How Uncertainty and Time to Expiry Affect Option Time Value
Summary
The question examines whether an American option on a deterministic, zero-volatility asset can have time value. Its proposed reasoning treats the option’s value as the best payoff reached along the asset’s deterministic path and argues that early exercise could reproduce that payoff. The response accepts that under this hypothetical deterministic setup there would be no time value, then explains the usual intuition: with an uncertain underlying, a longer time to expiry leaves more opportunity for price movements that can increase an option’s value beyond intrinsic value.
The answer contrasts a near-expiry option, whose price is described as more closely tied to intrinsic value, with a longer-dated option that may have a larger extrinsic component. This is an informal explanation, not a pricing derivation. It sets aside interest rates and does not specify option type, dividends, exercise policy, or a formal model, so it should not be read as a general valuation rule for every option.
Key ideas
- Time value reflects uncertainty about the underlying’s future price and the time available for it to move.
- In the question’s deterministic, zero-volatility example, the response agrees that time value would be absent.
- Options with more time remaining may have a larger extrinsic component than otherwise comparable near-expiry options.
- The explanation is qualitative and omits interest rates and other contract-specific valuation details.
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# Thinking about time value of an option
# Thinking about time value of an option
In addition to Wikipedia, YouTube and other internet sources, I'm reading Timothy Crack's "Basic Black-Scholes: Option pricing and trading". Most of these sources suggest that it is fairly obvious that an option has time-value. But I am not yet convinced -- could someone please clarify the following reasoning.
To me it seems that any time-value an (American) option might have is due pretty much exclusively to the volatility of the underlying asset (and partly on the riskless rate, but I'd like to ignore this for now), and so an option on a hypothetical asset with no volatility should have no time-value. My reasoning is as follows: suppose first that we have a hypothetical asset with no volatility (suppose also that the riskless rate is zero). This means the asset's price is deterministic. In this case, the value of a call option must be [the present value of] $\text{max}(S_m - K,0)$ where $S_m$ denotes the maximum that the spot price ever reaches (possibly infinite) and $K$ denotes the strike price. This remains the value of the call until the (first) time $t=t_1$ that the underlying asset reaches price $S_m$. After that time, the value of the option becomes $\text{max}(S_{m,2}-K,0)$ where $S_{m,2}$ is the highest price the underlying asset reaches after $t_1$, and so on. Indeed this reasoning does demonstrate that the option value changes in time but not because of "time-value". In particular one could exercise the option at time $t=0$ thereby obtaining the stock at the strike price $K$ and then simply wait until time $t=t_1$ (assuming it exists) to sell it, thus realizing the maximum value of the option without holding it beyond time $t=0$. This strategy would be the same whether time $t_1$ is tomorrow or next year, and so the value is the same in both cases, thus the value is independent of time to any maturity date of the option. So, since there seems to be no time-value when the volatility is zero, any time-value must be entirely due to non-zero volatility.
Where am I going wrong here? Thanks.
## Answer by Iloos (score 1)
https://quant.stackexchange.com/a/78080
I think its since you're taking the hypothetical situation of the stock deterministically having the same price for each time.
Yes, in that case it would not have time value.
But usually we think of it as the future being ucertain, and the assumtion for time value is that the longer the duration till expiery, the more value there is for speculation.
If some option expires in an hour, then the price will be much more determinant on the intrinsic value (the difference beteen strike and asset price), as there is less time and less chance for price to move a lot (variance). But the price of the option also has the extrinsic part which in turn is affected by time value.
In reverse, if there is a long time to expiery, the price difference between the price of the option and the intrinsic value could be much bigger, due to time value.
https://www.investopedia.com/terms/t/timevalue.aspShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.