http://www.risklatte.com/Articles/QuantitativeFinance/QF122.php this guy talks about the distro of extremes as typically used in exotics to come up with knock outs or look back pricing.. but i don't really see why you couldn't use it as an instrument to get dimension on variance .. meaning.. you could find stocks that cover alot of ground making more sense of your gamma scaples and or negate canidates for premium sales.. vanillas are non linear so what happens between entry and expiration makes a huge difference when delta hedging.. Delta in of itself really has less meaning the more you look at it by itself.. it comes from a formula that assumes continuous hedging when only discrete is possible , and when commissions, and markets with frictions are reality.. and everything is relative to time.. farther out vol is a better handle then gamma for risk........ and if you just look at a theta value it would look as if time is speeding up or slowing down in a very nonlinear fashion.. which maybe is closer to the truth haha..
A short gamma pos locks in a loss per delta hedge. A long gamma pos locks in a profit per delta hedge.
PnL curve is convex if you're long options, and concave if you're short. for exact PnL calculation on an option position, delta hedged or now, http://matdays.blogspot.co.nz/2012/12/delta-hedged-options-return-estimate.html
the more and more i read about delta hedging the more i find out that most market makers only use it sparingly and typically only hedge options with other options meaning synthetic equivalents.. reversals/conversions boxes/ rolls.. and basically they play on squeezes in order flow to basically either overprice options or front run order flow.. using Delta one is a measure of last resorts it seems.. static replication is the goal.... its relative valuation... scalp cheap options (relative) and sell overpriced.. and play on orderflow.. another thought to is... the idea of letting your gammas run.. . and short playing slow markets when short premium.. the slower your play your short premium hand with a delta hedge the more risk you take.. the less you bleed, the more risk of ruin you take on.. and the risk in letting your gammas run without adjusting deltas is boom you get mean reversion and you lost premium without gamma scalps.. theres so many assumptions to tweek in delta 1 delta hedging.. to me its harder then outright directional trading..
key words from this article.. "distance formula from mechanical physics. " as if finance was close to physics
That's more of a philosophical question. But the equation they show for P/L although not accurate has a lot of practical value to explain in one line what ppl can use pages of text. For example you can see that delta profit is sensitive to the stock going up or down as it is proportional to dS but gamma profit is always positive (for long pos where gamma>0) since it is proportional to dS^2. Delta hedging at least in theory eliminates the senisitivity to the sign of dS (ie direction of stock move) and you only have gamma profit as long as the stock moves. Of course it's not free lunch as you lose b/c of theta (for long positions)
yes i am being a little philosophical.. thats an equation from a linear world .. one in which we don't live in.. do you have any experience with delta hedging successfully? i don't but a "implementation shortfall" variable in the equation to me means.. how well can you game the market with your scalps.. which in this case could have a wide range of results.. and dS is implying you know the future distribution of price changes... which of course you do not! i'm not trying to be obnoxious.. i'm just saying
Hey Caveman thanks for the feedback. I want to answer your points in a constructive manner, since I just wanted help. The gamma portion of the equation is to show that the payoff is NOT linear, so that for newbies they'd see that gamma's really a means of variance in return. Implementation shortfall: from my experience it's mainly around speed of your execution, software errors (if automated), bid/offer spreads dS is implying that you should have an idea of AVERAGE future distribution, which is also necessary for risk management plans. There's a ton of quant finance research papers to verify this if you use google scholar.
Hey thanks for the feedback. I used to work for a regional index options market maker, and I'll try and address your points. -> If you look at the actual equation, the gamma portion is clearly nonlinear, which explains the convexity of a long option position. -> Implementation Shortfall usually lies in the areas of software glitches in the institutional setting. -> about dS. Future average change in vol can be easily worked out (a crude example http://matdays.blogspot.co.nz/2012/11/excel-data-analysis-33-volatility.html). It is needed for risk management, and a theoretical edge for the trader. hope that helped!