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# Basic question on synthetics

Discussion in 'Options' started by cdowis, Oct 6, 2006.

1. ### cdowis

Basic question here:

2 x XYX stock at 73, short 2 x 70 calls, and long 5 x 75 calls.

I am trying to understand how this works:

As I understand, the 73 calls "cancel" out the short 70 calls (almost), so you are left with two short 73 puts and 5 x 75 calls.

You are net plus deltas approx 3 x 75 calls (approx)?

Or am I totally confused.

2. ### momoneythansens

Long stock = long CALL + short PUT

It doesn't matter which strike. If you buy a CALL and sell a PUT at any strike, the position should behave like long stock i.e. stock at 73 is irrelevant.

Turn your 2 x stock into:

2 x long CALLs + 2 x short PUTs

(you can decide the strike later but they must be the same for both PUTs and CALLs)

Looking at your existing inventory you can choose to offset the 2 x long CALLs against your existing 2 x short 70 CALLs (this is just one option, but als the most logical) i.e. we have now settled on the strike for the synthetic stock to be 70.

So you are left with:

2 x short 70 PUTs (from synthetic stock at strike 70)
5 x long 75 CALLs

Yes, this is a very bullish position, net long DELTAs.

One possible way to dissect the position to help you understand it's characteristics are:

2 x split-strike combos (risk reversal) 70/75
+3 extra CALLs.

Good luck.

MoMoney.

3. ### spindr0

I think that your question is confusing because you have what I think is a typo. You have "short 2 x 70 calls, and long 5 x 75 calls" and they turn into 73 calls and puts?

Ignoring your conclusion and sticking with the original 70 and 75 calls and keeping it simple, if these options had a very low IV, say about .15, the 5 long 75 calls would "cancel" out the delta of the 2 short 70 calls at the current price of 73 (at higher IV, you'd have a net positive delta from these options).

But what about the 200 delta from the long 200 shares?

This is a bullish position with 200 long delta plus the delta of the option position.

4. ### riskarb

5-wide risk-reversals are roughly 75d at \$73 due to gamma. So long 150d on the 2 lot reversal and another 35d per call on the additional 2 75s. Perhaps +220 deltas at the moment. Don't hold me to that delta fig, as I have no interest in booting a modeling app.

The payoff is nonlinear, so it's nowhere near synthetic stock.

5. ### cdowis

Thanks very much.

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