'Let Gamma run' or Delta hedging
- Thread starter Cren1
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Quote from Cren1:
Please, could you explain this point in a bit quantitative way? I don't think we need stochastic calculus, but at least the hedge ratio written as function of Vanna.
Thank you
Not applicable.
The vanna will increase as spot diverges from your neutral strike. You don't need to know change per se, but should model +/- on the vol-line at each hedge trigger. IOW you need to be familiar with vol-smile. You'll want to shave deltas as the index declines and vice-versa.
You need to calc wing-sensitivity if you're trading a flat-smile (like most blue-chips).
How is it wrong?
Whatever vol you hedge an option at, you should theoretically have the same expected value. This of course in theory which is based on the black-schole model assumptions around volatility being static, no transaction costs, and log normal distribution with drift = risk free rate, etc.
If it were any other way then you could create synthetic options via hedging at different vols and make arbitrage.
Yes it does. But if you and I are trading the same option and we model it with different parameters we will get different hedge ratios. Our expected value is the same, but our pnls can be different because of the evolution of the stock price and the variance of our pnl will be drastically different.
You are saying that someone who buys an OTM call and doesn't hedge it has a different expected value than someone who has hedged it?
One guy is effectively saying the vol is zero and the other is not.
The midpoint of the OTM call market (vola) is representative of the expectancy under a perfect and continuous hedge under a flat surface. The transactional expectancy in aggregate should be zero-sum if your modeled vol = realized and your can hedge continuously and vol is static. BSM assumes static vol and therefore vanna is zero under the context of expectancy. It's not zero under a stoch-model or if you simply disassociate the concept of static vol and the current vol of the option in question when the position is hedged.
That is true, but how does your using a stochastic vol model change your expected value vs my using a static vol model?
If you use a stochastic vol model you might get a better hedge and thus a lower variance of pnl; but it should not affect your expected value.
It doesn't. Use BSM and accept the new vol-figure that is modeled at the time of the hedge. It's (more so) representative of the true expectancy. Are you stating that the assumption of static vol does not alter the expectancy? Intermediate vols under BSM and stoch will be different even if they are equivalent at the inception of the trade. "Inception expectancy" is really a flat-Earth argument. We both know that static vol and continuous hedge assumptions are bullshit.
Your expectancy argument assumes a perfect hedge and static vol. You cannot simply toss it out by stating expectancy is equivalent and model-independent when hedging is critical to the model.
Expectancy and hedging size, freq, etc., are inextricably linked and BSM assumes zero-convexity.
Quote from Cren1:
If you go short Gamma, then your goal is to earn the time consumption. Delta hedging helps you to protect the position from being damaged by underlying movement, there are no news about it: if you short Gamma and IV drops towards expiration, your Delta hedging will make money (I'm not considering bid-ask spread and transaction fees).
Now consider a long Gamma position, like a simple long straddle: if the underlying moves far away from the strike(s), you start earning. Here is the so called 'let Gamma run' technique, which is nothing more complex than to not cover the Delta.
Here is my question: if you correctly predicted the IV movement, what is better? I mean: let the IV starts rising after you opened that long straddle. In your opinion is it better to cover the Delta with the usual frequency or to let the Gamma works?
In the first scenario (Delta hedging), you will probably benefit of a P&L which rises but with no slope; in the second scenario (Gamma run) there's nothing to say: your position will behave like a long/short on the underlying if the underlying continues its trend.
Obviously some of you will probably tell me that they will let the Gamma work until some threshold, then cover the Delta... but my question is about extreme examples.
What do you think?
The house is short gamma. They cannot lose as a group, because the house is still there and was there. Who is then the sucker (as a group)? If you get an edge on short gamma, then I would listen.
Huh?