Calculating the Put/Call Ratio for Delta Neutral ?

A

Aston01

I am trying to calculate a delta neutral position. Most of the time it seems the size of these positions are based on the number of shares someone is trying to hedge and the cost is whatever it ends up being to create the hedge. I am trying to calculate it for a trade the other way around, assuming I want to buy $5k worth of calls and puts based on the delta and price of each, how many of each side I need to purchase to stay delta neutral and as close to $5k as possible.


Assuming I was buying a $5k combination of the following:

Call Option
Price - $.59 each
Delta - .0759

Put Option
Price - $.60 each
Delta - .0544


=5000*0.0759/(0.0759+0.0544)
which equals $2,912.51

and

=5000*0.0544/(0.0759+0.0544)
which equals $2,087.49

I end up with a Call Delta of 265.65 & Put Delta of 261.12 ... 4.53 Difference ...tolerable for my purposes.

My thought process was that if I could determine the relative difference between the 2 delta's I could determine how much of the $5k needed to be allocated to each side. The above calculation achieved just that, but I am missing something it seems. When I put in a second set of values like below things didn't balance as effectively.


2nd Set of Values

Call Option
Price - $.82 each
Delta - .1265

Put Option
Price - $.50 each
Delta - .0587


=5000*0.1265/(0.1265+0.0587)
which equals $3,415.22

and

=5000*0.0587/(0.1265+0.0587)
which equals $1,584.77

I end up with a Call Delta of 240.35 & Put Delta of 399.16 ... -158.81 difference ... Not so good


Any ideas where I messed this one up ?
 
You made this very complicated. Delta is used to calculate your equivalent share position. Your using dollars in your calculation. If you only want to use options in a spread and not hedge with stock, try inverting the delta with a spread to achieve delta neutral.

In your example, I believe you're buying a combination of an OTM puts and an OTM calls. Call delta .0759, put delta .0544.

If you buy:

Calls 544
puts 759

or stay in that ratio, you'll be delta neutral. The option price will not matter in your example.
 
I think you should be more specific in what you are trying to acheive... There are many option strategies that are delta neutral... Also who says you need to use both call and puts, you could use just 1 of the 2, again depending on your purpose... Also you can be delta neutral and long vol (like a calendar) or neutral and short vol (iron condor for example). Many ways to be delta neutral yet used in very different circonstances...
 
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