# Breakeven of a delta-hedged option

Basic question to which I surprisingly did not find an answer on here.

What's the best approximation to the break-even (with respect to stock price) for an option that was hedged fully at point of trade (and not adjusted later). (by fully I mean however many deltas the option had - not 100 deltas per option)

I have seen the approximation Premium/Delta and $\sigma * (\Delta t)^{0.5}$.

Are these model specific?

Am I incorrect to have thought that break-evens should be slightly asymmetric (the effect of charm will change the delta of the option leg, but the static stock hedge will not adjust)?

Any sources about delta hedged options are also appreciated.

• I don't understand what you mean with break-even. What variable are you targeting with break-even, the stock price at expiry? – luckylwk Oct 9 '13 at 17:39
• yes, that's what I was trying to say with "wrt. stock price" – frickskit Oct 9 '13 at 19:15