How does Gamma scalping really work or really mean? It seems there is no true profit scalped. If we look at the simplest scenario, Black-Scholes option price [$]V(t,S)[$] at time [$]t[$] and the underlying stock price at [$]S[$] with no interest, the infinitesimal change of the overall portfolio p&l under delta hedging, assuming we have the model, volatility, etc., correct, is
$$0=dV-\frac{\partial V}{\partial S}dS=\big(\Theta+\frac12\sigma^2S^2\Gamma\big)dt.$$
So the Gamma effect is cancelled by the Theta effect. Where does so called Gamma scalping profit come from? Is this just a folkloric myth stemming from misconception of how options really work or a gem in the rough?

Note: My condition implies that 
$$ P\&L_{[0,T]} = \int_0^T \frac{1}{2} \Gamma(t,S_t,\sigma^2_{t,\text{impl.}})S_t^2( \sigma^2_{t,\text{real.}} - \sigma^2_{t,\text{impl.}})\,dt$$
coming from the misspecification of volatility is [$]0[$] since I am have assumed it away.

 It's anchored in difference between theory and reality. In theory you have constant implied vol that exactly matches future realized vol of the underlying, and on top of that you can also continiously hedge. So your remark should actually be "It seems there is no *theoretical* profit scalped", which is correct under these assumptions

In the real world non of these assumptions hold,  you can't contiously hedge, the price isn't even continious -it's jumpy-,  the realized and implied vol will differ because future vol is non-constant and unpredictable etc etc.  Because of all these things you won't have exactly balancing gamma and theta P&Ls.

@outrun:

Are you then talking about the P&L coming from the second formula in my first post?

I think that's assuming continuous hedging?

Eg, suppose you stop hedgjng at some point, then surely you end up with P&L after that?

Gamma Scalping in practice is monetizing the volatility (i.e., turning the implied volatility into realized volatility) using the underlying asset's price action. For example, say you believe that the market is under pricing the true future volatility, and you buy the volatility (in theory you would want to buy the entire volatility smile, to ensure flat/constant  gamma exposure, similar to variance swap gamma profile) and by managing the delta/gamma risk you pay the theta/decay. If you were right, the realized P&L of your delta hedging would be greater than the premium you paid for the options at expiry

Let us look at the discrete time hedging scenario. Without interest, do we agree that for the time period [$][0,T][$], the P&L of an option-stock portfolio hedged only at time [$]0[$] is the following?
$$ P\&L_{[0,T]} = \frac12\int_0^T \Gamma(t,S_t,\sigma^2_{t,\text{impl.}})S_t^2( \sigma^2_{t,\text{real.}} - \sigma^2_{t,\text{impl.}})\, dt +\int_0^T \big(\Delta(t,S_t,\sigma^2_{t,\text{impl.}})-\Delta(0,S_0,\sigma^2_{0,\text{impl.}})\big)\,dS$$
If you do, we proceed to the following discussion. When we take expectation at time [$]0[$], the second stochastic integral disappears. In fact it disappears whatever the hedging [$]\Delta[$] we put on at the beginning. The best hedging ratio is to minimize the variance of that second integral. Suppose we know the real volatility in advance, or the real volatility is equal to the implied volatility, the first integral vanishes. From this I can only conclude the expected P&L comes from the accuracy of the volatility estimation. I do not see how this has much to do with Gamma scalping. Or I just do not know what Gamma scalping really means.

@VolMaster:

So you are basically saying the same thing as what I am expressing mathematically in my last post?

yes

@VolMaster:

Alright. Then I think the name Gamma scalping is really a bad name, as it is quite misleading and confusing, because the trading strategy is really about arbitraging or betting the volatility whilst Gamma is only a multiplier --- it could just as well be called Theta scalping or stock price scalping if we really have to emphasize the multiplier.

A fancy name for good luck, perhaps selling it as skill for a higher bonus.

A fancy name for good luck, perhaps selling it as skill for a higher bonus.

Agree. Actually, I think Theta scalping is a much better name if we really want to emphasize the multiplier --- not that it is a good idea in the first place --- as it absorbs all the multipliers.

Call it whatever you like, but the fact is that trading the volatility basically trading the underlying price action volatility (or delta). Obviously delta is a directional trade, whilst gamma is a non-directional exposure (i.e., represents the variance better).

Just my 2c

Imo it's letter delta accumulate in trending market, and more actively hedging in sideways markets.

@outrun : If only we could accurately predict trending markets (or mean-reverting)....

@outrun : If only we could accurately predict trending markets (or mean-reverting)....

Yes indeed! Or any other deviation from unconditional distributions!


I once just started trading fresh from school and was forced into a *huge* gamma long position (compared to my average and risk limits) ..and right then the market crashed! (maybe the 1997 mini crash?)
I was very inexperienced and eveyone was shouting like crazy and I was just standing there  "OMG I'm 100.000 stocks short now, my delta risk limit is 20.000,, oh 150.000 now, ... oh 200.000". My boss walked up to me and said "T, .. shouldn't you hedge?" so I said "ok" and I bought half my delta back at the low of the day. I tried to buy more but *maybe* because of my bids the stock kept going up and up and up again. .. and then I was long and had to sell! This was probably my best "gamma scalp" ever!
I've also had lot of bad days of course. What's interesting from a personal perspective the few exceptional successes/lucky days give you good stories that last a lifetime, and you quickly forget  about the bad ones. (unless they are life changing bad, something I've never experienced). I had a very fun boss who factored these things in, not just position P&L but he also recognised the important of "story value" (and non-fake risk management!)