Delta Hedging strategy - a peak into the rabbit hole

Warning - this is a long thread so I will TL;DR for you:
there is no right and wrong about delta hedging an option book... All we can do is getting a sub-optimal solution..
giving my take on the subject...

On the first day of my trading career my PM told me “go on one of these eFX platform and buy a 1-month USDJPY straddle. After that set it on your excel and let’s review it”… after I did that (had the position and 1/2/3order Greeks) he started questioning me about my position.

More specifically he was interested in the Delta and the Gamma… He wanted to know what the delta means, and despite I felt it’s too obvious, I gave him the full academic explanation (formula included). Then he said – “ok, so how frequent should we offset the delta?”

This question has probably been the cornerstone of my vol trading career. I made it my holy grail, and read/attempted dozens strategies to get that optimal frequency

Now we know that given that underlying spot price follows some kind of Brownian motion. We have no way of knowing a priory anything regarding its behavior…

So the delta hedging is merely a way to reduce our option book P&L variance, so ideally we should hedge continuously,

BUT, two things would probably prevent us
from doing so:
1. Transaction cost,
2. Realized P&L.
It is always a trade-off between return and variance, and how much we are willing to sacrifice one for another…

Over the years I came up with a simple 2x2 matrix that describes vol/trend regimes and gives a general strategy given each regime

This matrix might seem simple, and it is… The trick is to asses Vol and Trend, but once you are comfortable with these figures you can decide in which regime you are.
After you decided the above we turn to how we actually set the frequency…

Mostly when traders think about volatility they think of it as function of time, but we can think of it differently: It can be function of time/% change of the underlying/Accumulated delta… each hedging strategy will produce different P&L/variance under same underlying dynamic…

Time-based delta hedging – we want to use when we have trend (if we are long gamma) or mean-reversion (if we are short gamma)

% change hedging – we want to use frequent when we have mean reversion (from long gamma perspective) and less frequent when we have trend.

Delta-based hedging – similar to % change hedging, but more sensitive to the option book's gamma profile.

As both %change/Delta based strategies are more suitable in mean-reversion (from long gamma standpoint) we will usually alternate between them in MR market

As the underlying dynamic is constantly changing and evolving, we will want to be flexible and not stick to one strategy/hedging interval, and modify according to the market dynamic…

Over the years I developed more sophisticated models and ways to tackle this puzzle but this

initial strategy has been the cornerstone of my option trading.

If you are into this delta-hedging puzzle I encourage you to go on my shared dropbox (pinned tweet) and read the many papers exploring this field.

feel free to comment/share your thoughts...

*that should read Peek not peak ... Twitter please let edit already