# Asymptotic behavior of theta of vanilla call option

It is well known that the theta of call option is always negative. Also, the theta of (at the money call option) goes to infinity as the time approaches to the maturity. On the other hands, (ITM and OTM) call option has zero theta at the maturity. This can be easily checked by BS formula.

Here, i am wondering that the above fact also holds for other models (eg. CEV or advanced models).

As i know, the theta of call option under CEV is given by

where

X is a strike price and $Q(w; v, λ)$ is the complementary distribution function of a non-central chi-square law with v degrees of freedom and non-centrality parameter λ.

• Could you please be a bit clearer with your notation of the CEV; perhaps give the model dynamics explicitly. And as petercarr points out, it might be good to drop the risk free rate and dividend yield in your formulas. With CEV, if I remember correctly, you need a correction term for the 'strictly local martingale scenario'. – Kiwiakos Dec 31 '14 at 0:36