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Delta neutral option strategies



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(I've posted this to the omega-list as well since there may be others interested.)

In general, a 'delta neutral' options strategy refers to an options spread position who's net delta is 0, or close to it.

Briefly, options prices are sensitive to 3 major things. They are also senstive to the no-risk interest rate and dividends, but I will skip these for simplicities sake. The no-risk rate doesn't change frequently and there are no dividends to worry about in futures.

1) Price movement in the underlying asset
2) Time to expiry
3) Expected volatility of the underlying during the life of the option

Since each of these things affect the price of an option in a significant way, greek letters have been assigned to represent the option price's sensitivity to each of these components.

Delta = $ price change in option / $ price change in underlying, holding 2) and 3) constant.
Theta = $ price change in option per day, holding 1) and 3) constant.
Vega = $ price change in option / % change in implied (expected) volatility, holding 1) and 2) constant.

An example of delta. Suppose XYZ futures in trading at 100.00. The Mar 100 calls are at 2.00. The delta of these 'at the money' calls are usually around .50. This means if XYZ goes to 100.80, a gain or .80, then the Mar 100 calls will be priced at 2.40, a gain of (.80) * (.50) = .40.

The Mar 100 puts will have a negative delta since an increase in the underlying results in a put of less value. In our example, with XYZ trading from 100.00 to 100.80, the Mar 100 puts will lose (.80) * (-.50) = -.40.

Now, if you sold (or bought) the Mar 100 call / 100 put spread (a staddle), you would be 'delta neutral' for small movements in the underlying since the delta's of the spread components cancel out.

Notes:
In practice, the decimal point is often dropped for convenience. So it more common to say the delta of the at the monies are 50 with the decimal point being understood.

Delta itself changes as the underlying moves. It ranges from essentially 100 for deep in the monies to 50 for at the monies to essentially 0 for far out of the monies. The speed at which delta changes is called gamma. So a delta neutral position becomes more and more unbalenced as the underlying moves away from where it was when the position was initially established. How fast it becomes unbalenced is measured by gamma.

A trader long the delta neutral spread will profit the more the position becomes unbalenced. Presumably the spread was put on because the trader believed a price move was imminent but he/she didn't know the direction. However, this bipolar profit profile is purchased at the expense of time decay. If the underlying doesn't move soon enough, his options will expire worthless. Of course this is exactly what the short neutral spreader wants. He/she's the one who keeps the premium paid by the long spreader. However in a big move or price shock, the short spreader has essentially unlimited liability no matter which direction the underlying moves.

You commonly hear that short neutral spreads work about 80% of the time, but you can get killed on the big unexpected move. (Case in point, Neiderhoffer) This is compounded by spikes in implied volatility as well as the speed at which the position becomes unbalenced (gamma).

The above is a *very* elementary discussion. There is *a lot* to know about options before you should feel comfortable trading them. For the non-mathematical, McMillan's "Options as a Strategic Investment" is decent. Being an EE myself, I much preferred Natenberg's excellent "Option Volatility and Pricing" which IMO stuck just the right balence between rigor and practicality.

>I am interested in the Delta nuetural strategy as it pertains to bonds.  Could you elaborate on this for me?