Time Value (Options)

Time value, in options, is the portion of an option's market price that is not accounted for by its intrinsic value. It is the amount a buyer pays for the possibility that the underlying asset will move in a favourable direction before the option expires. It is also called extrinsic value. An option that is out of the money has no intrinsic value, so its entire price is time value.

The concept splits the option premium into two parts: what the option would be worth if exercised now, and what is paid for the remaining life of the contract. Time value falls to zero at expiry, when only intrinsic value is left. The term is separate from the time value of money, which concerns the worth of cash today compared with cash in the future.

The calculation is:

• $\text{Option premium}$ is the current market price of the option.
• $\text{Intrinsic value}$ is the amount by which the option is in the money: the underlying price minus the strike for a call, or the strike minus the underlying price for a put, and never less than zero.

Suppose a share trades at $52. A call with a strike price of $50 is priced at $3.20. Its intrinsic value is $52 - 50 = 2$ dollars, so its time value is $3.20 - 2.00 = 1.20$ dollars. A call with a strike of $55 priced at $0.90 has no intrinsic value, and all $0.90 is time value. A put with a strike of $55 priced at $3.70 has an intrinsic value of $3 and a time value of $0.70.

• Time to expiry. The longer the remaining life, the greater the chance of a favourable move, and the higher the time value.
• Volatility. Higher expected volatility of the underlying raises time value. This is the single most important input, and it is expressed through implied volatility. The sensitivity is measured by vega.
• Moneyness. Time value is greatest for an at-the-money option, where uncertainty about the final outcome is highest. It declines as the option moves deep into or far out of the money.
• Interest rates and dividends. These have smaller effects. Higher rates add to the time value of calls, and expected dividends reduce it.

A rough guide for an at-the-money option is that its time value is about $0.4 \times S \times \sigma \times \sqrt{T}$, where $S$ is the underlying price, $\sigma$ the annual volatility and $T$ the time to expiry in years. For a $100 share with volatility of 25 percent, a three-month option has a time value of about $0.4 \times 100 \times 0.25 \times 0.5 = 5.00$ dollars, and a one-month option about $0.4 \times 100 \times 0.25 \times 0.289 = 2.89$ dollars.

As expiry approaches, time value erodes, a process called time decay and measured by theta. The example above shows that the erosion is not linear. Cutting the remaining time from three months to one, a reduction of two thirds, removes only about 42 percent of the time value. The rest disappears in the final month, and the rate of loss is fastest in the last days before option expiry.

Time decay works against option buyers and in favour of sellers. Strategies such as the covered call are built to collect time value. The income is compensation for bearing the risk of a large move in the underlying, not a free gain.

Time value explains when an American option, which can be exercised at any time, should be exercised before expiry. Exercising captures only the intrinsic value and discards whatever time value remains. Selling the option in the market captures both. For a call on a share that pays no dividend, time value is always positive, so early exercise is never the better choice, a result established by Robert Merton in 1973.

Two cases differ. A call may be worth exercising just before the share goes ex-dividend, if the dividend exceeds the remaining time value. A deep in-the-money put may be worth exercising early because the strike price received can be invested at interest. A European option cannot be exercised early, and a deep in-the-money European put can trade slightly below its intrinsic value, giving a negative time value.

The split between intrinsic and time value shows what a buyer is paying for. An in-the-money option costs more in total but contains proportionally less time value, so less is lost if the underlying does not move. An out-of-the-money option is cheap, but every cent of it will be lost unless the underlying moves beyond the strike by expiry. For a buyer, the break-even price at expiry is the strike plus the premium for a call option, which means the underlying must move enough to cover the time value paid.

Time value depends on an estimate of future volatility, which cannot be observed. Two options with the same time to expiry can have very different time values, and a drop in implied volatility can reduce time value sharply even when little time has passed.