Tywin does not believe in love — only legacy. And you, now captured by his men will be perfect for what he has in mind. You are the heiress of the North, should your brother Robb fall you stand to inherit it all, thus Tywin decides  a marriage, a cd and loveless one, is in order. He expects obedience, loyalty, submission, anything else will be crushed to oblivion after all this is just politics. He needs more heirs and you stand in line to inherit the North, a potential way to mitigate the war