If you hire someone to do work for you and they exceed that agreed upon price, what are your options?

Did you sign a contract with him? Did the email contain the core elements of a contract and include a pretty clear statement you are only paying $1,600.00 for the work and spell out the work? Did you include anything about no additional fees or is it silent? If you don't have a formal contract, and the email states simply you are going to pay sixteen hundred dollars for such work, I would venture to guess this person you hired is out of luck.  Unfortunately, he basically entered into a bad agreement and would have to sue you to obtain said monies.  If he sues you, he would be most likely required to sue you in the states, and if he obtains a judgment, it won't be on the contract. The court would have to use a little rough justice if the court were to take his side and assign a value to his work. 

However, based on the brief description you have given regarding a person you hired as a work for hire to write software for you for a project for $1,600.00, it appears you would prevail.  Next time, the recommendation would be to very clear (even if you feel you are being overly careful or redundant) about what you expect and what the other person expects, so that no one leaves the table on different pages.