Frequency of Hedge according to the Underlying

Reading Taleb's Dynamic Hedgeing (pg 419)

The topic is regarding the random walk of an underlying and the fractal structure or jaggedness of the segments of its path.

Taleb indicates a relationship between the 'smoothness' of the curve of the underlying and the production cost of options in order to rebalance gamma in relation to the frequency of the hedge taken. (naturally we could add the additional variable of the magnitude of the hedge, but for now I'll assume the position is brought back to delta neutral if that is the goal of the book)

Taleb notes that BS does not account for such minute incrementalization of hedge.

For either long or short gamma, it is assumed that the most efficient position from front to back of month is one without adjustment. In the face of possible loss however, this is then not the most efficient use of capital.

Is there a formula or eyeball methodology to determine the optimum frequency of hedge according to either the underlying in order to achieve the most cost effective gamma over the course of time?

I would like your initial reactions and then possibly build on the ideas if applicable.

Best,
REF

 

There are about a zillion different directions that this conversation could go so I will just list a few thoughts.

You are asking if there is a way to evaluate the choppiness of the underlying's movements, and adjust gamma scalping accordingly? Is that an accurate paraphrasing?

I have never tried to quantify choppiness, so I am not sure on that question directly. I would love to hear more about this though.

I have spoken with many traders that thought they were on the track of the holy grail of gamma scalping. Most never accomplished this goal, or at least never told me about it.

The most real world useful way I have heard to juice your gamma scalping is to add in stock charting to your options strategies. During trading hours, over hedge your gamma by placing scalps just inside of support and resitance levels. I particularly like to overscalp on my stock buys since long vega will explode as the product crosses through support levels. If a product moves through a support and resistance level when you are not at your desk (i.e. you got lucky--assuming you are long gamma), then let the sucker ride.

Another method is to use calls to gamma scalp, rather than stock. If the product falls through the support level, vol will go higher, thus somewhat negating the effects of the deltas in the call purchase. Similarly, as the product goes higher, vol will tend to fall thus somewhat negating the deltas of the call you just sold (make sure the product is vacillating and not on a multi day upmove as that will typically cause vol to spike UP--BTW, my favorite pure speculation trade is to BUY little calls in a product that has seen 2 or 3 single st deviation upmoves in a row, assuming vol has been crushed over those two days. Vol typically will POP on the third day of an uptrend in a big way.)

There is a difference in hedge ratios, and also gamma scalping, if you are dealing with treasury options instead of stock options, for instance. Since rates have a tendency to revert back to the mean over time, whereas stock can keep moving in either direction, most models seemed to overestimate the deltas of OTM options.

Not sure if this rambling helps, but thems my 2 cents.

 

Excellent. Your thoughts are very much leaning in the direction of my inquiry. My intention is to find the math which will indicate if my scalp/hedge is efficient. I am almost entirely a short gamma position trader and consequently I'm always looking for ways to hand off risk and rebalance my greeks. At the end of the day and I've traded hundreds of contacts, I frequently review my position and sometimes find that the number of adjustments to my position is daunting - in that I may be over adjusting in place of 'efficient' adjusting. When you're spending most of your time pushing deltas around, most trades equilibrate, however I think that necessity to place the greek adjustment can be more accurately determined if one were to understand their greeks and potentially their greek ratios in reference to the structure of the underlying. (this could simply end up being that we use an oscillator or BBands which are weighted from a MA to emphasize an additional moment of risk)

I think Taleb is basically offering that underlying instruments with typical known whipsaw are allowed more premium than those which keep a tighter chart line and this is reflected in the real pricing of the options and cannot be reflected in Black-Scholes-Merton. (otherwise the gamma would be too cheap, and my guess would be that you could find any additional premium ATM) Taleb writes: " For an option trader, ... intuition is important: If there is a possible smoothness on the curve of the underlying, then the manufacturing cost of the option through gamma rebalancing would be lower..." and he then places the caveat: "...provided the operator picked a frequency of hedges that matched such increment."

It's the frequency I'm after. This will probably prove to be an academic exercise, but I'm curious to see if there are other traders are attentive to the smoothness of the curve and how they account for this, and if its expressed by an adaptive frequency of trades and/or managed convexity. BSM does not appear to account for noise, how should we as traders.

[As for your long gamma trades. I don't have a ton of experience doing that but when I do go long, I'm normally looking for some sort of spread overlay for entry and then almost always scalp with short options. This is nice because you can sell premium in place of actual movement, and you can also easily ratio write against the meat of your position. I think its interesting that you find vols to move after levels are breached - that such a large portion of the market is aware of these levels. I only use futures if the underlying throws me a bone in the overnight, which has been more rare of late.]

 

Lots of attention has been paid to optimal hedging frequency. It is an important topic and not one to be left to "intuition" unless you're clairvoyant. For your first crack at it, take a look at Euan Sinclair's book. You'll find plenty of citations to get you started.

 

Yep, I second that... Sinclair's books (including the new one that's not out yet) contain a discussion of the commonly used methods, including Whalley&Wilmott and Zakamouline.

 

Good, I just ordered Sinclair on Amazon. I read Wilmott's site on a regular basis, I'll look up your recommendation. Thanks.