# 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?

• 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 ... – Richard Aug 17 '12 at 20:46

This gives a Black-Scholes value of approximately \$230, so the time value is \$30, but the delta is 93.1%.
• 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? – Richard Aug 18 '12 at 19:42