Why Time Value Does Not Guarantee an Option Delta Below 90%

Summary

The document challenges a proposed rule linking an option’s time value to its delta. The claim is that when time value makes up at least a specified fraction of an option’s price, delta must be below a corresponding threshold. A Black–Scholes call example disproves the rule: a deeply in-the-money option with high volatility can have substantial time value while its delta remains above the proposed limit.

The example shows why option price composition alone does not impose a universal upper bound on delta. Delta depends on the option’s market inputs, including moneyness and volatility, so a broad statement needs either additional assumptions or a proof that covers those inputs. The excerpt supplies one counterexample, which is enough to reject the claim as stated, but it does not establish a replacement rule or explore how the relationship changes across maturities, rates, or option types. The conclusion should therefore be read as a refutation of the universal claim, not as a general formula for delta.

Key ideas

• A single valid counterexample is enough to disprove a universal claim about option value and delta.
• A deeply in-the-money call can retain meaningful time value while having a high delta.
• High volatility can contribute to time value even when the option is far in the money.
• The example refutes the stated rule but does not give a general relationship between time value and delta.

Tags

# Prove or disprove "If at least 10% of an option's value is time value, it has a delta less than 90"


# Prove or disprove "If at least 10% of an option's value is time value, it has a delta less than 90"












"If at least 10% of an option's value is time value (ie. time value >= 0.1*call price), it has a delta less than 90".

In practice and after doing many tests with an option pricing calculator, this statement seems to hold true. Can anyone mathematically prove or disprove this?

## Answer by user2825 (score 7)

https://quant.stackexchange.com/a/3965

This claim is false. A deep in-the-money option with very high volatility can have both large time value and high delta. As a counterexample, consider a call option with:

- K = 100 (strike price)

- S = 300 (spot price)

- r = 0

- T = 1

- vol = 150%

This gives a Black-Scholes value of approximately \$230, so the time value is \$30, but the delta is 93.1%.

Shown 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.