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Hi --
I am long gamma and currently flat delta (thru strads on futures, plus delta hedges) in an underlyer X. The general wisdom is -- "In a trending market, let the delta run & gamma hedge less frequently. In a choppy market, you gotta gamma hedge as often as possible" But is there a scientific way to detect this somewhat?
For this commodity, I am interesting in testing if hedging intra-day would be a better hedging strategy than close/close or even hedging every alternate 2-3 days. Effectively if the market is trending then I should probably let it run for a few days, if jumpy then I should increase my hedging frequency.
1. Can anybody suggest a few tests?
One test I did was to calculate the x-day changes. Then I calced stdev of these chgs and also averaged the absolute of the chgs. The ratio of these currently has been high for 3-day and 30-min changes indicating some trending behavior in the long run as well as swings in short term.
2. Can I use any feedback or adaptive methods based on tick data, so I can identify when trend changes to intra-day etc.
Also I heard a super trader once say "the higher the frequency of your data, the higher the degree of mean reversion in the spread" --> could there be a good reason for this?
thanks |
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Intuitively, the more you hedge the more profitable you will be, whether the market trends or chops, because you're taking into account more price movement. The only thing to really give pause at doing this is transaction fees, bid-ask spread, and if the change in gamma is efficient on that time interval.... which would require a lot of open-interest.
It would make more sense to do this with just a put or call, as oppose to a straddle, so you can hedge as many contracts as possible with the underlying (unless I misunderstood). |
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mib |
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| Total Posts: 350 |
| Joined: Aug 2004 |
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ribs&coke, in a trending market, more frequent hedges are less profitable. Suppose you are long gamma flat delta, gamma is relatively constant and is such that your cash delta changes by 1m per 1% in the underlying. If the spot moves 1% up, without rehedging you make gamma p/l 0.5*(1m/1%)*(1%^2)=5k. If the spot moves up 1% five times in a row and you rehedge after each 1% move, you make 5 times that, i.e. 25k. Now suppose you are expecting the market to trend and do not rehedge until the full 5% move. You make 0.5*(1m/1%)*(5%^2)=125k
on the original question, there are many kinds of mean-reversion and it is best to go for the one that matters most. This can be done e.g. via Bouchaud-Potter hedged Monte Carlo on intraday data. the tricky part for a serious position is the market impact of your hedging. A large long gamma position will smoothen the series considerably. |
Head of Mortality Management, Capital Structure Demolition LLC |
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| yeah, but that's if you consider there was no retracing in price whatsoever in that move. I mean if an options gamma was so accurately priced on small time intervals, you could hedge out any retracement. It's like taking every artery and capillary in your body and stretching them around the equator. I've never delta-hedged in this way, but I assume what nakedlunch is proposing would be difficult for lack of intraday liquidity in options. |
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mib |
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| Total Posts: 350 |
| Joined: Aug 2004 |
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| ribs&coke, I am afraid you do not understand what you are talking about. this thread has absolutely nothing to do with option liquidity. or with gamma pricing accuracy |
Head of Mortality Management, Capital Structure Demolition LLC |
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dgtvr |
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afaik, gamma hedging frequency is an art more than anything else. i've heard that someone backtested the optimal hedging frequency for tsy options and the result was that you would have made the most money by hedging every 6 ticks on 10 YR equivalent.
I would love to hear what others have to say regarding the OPs question. |
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akimon |
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>> Intuitively, the more you hedge the more profitable you will be, whether the market trends or chops, because you're taking into account more price movement. The only thing to really give pause at doing this is transaction fees, bid-ask spread, and if the change in gamma is efficient on that time interval.... which would require a lot of open-interest.
Hi, this is not correct. In a trending market, hedging infrequently will be much more profitable.
To take a simple example, say you own an option on a stock, so you are long gamma on this stock, and for argument sake, your gamma is one share/$1 increment. Say the stock trends, and moves up by $1 every minute, for the next ten minutes, and then stops.
After 10 minutes, the value of the option you own will increase by ~$50 (approx half of gamma * movement^2).
If you hedged once every minute for 10 minutes, after 10 minutes your pnl will be ~$50 - hedging pnl = $50-(9+8+7+6+...+2+1)=$5
If you hedged once at the end of 10 minutes, your pnl will be
$50 - $0 = $50.
Regarding the original question of this thread:
How you hedge your gamma is more an art, than a science. I don't think back-testing results will prove anything.
If I am going long an option solely for the purpose of making money on gamma hedging it (since I have the trading view that delivered volatility will be higher than the implied volatility), rather than using it for other reasons such as taking a direction bet, I would usually gamma hedge only when the underlying move is greater than the implied movement, otherwise I would be 'locking in' a gamma hedging pnl of less than my implied vol (against the trading view) and will suffer from negative time decay.
Most textbooks and academics study option theory in terms of replication, volatility, and gamma hedging pnl. I think those concepts may be important in liquid markets, but they fail to explain the value of an option from a liquidity standpoint, which I think is a far more important concept, especially since every market, even an fx pair like usdjpy, has become very illiquid at some time interval in the very recent past and suffered from 'liquidity holes'.
The real value of being long optionality is in illiquid markets. In those markets, it is not advisable to hedge frequently, since the underlying can be very jumpy due to lack of liquidity. In these markets, one can extract more value from being long an option when everyone is short (or if there is no liquidity) since one can be in a position to provide liquidity and get rewarded for it. In situations of distress and liquidity holes, the person who is long gamma can dictate to the market, at which price level, and in what size, the gamma hedge will trade at, and this can be very profitable. |
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Thanks mib, Aki, If daily move > "breakeven vol", the gamma > Theta(+ vega) .. What is interesting is how is the imp vol determined for mkts with liquid futures but with no options trading, only some OTC options…
So if
A) if the people are relying on using close/close prices (for lack of active options market)
AND B) there is intra-day swingy nature to the instrument
Then we can benefit by going long gamma and hedging intra-day. Any thoughts
Mib, can you explain why mkt impact is tricky to use the Bouchaud-Potter hedged Monte Carlo on intraday data. |
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Mib, you're right but you're discounting price retracements entirely, which is the point of delta-hedging. So it should at least be considered.
Assume as you said the price in one day moves 5%. Without hedging, p/l = 125,000$. Instead you can choose to hedge gamma twice every 30 minutes. We said we were in a trend, so let's fairly assume a 0.5*|x| retracement for every move |x|...
trading 26 times (13 up, 13 down)...
13 (|x| -|x|*0.5) = 5%
|x| = 0.77%
where |x| is the absolute value of one up-swing
(and 13 is the number of half-hours in a day)
gamma on |x|:
13 * 0.5(1m$/1%) (0.77%^2) = 38,538$
To add what was earned from gamma on retracements....
|y| = |x| * 0.5
...where |y| is one retracement.
|y| = 0.39%
gamma on |y|:
13 * 0.5(1m$/1%) (0.39%^2) = 9,886.50$
38,538$ + 9,886.50$ = 48,424.50$
Now, If you hedge 10 times (5 up, 5 down)...
|x| = 2%, |y| = 1%
p/l of trades |x| = 100,000$ and
p/l of trades |y| = 25,000$
total: 125,000$... effectively equal to holding gamma and risking losing it all.
At 8 trades ( 4 up, 4 down), it surpasses your net p/l if held all the way.
|x|=2.5%, |y|=1.25%
4 * 0.5(1m$/1%)*( 2.5%^2)
trades of |x|= 125,000$
and
trades of |y|= 31,250$
total: 156,250$
Of course I'm assuming a 0.5 retracement of every move, but that's much better than assuming none at all... don't you agree?  I am wrong in assuming the more you hedge the more profitable it is though, that was silly.
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| Anyways the point is... given a retracement rate >0 in a trend, by selecting a hedging frequency that returns the same pay-out if you let delta run, that pay-out is achieved at a fraction of the risk. |
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Baltazar |
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There is a paper from Derman I think that shows that scalping is equivalent as sampling/measuring volatility, which make sense.
Depending on the trending nature of the underlying, volatilities estimated at different frequency do not scale with sqrt of time.
Since your profit is a function of the square of the move, in a brownian motion, if you increase the scalp size you scalp less (in a sqrt relation) but make more (in a square relation). In the end it is the same. And that is straightforward to back test with a loop and a price serie in excel.
Now if your market is trending this is not true anymore and you'll make more by using bigger scalp size (the square profit does not change but the sqrt (T) number of scalp does).
Intuitively you'll understand that scalping more aggressively in a mean reverting market makes more money.
Trending is just the other end of the spectrum.
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Qui fait le malin tombe dans le ravin |
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But there must be an optimal hedging frequency to use basing your judgment on the implied volatility of atm options at varying maturities. I think that would be a reasonable approach. For example:
i.v. on SPY contracts with maturities of 1 month and 6 months indicate 40% and 30% respectively.
for i.v. on IBM contracts , they are at 45% and 30%.
for i.v. on MSFT contracts, 35% and 30%
So relative to the bench mark (SPY), these values imply that it would be better to delta hedge less frequently with MSFT, and more frequently with IBM.
I believe this should be profitable, because if you buy the 6-month dated options on MSFT and IBM, both options assume the same 6-month volatility. But because you know the short term volatilities are different, you could hedge them accordingly and profit from the difference. |
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Baltazar |
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The thing is the implied volatility is the average volatility for the frequency you plan to hedge with for a given maturity.
This just tells you what the market expect for the coming month and for the 5 months after that. It does not tell you anything about the trending nature of the stock and how to gamma scalp them.
IBM option traders expect more movement in the first month, less in the following one than MSFT that's it. |
Qui fait le malin tombe dans le ravin |
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well that speaks volumes to me. If I see 45/30 and 35/30, to me that says the former has a greater probability of finishing 6 months with a more mean reverting price distribution relative to the latter.
Why can't it be interpreted this way? |
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Baltazar |
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I think this might be relevant if you wanted to gamma hedge once every 6 month. But to me that's not gamma hedging, this is plain directional trading.
I assumed, but that might be incorrect, that we are speaking about hedging frequency ranging from 1 per hour say to 1 per 2 days or so.
Assume you pick once a day as a rough frequency, then the 6 month trends/ mean reversion do not matter, only the ones in orders of hours.
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Qui fait le malin tombe dans le ravin |
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| yeah generally we were talking on an intra-day time frame, i was just tossing the ball around. Maybe you quote iv on options expiring in a couple days then, I'm not sure how that would fare. |
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r&c, I don't think the term structure of iv enters into the picture. There is a "term structure" (if I may call it that) of realized vol sampled at varying intervals, as others here have pointed out, but this has nothing to do with i.v. term structure.
For instance if realized vol sampled from 2-day returns over the past 60 days is greater than realized vol sampled from 1-day returns over the same period, then presumably "trending behavior" exists. A rolling autocorrelation of returns would give you the same info. This all begs the question of how you define a trend and if the effect isn't due to noise; note the vol estimate from 2-day returns is about sqrt(2) times as noisy as the vol estimate from 1-day returrns. But if the trend really is a persistent effect, you would do better to let your deltas ride when long gamma and widen your scalp width. |
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after tons of gamma hedging i have realized that calculating constant-time vol is plain bs when it comes to gamma hedging.
Has anybody really experimented with tick data? How can I look at tick data (where time is not constant), smooth it and scale it to daily vol.
thanks! |
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Baltazar |
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| Total Posts: 1722 |
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I'd be interested to know why you think that way about volatility.
Athletico, maybe we can define it as the scale structure of volatility as opposed to the term structure. |
Qui fait le malin tombe dans le ravin |
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for short-maturity options, instead of vol based on business time, we need to atleast look at "financial event" time. for e.g. when ISM or unemployment numbers come out for FI or stats come out for commodities.
if I sell you an option purely for 30 days, would you use the same vol for 31 days options? -- probably yes. what if the 31st day is big-news day?
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schmitty |
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@nakedlunch: > instead of vol based on business time...
You are using business time in the wrong sense, as a synonym for calendar time. Usually, in the literature, business time means information time or transaction time.
As in the attached paper, and many other easily googlable papers.
Attached File: Calendar_vs_Business_Time.pdf |
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thanks i meant working days calendar time which is how BS vols are quoted.
i see so much expectation build in at start of the day which could vanish by end of day. There is a certain time in which you can capture a chunk of the move, the rest of the day is just a filler.
apprarently only Zhou's method seems acceptable by the academic community, any word from the trading community? |
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Fossilus |
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| nakedlunch, take a look at gamma and you'll realize whichever model you use, whether it is sv or bs or jumps gamma always peaks around at the money strikes. As markets trend you tend to move away from the specific level or towards it but you don't jump from high gamma to low gamma or vice versa as much as in a ranging market. So whereas your delta remains relatively constrained in the ranging market the gamma will jump high low and low high as the ranges take place. That's why your gamma risk is easier to take into account in a trending market. |
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jungle |
Chief Rhythm Officer
CSD LLC |
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if I sell you an option purely for 30 days, would you use the same vol for 31 days options? -- probably yes.
You really think people do this? |
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Fossilus |
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| :-) look at the vol differences between dated Brent and the frontline contracts....a few days difference but a butcher concentrated around the loading days...and not to mention the squeezes. |
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