I’ve been going through John C. Hull’s classic, ‘Options Futures, and Other Derivatives’, and have been enthralled with the process of neutralizing the delta in your portfolio and when the opportunity arises improving the gamma and vega embedded within your positions.
Below I’ve included some notes from Quora that were taken from, ‘Dynamic Hedging’, the author not to be mentioned because I was blocked on Twitter by the author’s mathematical cohort, Alexander Bogomolny, @Cuttheknotmath.
Reason unknown. But I did enjoy the daily problem and the comments that the two mathematical savants would exchange. The comments were mostly a self-reinforcing dogma on why other people even attempting maths should just stop and kill themselves so there would be more air for the two of their brains to consume.
I digress to the main topic of interest.
Delta is the slope (first derivative) of the P&L/underlying curve. A delta hedge protects only against small movements in the price of the underlying. An example of a delta hedge is when you buy a put, which gives you negative delta and positive gamma and then buy enough of the underlying to zero out your total delta. This hedge does not protect against larger movements of the underlying. When the underlying moves, the non-zero gamma will change your delta, causing you to need to re-hedge. Many people mistakenly call this re-hedging “gamma hedging”, but it’s not; it’s just dynamic hedging of delta in reaction to gamma.
Gamma is the second derivative of the P&L/underlying curve. A gamma hedge protects only against small movements of gamma; gamma will move when either the underlying or its implied volatility move. An example of a gamma hedge is when you buy a put, which gives you negative delta and positive gamma, then sell a call to zero out your gamma but give you even more negative delta. This exposes you to large movements of the underlying, so you will likely want to then buy enough of the underlying to zero out your delta. A gamma hedge does not protect against larger movements of gamma, because the put and call each have non-zero “speed”.