You're mostly correct. As to your questions, think about it this way... Disclaimer: this is a perspective of a gamma trader in my world, so take with a pinch of salt. Firstly, when if you delta-hedge in the real world you need to make discretionary decisions about when and how much delta to hedge. If we leave aside the transaction costs for the moment, you already know that if you delta hedge continuously and the option is fairly valued, your relative return will be zero. If you don't delta-hedge at all, as you pointed out, your return will be what you mentioned in point 1. Around these two extreme outcomes lies the uncertain path-dependent return that you produce with your specific delta-hedging methodology. Different people have different rules that they follow and there is a lot of variation. Regardless of the methods, it's easiest to think of the outcome this way (and we're leaving aside the mark to market aspects here, this is accrual accounting; also this is a gross simplification): 1) you have bought a call w/IV of X. 2) on a given day I you delta hedged, such that you bought some quantity at price P1I and sold at price P2I for a PNL of ZI; ZI is a measure of realised variance/volatility/etc that you've "locked in" for the day. 3) if ZI is equal to X*sqrt(T) (where T is time to expiry), congrats, you have broken even. That's why this X*sqrt(T) quantity is known as your "daily breakeven". If ZI is less than the daily breakeven, you didn't do so well on the day and vice versa. 4) Lather, rinse, repeat, until expiration 5) At the end your PNL is the sum total of all the ZIs over the course of the procedure. If that number is greater than the premium you paid, congrats! Otherwise, not so lucky. This brings us to why our young turbulent friend is not so right. Observe that the premium you pay for the option is a certain, known expenditure. The delta hedging PNL is uncertain and depends on a lot of factors. In a high-volatility environment you will definitely have to pay a lot of premium, but will you be able to delta-hedge to recoup it? My personal preference is to buy "cheap" options and leave the selling/buying of expensive ones to other people. My Z$2c... I cannot guarantee everything I've said here is correct. Hopefully, peeps can weed out any obvious silliness.
Is dynamic hedging more trouble than it is worth? If the option is fairly priced, hedging will net me zero. If not, perhaps I could profit but the transaction costs and the slippages will likely eat up all of the profits? Looks like there is no free lunch for me here. But I learned a lot and had fun learning. Regards,
Another point I just thought of: When delta hedge what do I use for volatility? Implied volatility to determine delta neutral or use the realized volatility? Of course I don't know what the future realized volatility is. But if I use the implied, since it is not actual, it will create an error in the hedge.... Very complicated. It will take me a long time to figure this out. I am going to stay with simple stuff like going short or long betting only on directional.
Well, free lunches don't really exist in mkts, no matter what our turbulent friend botpro imagines... What you need to do is start from a different angle. While options are "fairly" priced, you don't necessarily have to agree with this pricing. You may have a subjective view that, effectively, tells you that the option is "mispriced". After all that's what makes a market. In the case where you believe the option is too cheap, you can buy it and delta-hedge. If you're right, you will make money, even if, for whatever reason, the mkt doesn't give you that money in the form of a higher option price. In that way, delta hedging PNL represents the option's "fundamental" value. This is not a free lunch by any means, as you're taking a risk, but if you look carefully you might find some "cheap" lunches. Delta hedging is one way of eating those. Ah, that's where it gets interesting and hairy... Generally speaking, for liquid(ish) options (e.g. ATM) you could make an argument that "the mkt knows best". The price of the option tells you the IV and the delta and that's it. For less liquid OTM options where there can be no mkts, the problem becomes circular and tricky. If you want to delta-hedge such an option, but the mkt doesn't actually give a price, what are you supposed to do? That's traditionally where you need some more sophisticated approaches. If you want a glimpse of those, try this: http://www.emanuelderman.com/media/smile-lecture9.pdf
Great answer, very clear and succinct. For IronChef: Dynamic delta hedging of options is better left for MM's or pure volatility shops. For a retail trader that is long gamma, the edge resides precisely on the non hedging side of it. If you look closely at the problem of the dealer is that he is not interested on taking directional risk, however you as retail trader are actually very interested on it and also handsomely rewarded in a non-linear fashion when you are right, there is where the edge resides (the nonlinear effect of gamma).
Great points. After 3 1/2 years and after participating in ET discussions, your comments are what I now concluded for me personally. To trade otherwise I am competing with all the experts who make a living trading options. The other comments that are invaluable to me from ET are that in trading options, start with first have an opinion on the market, the underlying and then formulate your trades around those opinions. If your opinions are correct, the non-linear rewards will out weigh the times you are wrong (Taleb). The other thing I learned was to limit my risk so when I guessed wrong I won't get wipe out. Happy trading and regards to all,