The Options Ratchet Effect - making money out of thin air?

In my continuing communication on the use of equity options as a surrogate for the underlying instrument, here is a scenario that may appeal to the non-technician investor/trader. In this example, let us say, an instrument (say, NYSE:SPY) which is trading at $477 as of now (around 1400 hrs EST on December 29, 2021) drops by 4% (ie, by $19) and recovers back to its current value shortly thereafter.

Suppose we decide to buy an at-the-money (ATM) Call Option with an expiration of March 18, 2022 instead of buying the stock. This option, with a strike price of $477, would cost $13.73, per the snapshot of the option chain below:

When SPY drops by $19, this option is out-of-the-money (OTM) by $19. The estimate of the value of this option can be made using the above option chain by looking at the call option that is OTM by $19. This value is $4.37 (the call option value for a strike price of $477+$19=$496). Suppose we decide to sell the original option and buy an ATM option. We would incur a loss of $13.73-$4.37=$9.36.

When SPY recovers its value, the option is in-the-money (ITM) by $19. Its value will be $27.85 (the call option for a strike price of $477-$19=$458). This represents a gain of $27.85-$13.73=$14.12

Thus, the round-trip of the stock has resulted in the corresponding options trades to create a value of $14.12-$9.36=$4.76.

Here is the above options play, in a tabular format:

• "Today's" Time/Date: 1400 hrs EST, December 29, 202; SPY=$477
• Buy an ATM Call ($477 Strike Price) with March 18, 2022 for $13.73
• SPY drops 4% to $458. The Call's value is now $4.37
• Sell the Call for $4.37, and Buy an ATM Call ($458 Strike Price) with the same expiration for $13.73 (this operation is called "Rolling Down")
• SPY recovers back to $477. The Call is now worth $27.83. Sell the Call.
• Cash Flow: -$13.73+$4.37-13.73+27.83 = $4.76

The value is created by the asymmetric profit curve for a call option. When the underlying stock drops, the call option keeps dropping at a slower (and slower) rate. When the underlying stock rises, the (rolled over) call option rises at a faster (and faster) rate.

It's only Greek - specifically the "delta" - say us options technicians!