Imo it is the skew, or the non intuition of it, that makes (pure) option trading hard to manage a book risk (not necessarily as a mm). There are no conservation laws. For example, if you hedge at the wrong delta not taking into consideration how skew changes as the underlying moves, or even harder, when a support point causes mm's to flatten skew (greed overtakes fear), you will overhedge, causing an already non-linear effect of path dependency to be even more pronounced on PnL. You have to anticipate these regimes and hedge accordingly. Something extremely hard to do, imo. Option trading just shifts predicting directional underlying moves to predicting skew+vola+gamma risk (if you get skew and vola right, it seems delta is pretty easy), in that order of complexity. It is almost as if delta needs to be computed based on model+market regimes (fear dominated, greed dominated, etc): http://www.math.columbia.edu/~smirnov/Derman.pdf
On Wilmott, someone recommends skew-delta as: sDelta = Black Delta + (( (vol of 1$ higher - vol of 1$ lower)/2 )*100*vega ) That doesn't seem right...
I've never understood hedging for the small time player. I can't figure how I could hold a position, hedge it, and come out ahead of just unwinding the position outright. I always figured it was for big players who were scared about a near term event, but held too large of a position to sell without moving the market. The only thing I could see a private player wanting to hedge is let's say you've held a stock that had a good run for 10 months and now you're done with it. You might as well buy some puts to protect your profit, at the same time hang on for those couple months to qualify for long term cap gains tax rate. I'm certainly missing something.
Let's say you put a strictly vola play on, which means you want close to zero delta for the position(s) as possible. For example, say you sell front month ATM straddles and buy further back month ATM straddles. Since delta is affected by vola, as the vola relationship between the two months changes, your deltas are going to be off. If you don't want directional exposure and only want vola exposure, you need to hedge this position something like once a day. This has come up a million times before. Lots of traders use options as a vehicle to leverage trading the underlying directionally. That is not the way pure options players trade options, most of the time.
Well most of the time if you think a stock is likely to go down your best bet is simply to sell it. But there are special situations where hedging with options makes sense. Here's an example: I bought shares of Facet Biotech at about 8.10 because it was underpriced. Later Biogen apparently agreed because they made a bid to take over the company at 17.50. The management of Facet decided this was still too low and is holding out for a better bid. My shares jumped into the 17.50 - 18.00 range. The issue I faced was this: Facet's management might squeeze a couple extra bucks out of Biogen so maybe I should hold out for a better price. Or Biogen might walk away and my shares might crash. So... I bought March 17.50 puts to hedge the stock, and sold March 20 calls to pay for most of the cost of the puts (net cost of the hedge - 0.30 per share). So now I wait a couple of months and see what happens. On March expiration I will close my position: 1. Exercising the put if Facet is less than 17.50. 2. Selling Facet outright if it is between 17.50 and 20.00. 3. Facet gets called away at 20.00 if it's price is greater than 20.00. Obviously I'm hoping for case (3), but with my hedge the worst case of (1) isn't too bad. Right now Facet is down to 15.75, obviously the market is concerned that Biogen will walk away. so my hedge is looking pretty smart so far. As nitro has pointed out, people who are primarily option traders (not stock traders) will use the underlying to hedge a play where they're basically betting on volatility rising or lowering, and want to remain delta neutral.
I don't quite understand the point... Isn't the whole point of most stochastic vol models to ultimately determine the correct deltas? So much work on this has been done by Derman and Dupire in equity vols and by Hagan and Rebonato in rates, just to name a few. The paper you cited by mathmarc is just an illustration of some of these issues...
It appears you are right actually... http://www.math.nyu.edu/research/carrp/papers/pdf/FXprofessionalsTalk.pdf
Maybe, maybe not... filthy's book covers some of these issues in a reasonably sensible way. I'm sure there's also other material written by the usual suspects.