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Don't you think that if an unkown position shows up in your account the first person you should contact is your broker rather than posting it on a public discussion board!? I mean, if you have already contacted your broker and the issue has been addressed then why post it here. On the other...

Ahh, the good old greed has got to you!

It depends on what you expect the stock to do!?

Exercise of an OTM option doesn't make economic sense so, no, an option will not be exercised if it is OTM. An ATM one or very close to ATM may be exercised due to the cost associated with exercise vs. selling.

That must be some kind of a record!:D :D :D

Actually, there are variations of Black Scholes that adjust for early exercise, so not all is lost for the good old BS.:D

OK, I'm no expert on VIX futures/options, so feel free to correct me, but as far I know VIX futures/options are priced off the variance swap, which means that it's not that simple to exploit any arb opportunities.

I usually go thru some possible adjustments when I have a loser on my hands, but every time I come to the same conclusion that my time, effort and capital would be put to better use if I just close out and move on. I don't know, maybe my view is flawed in some way and maybe some of the losers...

I find value in adjustments only when the position has moved in my favour and I want to take some profit or protect the profit. Whenever the position goes against me I find that closing out and taking a loss gives the best risk/reward, all potential adjustments yield inferior risk/reward...

Any theoretical model needs inputs to produce an output. Volatility is the only undefined input so your model is as good as the volatility estimate that you use.

As I said, opinions vary. I like their platform.

Opinions vary, but I doubt anyone can beat Thinkorswim when it come to options. True, commissions are higher than IB's, but commissions are not everything...

Check out broker reviews for both, you'll get the idea.

Well, then just short any other stock.

Yeah, SPY has a beta of 1, but if you short it you automatically have a beta of -1. There are some short ETFs available. That is, they move exactly opposite, so you actually buy them to have short exposure to the market. Search for them, I can't remember the tickers.

By the way, mo's suggestion is the synthetic alternative of my suggestion. :)

Check out "Option market making" by Baird.

You just sell a call vertical, where the short call has the strike of your current long call and the long call has the strike of a new long call. For example, you are long 45/50 call vertical. To roll up the 45 call to 47.5 you sell a 45/47.50 call vertical, thus leaving you with long 47.50...

"Delta neutral" is a bit too general to give you anything meaningful. That is, most option books discuss "delta neutral". What exactly are you looking for? The definition of delta neutral, delta neutral trading, neutralizing delta?

All of your questions can be answered by simply visiting the exchange's website CME, and the margins can be found here. Also, some brokers offer lower margins for intraday trading, you can find those on your broker's website.