First of all, as you figure out how to tell them about your interest, read up about naturists/nudism so you're prepared for their questions/comments about it. A good place to start is "205 Arguments and Observations in Support of Nudism", written by The Naturist Society and easily found on Google. Also, think about yourself and your own motives and reasons for why you enjoy nudity and want to openly be a nudist. (You're already a nudist even if you have to keep it private.)
I understand your dilemma, wanting to freely be open about something so innocent, harmless, natural, comfortable, and beneficial while being afraid of punishment or humiliation for having such an interest. I was about 14 when I discovered nudism for myself after a lifetime of being taught body shame and embarrassment about nudity until I had a terrible phobia of it. There was no way I could talk to my parents about it because it was their close-minded, immature attitudes about nudity that caused me to have those phobias in the first place. I tried talking to them about it once and the topic was met with hostility and bad jokes. In your case you will have to determine of what sort of mentality your parents have towards nudity or "taboo" topics of conversation because you know better than anyone else here what they're like.
Think back about when you've heard them talking about various things. Have you ever heard them make specific comments about nudity, nudists, nude beaches, or the nudist/naturist lifestyle? How do they react when there is nudity in a movie? How do they handle times when you're naked such as in the shower; do they knock before entering the bathroom or do they just come in and say "I've seen it all already"? Is there ever an occasion where they see you naked even briefly (changing, running from the shower to your bedroom, locker room at a pool, etc.), and if so, do they say anything or express any kind of reaction? In addition to past things, pay attention to anything new from them. Any answers to questions like these will provide you clues about how they think about nudity.
There are a few different methods you can try to introduce them to the idea (all your choice depending on your situation). An indirect approach would be going nude in your bedroom and leaving yourself vulnerable to someone walking in and finding you nude. If they ask why you're naked, just say you like it better that way because it's more comfortable. If you have pajamas, stop using them and start sleeping nude; if anyone asks, say you don't like wearing clothes to sleep and nude is more comfortable. If you're in a situation like a pool locker room or something (probably with your dad), strip nude and change without a care in the world to show it's perfectly natural for you.
A slightly more direct approach would be to look for the topic of nudism or nudity in TV shows or newspaper articles, and use that as a way to introduce the subject to ask them what they think about it. That would allow you to state your thoughts and feelings about it without directly saying you're a nudist, and the conversation could go from there however you feel is best.
Even more direct, which I know you're reluctant to try, is to specifically tell them you're a nudist, love wearing nothing, prefer to be nude at home, and want to know how they would feel about you openly going nude at home. That's where your knowledge of naturism and its benefits would come in because you'd have to convince them your interest is harmless and innocent and they would get used to it. Even if you can't openly go nude, maybe they’ll agree that you're free to be nude in your room and around the house when nobody else is home so that if they ever do find you nude there won't be any shock about it.
And last, most direct but maybe not the best method, is to just start pushing your boundaries and go nude in front of them. Always treat it as no big deal, however they might find it so shocking or upsetting that they would go even more negative about it, refusing to let you go nude at all or talk about the subject.
One major bit of advice, though: no matter what their reaction, especially if it's negative or derogatory, always show pride and enthusiasm about nudism and your interest in it. Never show them any response of embarrassment or shame or they will perceive it as something to be embarrassed and ashamed about. Ultimately you'll have to follow their rules but if you handle the matter well enough and if they're open minded enough, they may compromise and bend their rules to help you be more comfortable and happy in your home. If not, you'll just have to enjoy nudism in privacy when you get the chance and wait a few more years until you're able to move out to your own place, gain independence, and set your own house rules.