Options move differently when underlying goes up vs down

Question

I have been researching options and I have noticed that call options move differently when the underlying goes asset up vs. down. Mostly negatively for the investor.

For example, I have narrowed my research to one type of example. Call options dated two weeks out. Now when the underlying asset (in this case SPY since it is the most liquid) moves by 30 basis points, the call option is up ~9%. However, when SPY falls 30 basis points, the option falls by ~13%. This effect stays the same across the board for in / out of money options and even different expiry periods.

Call options gain less on upswing and lose more on the downswing even though the upswing and downswing is the exact same in basis point move of the underlying asset.

Can someone explain why this happens?

Answer 1

You may have some built in errors such as looking at stale quotes (not real time) or not evaluating bid to bid comparisons.

The short answer is that option pricing is complex and involves multiple pricing variables that are not all equal. ITM options have higher deltas and while they have larger dollar gains on price rise than OTM options (calls), the percentage gain is lower. Implied volatility can vary by strike (volatility smile/smirk) as well as from expiration to expiration. As one variable, share price change cannot have the same effect because the other variables are mitigating in varying degrees.

Your perception can't be correct because if it was, there would be an arbitrage available and without seeing the actual data, an answer is no more than a guess.