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How can I replicate a long put option on S&P 500 index? I believe the best way is to short delta shares and put the proceeds plus the value of the put in t bills but i am not getting the same P&L as from the long put position.

if someone can share an example to explain that it would be great.

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    Can you explain what you mean by replicate? The CME already offers such a product. How much unlike the actual thing do you want your replicant to be?
    – dg99
    Sep 5, 2017 at 20:01
  • i mean to break the option in terms of long and short position in stock and cash in a way that you are indifferent between holding a position in a put option or its equivalent long /short position such that the payoff is equal.
    – Hiba
    Sep 6, 2017 at 6:45
  • @dg99 Some brokers do not allow naked puts (or have strict margin/experience requirements) due to the unlimited downside risk; although I suspect that replicating one through that same broker would not be allowed either.
    – D Stanley
    Sep 6, 2017 at 13:52
  • @dg99 synthetics are handy when you want to hide your intentions from the market. If you buy a bunch of long put options, then people will see the volume and you've shown your hand. If you come through the share market + futures market + a different options contract in order to create the same risk profile, nobody will extrapolate what happened.
    – CQM
    Sep 7, 2017 at 8:28

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The typical way to replicate a long put option is to short the underlying and buy a call at the strike you want.

So in your case you would sell S&P 500 futures at the expiry you want, and buy calls at the expiry and strike you want.

Since selling S&P futures require significant margin, you could also look at short ETFs that closely track the S&P 500.

Note: I am NOT recommending this strategy; just illustrating how you could short the index.

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