In a hypothetical trade on January 1st, with the ES is at 900, March ES calls have around 3 months before expiration. During this time the March 700 put options are trading for 2pt (100$)
If a 700 put is sold and the market has a huge drop in two weeks that stops around the 700 area, then the premium for that 700 put could be 50x times what you paid for it.
What if instead, the trader on Jan 1st went long a march 2008 ES contract at 900 and on the same day sold a March 2008
700 ITM call for 202pt ($10100) This would be hedged all the way to 700. In this example, if prices fell exactly the same way they did in the first example by landing around 700 in only two weeks, would the 700 ITM call more than likely have a similar extreme rise of its implied IV in comparison to the 700 put from the first example? If a 700 put from the first example had a 50x rise in value after the move downward causing the put to be now worth 100pt ($5000), then would the 700 ITM call be around 100pts also?
Of course it would. The put and the call at the same strike HAVE to trade at the same IV, or else there is a very easy arbitrage, called a conversion or reversal. That's what keeps things in line.
In stocks there are exceptions. Put-call parity can get distorted by hard-to-borrow situations, SEC proclamations or other circumstances where the stock cannot be freely sold short. That does not exist in futures however. So you can count on put-call parity staying in line, meaning that the put and the call at any given strike will trade at the same IV.