It really depends upon the circumstances of the affiliate offer. Many merchants do not want you to direct link, because they already do that themselves. Some merchants will not want you to use their brand name, or product name in the keywords you are targeting. If the merchant does allow direct links, only one AdWords account will be allowed to receive impressions for that website, so unless you are the only affiliate marketer using AdWords you may not be able to direct link successfully.
Additionally, many merchants that have affiliate programs do not have offer pages that comply with AdWords advertising policies. So that rules out a lot of possibilities.
You can create your own landing page, but you must follow AdWords policies, including no bridge pages, which is what many affiliate marketers try to get away with. You have to have an offer page, for whatever you are advertising, on your own website and not redirect or forward users to an offer page on a separate website.
In some cases, where the merchant permits, you can create your own offer page and use the merchant’s checkout page or the checkout page provided by a 3rd party affiliate platform. This is one way of avoiding the Bridge page policy issue.
Another way to avoid the bridge page policy issue is to create your own product offering, advertise your website with that product/service/info on AdWords and build a list that you can then use for email marketing campaigns to your affiliate offers.