How Time to Expiry Affects Option Value
Summary
The document explains the effect of remaining time on option value through uncertainty in the underlying price at expiry. For at-the-money and out-of-the-money options, more time can increase value because a larger range of outcomes creates more opportunity for a favorable payoff, while an unfavorable move cannot make the holder’s option payoff negative. The discussion illustrates this with an at-the-money put: a longer period gives more time for a severe decline that benefits the holder.
The effect is not uniformly positive across all options. An in-the-money put can lose value as time passes because the stock price has a lower bound, limiting further gains from a fall, while a recovery can reduce the option’s value. The answer therefore emphasizes uncertainty and payoff shape rather than a simple positive-drift argument. It gives a qualitative explanation, not a pricing formula, and the stated direction depends on moneyness and option type.
Key ideas
- More uncertainty before expiry can increase the value of at-the-money and out-of-the-money options.
- Option holders benefit from favorable moves while their losses are limited to the option premium.
- Time can work against an in-the-money put because the underlying price has a lower bound and can recover.
- The time effect depends on the option’s moneyness and payoff structure, not simply on expected drift.
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Full text
# Dependency of an option price on time till expiry # Dependency of an option price on time till expiry I am trying to seek satisfaction when it comes to understanding why the price of an option is dependent on the time until expiry. I have read that the longer till expiration, the more time available for movement in the underlying stock price, and more chance of being on the desirable side of the strike price (assuming positive drift), so this should mean that the option price is higher than when we have shorter times till expiration. But if the drift was a larger positive, this should mean that the price of the option is greater as we have even more chance now of landing in the money. But this isn't true since the drift does not affect the option price, telling me that the reasoning above isn't quite right. Could someone please shed some light on how to understand how the time till expiration affects the option price. ## Answer by Bob Jansen (score 6) https://quant.stackexchange.com/a/43749 You've tagged this with 'black-scholes' but you don't have to make the assumptions of the Black-Scholes-Merton model to understand why the option price with time to expiry. Consider this example: Consider 2 ATM put options on a stock with a time to expiry of one month and one year with some strike price. The maximum pay-out is achieved when the company goes bust, what is more likely, and which option is thus more valuable, that the company goes bust within a month or within a year? More generally, the price of an ATM or OTM option increases as uncertainty about the price at expiry increases. More uncertainty allows the stock price to move further away from the strike in the profitable correction which is increases the value, for a call the value can grow without bound. It also can move the other way in which case the option becomes less valuable but never zero or less. For ITM put options, time can work against the put option holder. The stock has a hard lower bound so the upside for the put option holder is limited but it could make a recovery in which case the option decreases in value.
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