"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?

  • $\begingroup$ How could the proof (if it is true) work. The first lines: $$C - (S-K)^+ \ge 0.1 C$$ where C is the call price and the left hand side is the time value. If we substract the rhs we get $$0.9C \ge (S-K)^+$$ and on more step gives $$0.9 \ge (S-K)^+/C$$. But at the moment I can not conclude for the Delta ... $\endgroup$ – Ric Aug 17 '12 at 20:46

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%.

| improve this answer | |
  • $\begingroup$ That's why the maths in my comment did not work out ... I didn't try myself but what about more realistic parameters such as vol around $30\%$ and not that deep in the money? $\endgroup$ – Ric Aug 18 '12 at 19:42
  • 2
    $\begingroup$ As far as I could tell in my tests, with more realistic parameters the claim is usually true (presumably why the OP inferred that it might be true in general). $\endgroup$ – user2825 Aug 18 '12 at 19:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.