According to a New York Times article, calmness in the face of stressful situations is linked to neuroticism levels and emotional regulation.
That is, the amount of anxiety or calmness you feel in a situation is connected with how neurotic you are, but even if you are highly neurotic, you can learn skills to regulate your emotions and appear calm in stressful situations.
From the NYT article:
"Even if you're someone who is initially anxious, you can develop tricks and strategies, so someone on the outside would say: 'Her, anxious? She's awesome at cocktail parties, she's great at public speaking,'" Professor Gross said. "They wouldn't understand that if you didn't have those strategies, you wouldn't be able to do those things."
And from the BPS article:
"Zernike's article describes how self-regulation can be achieved by identifying the beliefs you hold that link a given situation and your typical behavioural response. For example, an angry boss might lead you to break down because of your intervening belief(s) 'my boss hates me, everyone hates me, I'm a failure'. By changing your mental interpretation of the situation to a more rational version 'my boss often gets angry with staff, this isn't personal, actually he praised me the other day' - the breakdown can be averted. Indeed, attempting to break dysfunctional links between thoughts, feelings and behaviours is exactly how cognitive-behavioural therapy aims to help people deal with symptoms of anxiety and depression."
(For more on the dysfunctional links between thoughts, feelings and behaviors, check out my Thought Traps series.)
An interesting point that comes up in the article is that it's not always desirable to be calm; calmness can be perceived as uncaring or aloofness. Something to think about as a speaker: calmness in the face of nervousness is good, but you still need to express some emotion to engage the audience. Otherwise you might come across as distant and dull.
Read the BPS Research Digest Blog for a synopsis and supplemental links, and the New York Times article for more detail.
You can take an online version of the Big 5 test here to see how neurotic you are. (I scored low -- whew!)
And for some calming strategies:
What if your worse public speaking fear comes true?
Preparation Rituals Series
Don't rush it
Four steps to controlling your fear
See, hear and taste your audience