I haven't had the chance to dig into the active ingredient in Saffron responsible for this effect. I don't know if the active ingredient is even known. But I thought the following might be relevant to some people's interests.

As I understand it, estradiol is a direct breakdown product of testosterone, and women exposed to saffron produced more estradiol regardless of where they were in the cycle. But they made less cortisol. Since androstadienone also helps with PMS, but it seems like it lowers Testosterone by upregulation of cortisol production this seems to suggest that one critical aspect in helping with PMS might be lowering testosterone rather than raising cortisol, specifically. Does that seem like a valid interpretation?

That seems reinforced by the notion that androstenone may worsen the symptoms of some women with PMS.

The next big question would be; why do some women have bad PMS and others don't?

Quote:Our results indicate that saffron odor exert some effects in the treatment of PMS, dysmenorrhea and irregular menstruation. This is the first report to suggest that saffron odor may be effective in treating menstrual distress.

Psychological and neuroendocrinological effects of odor of saffron (Crocus sativus).

...

Thirty-five women with a normal sense of smell were exposed to saffron odor for 20 min. Saliva samples were then collected to measure levels of cortisol ©, testosterone (T) and 17-β estradiol (E) by enzyme immunoassay, and the State-Trait Anxiety Inventory (STAI) was administered as a psychological test.
RESULTS:

Saffron odor significantly decreased C levels after short-term stimulation (20 min) in both follicular and luteal phases. E level after exposure to saffron odor was increased in both the follicular- and luteal-phase groups. STAI score decreased in the follicular and luteal phases in the saffron group.
CONCLUSIONS:

The present findings support the existence of physiological and psychological effects of saffron odor in women. Our results indicate that saffron odor exert some effects in the treatment of PMS, dysmenorrhea and irregular menstruation. This is the first report to suggest that saffron odor may be effective in treating menstrual distress.

http://www.ncbi.nlm.nih.gov/pubmed/21242071