Calculating the synthetic equivalent

Discussion in 'Options' started by Pinozi, Jul 28, 2009.

  1. Pinozi


    I know that a covered call is the synthetic equivalent of a sold put

    Question is how do you calculate the actual equivalent strike/prices?

    So if Im long NBA @ 50 and sell a $45 Call - is that the same as selling a $47.5 put?

    Im sure its not that hard but my brain is switched off at the moment
  2. It should be the same strike price, so sell the $45 Put.
  3. Pinozi


    But doesnt the level you are long the stock from make a difference?

    i.e. if I was long NBA from say $30 and market goes to $50 and I sell a $45 call - what would be the equivalent put sale strike be?
  4. wayneL


    No, still no difference. You just have some open profit to add to the equation.

    Think of it this way. You could sell your stock and short the put. That would be the same thing synthetically. So you end up with the short 45 put and some cash in the bank. The only difference is that you have the cash in the bank instead of as open profit in the stock and a short call. Risk and reward still the same.
  5. Just in case you want another opinion, the synthetic of a covered call is a naked put with the same strike and expiration date as the call.

    The position is stock vs. call. Period. Current stock price; price you paid; option premium - are all immaterial.

  6. spindr0


    While many people can tell you the answer, it's usually a meaningful light bulb moment when you see it for yourself.

    Here's a little exercise that might help. For simplification, let's pretend that stock XYZ has no dividend and there's no borrow or carry cost.

    XYZ is 45. The Aug 45 put is $1 and the Aug 45 call is $1.

    Compare the potential return of the covered call to the naked puit at various prices. Set up a spreadsheet or stubby pencil the answer. You'll see that they're the same.
  7. MTE


    The synthetics are always based on the same strike price(s), no matter which strategy you use. A 45/50 long call vertical is a synthetic equivalent to 45/50 short put vertical, a 45/50/55 call butterfly is equivalent to 45/50/55 put butterfly, 45/50 strangle is equivalent to 45/50 gut strangle and so on.