of the underlying, discounted to today, instead of against the spot price.

Intrinsic value says what an option is worth if exercised now, not what it is worth to hold. Exercising an American call early on a share that pays no dividend throws away the time value, so selling the option is the better choice. Intrinsic value is also not profit: a buyer who paid 11.50 for a call with 8 of intrinsic value is still 3.50 short of breaking even. Finally, it changes with every tick in the underlying, so a figure quoted for an option is accurate only for the price at which it was computed.