Delta Analysis

OddTrader · Oct 29, 2010

Quote from ivanbaj:

I found this:

...
This may be difficult to maintain, but if you can, then you will be at the bottom of a "profit well". It's a standard theorem in analysis that whatever directions spot and volatility move, together or independently, the value of your position will always increase. However it is not a risk-less profit because theta will lower the bottom of your well over time. On average it will keep you hedged against theta. If spot and volatility are changing rapidly, however, then you'll make a profit. If they are frozen, you'll make a loss. If you can build this position with mis-priced contracts, then you may be able to cut out most or even all of your theta and guarantee a profit!! (All this ignores trading costs, of course. It also depends on how you calculate your position vega, volga and vanna, since, strictly speaking, you need to do this with respect to a unique common indicator of volatility, not IVs.)

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And I found this:

"A smart strategy seeks to avoid catastrophic risk at all times, to profit by real or implied volatility explosions, and to limit time decay loss." --- Baird

ivanbaj · Oct 29, 2010

Oops wrong thread. I meant to post this here:

http://www.elitetrader.com/vb/showthread.php?s=&postid=2995517#post2995517

Quote from ivanbaj:

I found this:

So gamma scalping is just a standard delta neutral long vol play for which you pay your theta decay?

Here is a more general method that enables you to scalp volga as well as gamma.

Dynamically hedge your net position such that:

1. You are delta-neutral.
2. You are vega-neutral.
3. You have positive gamma.
4. You have positive volga.
5. You have gamma*volga > (vanna)^2.

This may be difficult to maintain, but if you can, then you will be at the bottom of a "profit well". It's a standard theorem in analysis that whatever directions spot and volatility move, together or independently, the value of your position will always increase. However it is not a risk-less profit because theta will lower the bottom of your well over time. On average it will keep you hedged against theta. If spot and volatility are changing rapidly, however, then you'll make a profit. If they are frozen, you'll make a loss. If you can build this position with mis-priced contracts, then you may be able to cut out most or even all of your theta and guarantee a profit!! (All this ignores trading costs, of course. It also depends on how you calculate your position vega, volga and vanna, since, strictly speaking, you need to do this with respect to a unique common indicator of volatility, not IVs.)

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volga = dvega / dvol

vanna = dvega / dspot = ddelta / dvol

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Gamma > 0 gives you a 1-dimensional well along the spot axis. Volga > 0 likewise along the volatility axis. The extra condition you ask about prevents leakage from the well in any other direction in the 2-d spot/volatility plane. (It guarantees a 2-d minimum.)

I dug out my old Analysis text-book from when I was an undergraduate. The book is "A Course Of Analysis" by E.G.Phillips, CUP 1962. The reference is section 10.5, pp256-259. See also "Partial Derivatives" by P.J.Hilton, Routledge & Kegan Paul, 1963, Chapter 4. Younger members of the forum may be able to point to more recent texts still in Print
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froluis · Oct 29, 2010

quote from: thenmmm
"plus no real trader uses delta...
only geeks who lose money".
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what do real traders use instead??

Chelsea_FC · Oct 30, 2010

Quote from froluis:

what do real traders use instead??
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Don't listen to him, he has no idea what he's talking about. Of course "real traders" use the greeks. What an ignorant comment.

Jerkstore · Oct 30, 2010

Quote from thenmmm:

plus no real trader uses delta...
only geeks who lose money.
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Delta is not an exact science by any means. In practice, delta is nothing more than a hedge ratio. Every trader and large trading firm in the world uses delta--even the ones that dont trade options. All of them have a need to hedge illiquid risk. By definition, a delta calculation is required for hedging. The assumptions used to create a delta number can vary wildly though. The large options market making companies spend a lot of time, and money trying to perfect their assumptions used to create the proper hedge ratios

The trick is knowing how precise/variable, or how smooth/bumpy your "delta" numbers are, given the portfolio of risk in question and the market situation.

Creating accurate deltas is incredibly difficult.

thenmmm · Oct 31, 2010

Quote from Chelsea_FC:

Don't listen to him, he has no idea what he's talking about. Of course "real traders" use the greeks. What an ignorant comment.
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and on average every chelsea fan is better than any trader on wall street? i guess that's your stupid logic. Anyhow...

Chelsea_FC · Nov 1, 2010

Quote from thenmmm:

and on average every chelsea fan is better than any trader on wall street? i guess that's your stupid logic. Anyhow...
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I do not think that was a coherent thought, but anyway just ones who work in the city as an options trader at one of the BBs. So yeah I think my word is good.

stoic · Nov 1, 2010

Quote from Martinghoul:

But surely you must realize that you're in proper "apples 'n oranges" territory? Is that an intelligent enough response for you?

I am sorry to disappoint, but there's no reason to have an intellectual debate. You're misunderstanding the purpose of the Greeks and the BSM model. That's all there is to it.
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So enlighten me.....

However, since I've traded options professionally for 30 years, and currently work as a Business Systems Analyst in the brokerage industry as a SME to support software development in margin, CPM, and complex options handling, I won't accept an explanation overflowing with key buzzwords and a plethora option jargon. I want facts and figures. Details in real time. Formulas and values.

stoic · Nov 1, 2010

Option prices used were based on the midpoint between the Bid and Ask. In most cases the spread was .05 or less.

All model data figures were generated using the option pricing model online at the CBOE.

I intentionally picked a stock that did not pay any dividends.

Theta was accounted for.

OddTrader · Nov 1, 2010

"plethora"?

imo, to be fair, Greeks/Deltas have their values in analysing, evaluating/presenting and structuring/formulating the dynamics of complex strategies, if we really want to.