The original question was about the use of a long put to give some crash protection. As an example, using the FTSE (and the principle is exactly the same with the S&P) you could buy a March 4575 put for 18 (i.e. £180 per contract) which simulates exposure to £45,750 in the FTSE. Those who have read my previous posts will know that I am allergic to using my own money to buy an option, so you could sell 2 x March 5025 calls for 12 each, giving you a net +6 to cover commissions etc. This gives cover for any crash below 4525, and in this event Implied Volatility would rise smartish and increase the value of the long puts considerably - particularly if there was a reasonable time left to run. There would be no profit other than the +6 credit on expiry between 4575 and 5025. Main drawback would be a sustained rally thru 5025, above which you lose £20 per point if left uncovered. This is a 1 x 2 short split strike synthetic.
An alternative could be a ratio backspread. Say, sell 1 x April 4825 put for 85, and buy 2 x April 4625 puts for 38. This gives a net credit of +9. If expiry takes place above 4825, then all expire worthless and you keep the net credit. Between 4825 and 4625 you lose on the short 4825 put but without gaining on the long 4625 puts (at expiry) giving a max loss at 4625 at expiry of 200 points (£2000). Below 4625 the long puts go into the money and overall will show a profit below 4425 at expiry. In practise a sharp fall immediately would show a profit at all levels because the increase in IV would be in your favour because you are net long 1x put.
The synthetic theoretically could lose you more because there is unlimited exposure above 5025 - and at 2:1. However, the FTSE would have to rally above 5125 by April expiry to exceed the maximum theoretical loss on the backspread, and I think there is more likelihood of March expiry being close to 4625 than the April expiry being above 5125.
I guess you need to decide which risk you most want to take! 🙂