If I wanted to write puts at a strike of 80, but the options series doesn't go below 100, is there a way to synthesize this position?
Not in the public market. If you are capitalized enough, you could have an investment bank price and arrange for someone to take the other side on an over the counter basis. Like, Warren Buffet has SPX puts out 15 years.
Depending on how big a trade you wanted to put up you could request the strike be added. Obviously they're not going to add it for a small retail trade. Both the PHLX and CBOE also offer FLEX options with custom date and strikes, but I dont recall off the top of my head what the minimum size is.
Yes I've read into cboe Flex options. I don't think it's right for me because you need pretty big size and even then, liquidity would suck. I'm big for retail but probably small fish compared to institutions... i was just hoping there was a way to synthesize using existing series so I would have good liquidity. Guess not..