This forum focuses more on Indian markets and thus it may not be the best place to ask about stocks listed in US/EU markets...

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I searched on the internet, but couldn't find any news related to BAE's interest in L-3.
I am not sure how reliable these "rumours" are.
If you want to benefit from any such development, you will have to
take a position before the announcement.
Usually, when such news is made public, the market
immediately adjusts the stock price to reflect the consequences of the development.
Taking a position after the announcement won't bring much gains.
As the saying goes "Buy on rumours and Sell on news".
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I looked at charts of L-3 at Google Finance. The stock seems pretty stable.
As the stock hasn't moved much in the recent days, even if there is no such deal, the stock price should remain unaffected.
Different options behave differently. It depends a lot on
how far the expiry is and
how close the strike price is to the current price.
You need to understand about
"Delta" for options.
Delta for In-The-Money options is maximum.
Delta for options closest to expiry is maximum.
If you have further doubts let me know.