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I'm reading Natenberg's book, and he says that all options trades should be delta neutral.

I understand that this prevents small changes in the underlying price from changing the price of the option, but couldn't there be a case where you would want that?

I (think I) also understand that if you're betting against just volatilty, it would make sense, since you don't care what direction the underlying price moves, but I don't entirely understand why he says all options trades should be delta neutral.

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Can you supply the context to where Natenberg states that all option trades should be delta neutral? If I remember correctly he also has a couple of chapters on directional trading which would run counter to that point. – Ralph Winters May 4 '11 at 18:06

5 Answers

up vote 9 down vote accepted

I haven't read Natenberg but it of course depends on your side in the trade:

Are you a market maker or a risk taker? So do you live on the spread (first) or are trying to make money based on e.g. forecasts on direction (second).

This is the great divide in QuantFinance!

Only in the first case will all your option trades be delta neutral.

There is a nice short paper which elaborates on both concepts (it calls the first one Q and the second P):

Meucci: 'P' Versus 'Q': Differences and Commonalities between the Two Areas of Quantitative Finance http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1717163

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So, let me get this straight: There's nothing wrong with betting on direction, but in doing so, you need to perform proper market forecasting, which is generally much harder. By betting on the spread, you're aiming to make money from a mispriced option, and the only piece of option pricing that isn't a known fact is future volatility, so the work that needs to be done is calculating theoretical future volatality and comparing it against implied volatality. Is that right? – Reverend Gonzo May 4 '11 at 16:09
(Continuing) The reason to keep it delta neutral is because you don't care about direction so much as changes in volatality. You'll make money over the long term by adjusting your position to maintain delta neutrality. However, all of this lies on whether your calculation of future volatility was actually correct (or close to correct) relative to implied volatility. (Is that right, too?) – Reverend Gonzo May 4 '11 at 16:11
In general it is right what you say but it is also very academic. In practice forecasting vola is as hard as forecasting direction so finding mispriced options is again something for risk-takers and not for market maker traders. These either calibrate their models to market given impl. vola or, even better, hedge options with other options. Search for e.g. Taleb who wrote several papers about the practice of option trading. – vonjd May 4 '11 at 17:20
up vote 5 down vote

Well - if you're not delta neutral - this means you take a position with certain view on the market.

This can be very comfortably done when you think that a stock price will go high up, but you don't want to spend all your money on acquiring the stock - you buy a call on it, which is quite cheap, and get the same payoff.

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up vote 4 down vote

One other consideration is the cost of the trade. If you're not delta-neutral, you're expressing a directional view, and there are cheaper ways to express a direction view than options. (Namely, just owning the underlying.)

So, conceptually, it's a little easier to think of there being two separate trades going on: an expensive vol trade (the options) and a cheap direction trade (underlying).

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up vote 2 down vote

As I recall, Natenberg recommends selling time premium and places himself in the market maker camp that @vonjd describes.

You are correct in noting that delta neutral holds for small changes in the underlying price. You can probably imagine a case where you sell a lot of deep out-of-the-money puts and sell a few slightly out-of-the-money calls. This would be delta neutral while the underlying remained steady, but would not be delta neutral if the underlying dropped sharply.

Part of the reason why is because this position is not gamma neutral: the deltas of the puts and calls would change as the underlying moved away from its opening position.

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up vote -2 down vote

(Edited)

An option trade has 2 main components : 1st derivative, and 2nd derivative wrt to the spot.

But if you need to play 1st derivative, you just buy the stocks right?

So if you consider buying a stock that mean you are there for the 2nd order derivative. That's what options are all about. And that's why your book says option trades "should" be delta neutral.

PS : volatility sensitivity is just the integrated form, over the life of the option, of that 2nd order spot sensitivity...

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or so they say... Who says this? Options traders are interested in volatility. – chrisaycock♦ May 23 '11 at 0:26
the theory book says that. call it 2nd order derivative, convexity, or volatility, they are just different facets on the same thing. – nicolas May 28 '11 at 16:32
"or so they say" because if you tell me that vol does not change with spot, I propose we do business together. – nicolas May 28 '11 at 16:49
hey stop the massacre... or give constructive comment. my answer is reasonable if not complete. of course you can give the answer by the book, but that's not where it stops ! – nicolas Jul 16 '11 at 14:01

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