When there is a merger or takeover, options on the stock of the
acquired company are adjusted according to the terms of the deal.
With a call option, your right to buy the stock is converted to a
right to buy a corresponding quantity of whatever shareholders receive
for their stock.
Say you have options to buy ABC stock and XYZ acquires ABC. Whatever
deal ABC's shareholders get carries over to your options. For
example, if you had an option to buy a share of ABC for $1 and the
takeover deal was that every ABC share is exchanged for two shares of
XYZ, after the takeover, you would have an option to buy two shares of
XYZ for $1.
If the transaction between the companies is more complicated (e.g., a
combination of stock and cash), what happens to the option will be
correspondingly more complicated. But in any case, the exchange where
the option is traded should publish what is going to happen to the
options before it actually happens.
This is just the general principle. For more details, see the
Detailed explanation by Frederic Ruffy on Yahoo! Finance
FAQs on splits, mergers, and spinoffs from the Options Industry Council
E*TRADE Options FAQ on splits, mergers, spinoffs & bankruptcies
FAQ answer from the Montréal Exchange