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Continous hedging as a rachet device to lock-in profits
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Guess what... ;-)Are you asking me?
What? I am missing the funny, sorry...Guess what... ;-)
The question has been edited, so that finally even you will understand it... ;-)What? I am missing the funny, sorry...
Whatever, man... I have absolutely no clue what you're saying, so, for that reason, I'm out.The question has been edited, so that finally even you will understand it... ;-)
Well, I'll be damned... Looky what interesting things you'd find in that article:
"First of all, the portfolio loses money with dynamic hedging because it has negative gamma—something the dynamic hedging cannot change.
...
The fact that the portfolio has negative gamma means that the dealer is going to lose money dynamically hedging it. If the portfolio had positive gamma, the opposite would be true."
I now read the article, and it very well makes sense. The losing does not mean real losing. It is just the effect when shorting options (because you already rcvd the credit).
In the opposite case (long) you gain value (ie. that you paid for buying it). So in the end everything is in right parity or equilibrum, so to speak.
HALLELUJAH!I now read the article, and it very well makes sense. The losing does not mean real losing. It is just the effect when shorting options (because you already rcvd the credit).
In the opposite case (long) you gain value (ie. that you paid for buying it). So in the end everything is in right parity or equilibrum, so to speak.
Thank you for this link, it is an excellent article for someone new to options.And here is also a "modern" hedging text especially for the MM types:
http://www.riskencyclopedia.com/articles/dynamic_hedging/
It all make sense to me and Martinghoul is right. First of all I modeled dynamic hedging short puts using Black Scholes and came up with ~ zero profit though each option chain could be slightly positive or negative (I used Excel to program the Black Scholes equations and assumed normal distributions for short durations of ~30 days using a random # generator within the normal function). It is consistent with Black Scholes' original analysis and options pricing theory and supported the Goldman conclusions. You make money only when the option is mispriced and deviated from Black Scholes or the volatility changes significantly during the period of the contract. And I ignored transaction costs.
When gamma is negative, you essentially buy high and sell low to maintain delta neutral. When gamma is positive you do the opposite.
Am I making any sense? Please comment, especially about my modeling approach.
By the way this thread is a great learning experience for me personally, thanks to all.
I don't understand what you are doing. I can only program in Excel (or Fortran if I have a main frame).I tried many variations. Latest params were the following:
.Code:// define the input params to use in GBM / BSM: const double dbDaysInYear = 252.0; const double dbMktSecondsPerDay = 23400.0; // US regular market hours make up that much (6.5h/day), excluding premarket and aftermarket hours const double dbSpot0 = 100.0; // start with this stock price const double dbVolaPct = 20.0; // historic volatility const size_t uExpDays = 21; // 252 const size_t uHoldDays = 21; // uExpDays; const double dbEarningsYieldPct = 0.0 ; const double dbDividendYieldPct = 0.0; const double dbStrike = 100.0; // 95.0; // const size_t nBarsPerDay = 780; // ie. 30-sec bars @ dbMktSecondsPerDay const size_t nBarsPerDay = 390; // ie. 60-sec bars @ dbMktSecondsPerDay // const double dbBarSizeInSec = dbMktSecondsPerDay / double(nBarsPerDay); // 60 s, ie. 1 min const double dbHedgeEveryNsec = 300; // 3600; // set this const size_t uHedgeEveryNbars = size_t(double(nBarsPerDay) / (dbMktSecondsPerDay / dbHedgeEveryNsec)); // ie. 5 bars
But I think I finally grasp the hedging case for long options too. In an other discussion somewhere else someone wrote this:
So, in the long option case dynamic hedging should result in a PnL of about the same size like the premium one had paid.Code:"This means that if you hedge dynamically, then you'll/should make a tidy profit. In fact, if you hedge continuously over the lifespan of the option, you should, theoretically, make exactly the premium that you paid for the option, assuming BS pricing."
Yes, then it of course would make a big sense!
But the book and paper authors simply neglect to mention this important bit of information, and the poor reader like me just wonders where the logic is in what the book/paper author writes... ;-)
But I've not been able to replicate this yet, ie. to prove it, due to my q&d framework I quickly developed but which still has some bugs; will need more time to fix it.
If shorting is involved, then coding becomes a nightmare, I made this discovery many times... ;-(
Yes, the article is indeed very good.Thank you for this link, it is an excellent article for someone new to options.
Hmm. IMO you have misunderstood the most important thing of this kind of hedging.It all make sense to me and Martinghoul is right. First of all I modeled dynamic hedging short puts using Black Scholes and came up with ~ zero profit though each option chain could be slightly positive or negative (I used Excel to program the Black Scholes equations and assumed normal distributions for short durations of ~30 days using a random # generator within the normal function). It is consistent with Black Scholes' original analysis and options pricing theory and supported the Goldman conclusions. You make money only when the option is mispriced and deviated from Black Scholes or the volatility changes significantly during the period of the contract. And I ignored transaction costs.
When gamma is negative, you essentially buy high and sell low to maintain delta neutral. When gamma is positive you do the opposite.
Am I making any sense? Please comment, especially about my modeling approach.
Just re-read the article where it discusses the outcome of the long options, and then that of the short options.
It's very important to understand the difference.
In theory you do profit under very normal conditions, not necessarily with mispriced and deviated prices.
You are welcome, I'm learning that stuff too. ET gives a good platform for discussing such studies. Thx also to them.By the way this thread is a great learning experience for me personally, thanks to all.