In the idealised black-Scholes world...Although, as a general rule, the (absolute) theta for ATM options is higher than that for OTM/ITM options I get confused as to where the precise maxima for theta occur. For instance, given the following;Asset price (no dividends) 100Volatility 25%Interest rate 5%Maturity 0.25 yearsThe theta for a 100 call is -12.3855, for a 101.26 call (the forward) it is -12.329 (lower absolute value), for a 102.05 call (volatility-adjusted forward) we get -12.243 (smaller again). The 100 value is not even an absolute maximum - if the strike was 99.95 then the theta would be -12.3856, which is in absolute terms greater than that at 100. Consequently, a slightly ITM spot call option would appear to have greater theta than ATM spot, which in turn has a greater Theta than ATM forward.Why is this? Shouldn't the maximum Theta be where the strike is equal to the ATMF? I am not clever enough to disentangle the various formulae which calculate Theta. Any non-mathematical insight be greatly appreciated.I am confused (no change there)Buffoon

Theta is a maximum where it's K-derivative is zero. A fewlines in Mathematica convinced me that the location of this maximum isnot simple. For your example, it's very close to 100 -- I find K = 99.9366.But try 5 years to maturity; it's nearer to K = 123Certainly, the time value is a maximum exactly at the money. A very crude theta approximation would be the time value dividedby the time to maturity. So, this crude approximation would bea max exactly at the money. But it doesn't quite work out for theexact theta, perhaps due to the skew of the lognormal.regards,

Differentiating Theta w.r.t. strike and letting time run to infinityapproaches 0, i.e. the maximum approaches infinity for increasing timeand that also holds if working with Future instead of Spot (settings=1*exp(r*t)). One can 'confirm' this by a 1st order approximationans solving for strike. A non-formal reasoning might use to expressTheta in terms of Gamma and dualDelta cdfN(d2) (=the hedge part).The exact solution means to intersect a skewd cdfN witah a pdfNand this mostly is of the form of a 'not known named function'.

maximum theta is when your long straddle which expires tomorrow closes atm with a 200k premium (mark-to-market in your book) and of course rates move in a 1/2 bps range the entire next morning until the 11am expiry.....

Near expiration theta is highest (most negative) close to at-the-money.For European options on non-dividend paying stocks the exact answer is: S = X e^((r+0.5sigma)T).You can find the answer and derivation herehere.