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I was trying to create a replication portfolio of options for a Variance Swap and noticed that there is a jump when moving from below strike puts to above strike calls. Something similar to this:

enter image description here

I was curious why would that happen and a quick search brought me to this discussion.

The accepted answer states that:

In practice you use puts for low strikes and calls for high strikes, since the OTM are more liquid. Low/high is relative to the forward price.

  1. So if we are using puts for low strikes and calls for high strikes, wouldn't the IV curve be broken at Forward Price?
  2. Is the reason for using puts for low strikes and calls for high strikes just the liquidity issue? Or are there other reasons for this?
  3. And finally, why would we use Forward Price, not Spot Price?

Thanks!

AK88
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  • The answer is simply that the forward is wrong. – will Feb 20 '20 at 23:46
  • @BrianB, thanks for pointing this topic. I have read your post, however, it still does not click for me. Especially when we have close to zero interest rates. Perhaps I will try to replicate this and see if this will offer further clarity. – AK88 Feb 25 '20 at 00:10
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    @will, can you please elaborate your comment? – AK88 Feb 25 '20 at 00:10
  • Calls and Puts at the same strike have the same implied volatility. If you get the forward wrong (i.e. divs, borrow cost, discounting) then you'll end up with one of puts or calls being over priced and the other under priced, which translates to the vols being too high/low. – will Feb 25 '20 at 11:30
  • @will put-call parity for European options guarantees the put price equals the call price when the strike equals the forward. In the graph above there is no strike at all where it happens. My guess is that the spread is due to the fact that SPY options are American and put-call parity does not hold for them. – Appliqué Oct 10 '21 at 15:03
  • @Appliqué the graph above is implied volatilities, which require a number of parameters which haven't been provided in the question - the forward, discount factor, day count fraction, etc. To see what the issue is, we need to know what was used for these. Often the issue is an incorrect forward (which breaks put call parity). Though the implied vols created don't look qualitatively as they do when the forward is wrong, so we need more info to say what's wrong. – will Oct 10 '21 at 15:33
  • @will curiously, sample mid implied vols for SPX from http://www.historicaloptiondata.com/ also look the same way. I have pictures, but don't know how to upload them into a comment here – Appliqué Oct 10 '21 at 15:44
  • @Appliqué do you have the option prices too? Can you plot the time value of the calls and puts (i.e. option price less intrinsic value)? these should match exactly, but again you need to know the forward correctly. – will Oct 10 '21 at 16:08

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