The calls that I sell are underpriced due to skew. I find this unfair. This makes covered call strategies unattractive. What can be done to improve this?
Hmm are you sure? Normally the "V" like skew is in your favor when selling. The higher IV, the higher the credit you as the seller get. Example: https://finance.yahoo.com/quote/PROG/options?p=PROG&date=1639699200 Otherwise: average down, by using multiple strikes, and/or of multiple underlyings,...
That's the good thing about a two-sided market; if you think it's "unfair" on one side, simply take the other side of the trade. But I suspect you'd complain about it being "unfair" when you lose there, too... Prices in the market are not "fair" or "unfair"; just like the color of the sky can't be right or wrong, they are what they are. If you believe the asset is mispriced to one side or another, that's either a trading opportunity or a way for you to find out that your perception is wrong - so you'll either make money or learn to refine your view on the market (although you'll pay for that knowledge.) But assigning human or moral characteristics to prices is a priori wrong, and will screw up your trading if you stick with it.
I know a market maker who will happily pay more than the market for out of the money calls. he makes his money on volume.
Just like what @qlai said, you can sell put + sell stock to do a box or you can also do a vertical put credit spread so that way you reduce the risk of being short squeezed on the underlying in case the price of the underlying takes off
Makes sense. Although it might also be index ETF options where the skew makes covered calls unfavorable.