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# S = C - P

Discussion in 'Options' started by JavaBen, Jan 18, 2008.

1. ### JavaBen

I'm a rank novice boot-licken Options beginner. I lurk a lot, because I don't have much I can contribute.

But I've found these formula's to be easy to remember, and very useful for me. They aren't mine, I just haven't ever seen them presented this way.

Some definitions:
S => Stock
C => Call
P => Put
+ => Long
- => Short

So S (Stock) = C (long call) - P (short Put)
S=C-P.

It proves what the more experienced guys are saying - selling a covered call is the same as being short the put.

Through some simple algebra:
S-C = -P (Long stock, selling covered call (short) = short Put

So, with that in mind, here are some more:

S=C-P (this is the one I memorize, derive the others as needed)
S-C=-P
S+P=C
-S=-C+P
-S-P=-C

So, if I'm wondering what a MM would have to do if he was having to make a market selling stock, then he's -S. To hedge that he would have to go (-C+P).

Hope they are useful to you.

2. ### MTE

To hedge a short stock you go long synthetic so that's long call, short put or +C-P.

That is,

-S=-C+P so to hedge -S you need to reverse the other side, so -(-C+P)=C-P.

3. ### cgar

Go get a copy of Natenberg,s book Option Volatility and Pricing, and all will be clear.

4. ### donnap

Yes, it can be very helpful to know equivalents but it is not exactly S-C=-P. This is not an mathematical equation or rather it is incomplete. It merely illustrates equivalent positions.

S-C = -P+X Solve for X.

5. ### JavaBen

MTE, exactly correct.

donnap, I believe that would end up with

0=X

I did a poor job of explaining how I used these, as well as who I was targeting this information at.

This was posted for the other beginners out there like myself, as the pro's already know it.

I have always found it confusing to recall the different synthetic positions, so this approach helps me to be able to derive it on the fly. If it helps you, as a beginner such as myself, then great!

6. ### neophytenate

S-C=-P is probably all you really need to know for now. Believe me - it's great for a beginner to know equivalents. You may see that options are really bits and pieces of the underlying.

The cost of carry is missing from the equation. In the equation we assume P,C are at the same strike. For example, C-P is often called a synthetic long, but it is really equivalent to a synthetic future - with some differences due to the contract specs.

Example S-C = -P+ risk free bond (strike value) less dividends. Even this simple model does not account for all valuation nuances. Plug in some real numbers - it's fun.

I recall talking to a stock trader who said options are too risky. As opposed to what I thought - the underlying? Options are a great risk management tool. Trading options in illiquid markets is problematic, however.

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