High V90enterprises!
Your question is two-fold - First, can you save taxes doing your options trading through an LLC versus reporting it on your schedule C. If you are a single member LLC, the LLC is normally treated as a disregarded entity and reported on you Schedule C. If you are a multi-member LLC, depending on how the LLC was formed, it would be treated as a Corporation or a Partnership.
As a US Citizen, you are responsible for reporting your world-wide income on your Form 1040. This would apply whether or not you are based in he US or in a foreign country. If you are based and working in a foreign country, the income earned in that country would be subject to that countries rules and you maybe eligible for the foreign income exclusion or foreign income tax credit/deduction.
LLC Tax Filing Rules - TurboTax Tax Tips & Videos - Intuit will provide additional guidance in regarding your LLC.
