The longer the time, more chance something unexpected may happen (thus more volatility). Besides, over a long time things may change so much that they become even more "unpredictable". Although we just can't predict. Thus LEAPS are underpriced, and short term options overpriced?
A little too simplistic. Short term uncertainty would not move the 1 and 2 year options as much as their expected returns from those moves would not be expected over that time period. And, if you buy a calendar - Long 1 or 2 year options and short options say out 30 days, and you get a big move, the value of the spread will decrease. If you think LEAPS are underpriced, they might work better for a retail account as a stock replacement. This requires a directional bet.
You have conflated the probability that something happens, with the magnitude-expectation of that event happening. More rolls of the die ("the longer the time..."), the more opportunity for mean-reversion: Yes, more events will increase the number of ±2σ events. But on a cumulative scale, you will by-far-more increase the events which return you to µ -- your population mean -- your expected result in a mean-reversion world.
There are a handful of older threads on the forum that delve into leaps pricing. Three important points 1. As @tommcginnis said long volatility is actually lower 2. Net carry now becomes a much more important variable and can outweigh the importance of net carry over volatility - not the case in short-dated options 3. Leaps actually price off of a "Leaps" model and most folks who had successfully developed one commercialize them If you trading Buffet like very long-dated options the volatility becomes almost irrelevant
Ok, I have not heard that one before. Why would you use a different model for Jan 2020 and Jan 2021 vs Dec 2019 or Aug 2019? I would need to make assumptions on the inputs, but I would use the same model.
The distribution becomes less log normal. When you have a chance go back through the past postings. The prices using conventional models aren't too bad, but a lot of that is the generous spreads. The greeks are way off. http://www.pbcsf.tsinghua.edu.cn/research/caoquanwei/paper/15.Pricing and Hedging Long-Term Options.pdf Just one of many - I would go back and search the sight archive. One thing you'll find is the carry function - comes to outweigh the volatility. If you play with volatility for longer-dated stuff it's not as big a deal as if you play with carry.
I skimmed the paper and read the Conclusions. It seemed to imply that valuations were OK but BS did not provide an accurate delta. If the average retail trader used .42 or .40, it is really not much different. As a market maker I used Actant Quote which used a variation of the Cox, Ross and Rubinstein binomial model. I'm not a math expert and never wanted to be. It worked fine for my book of 12 option symbols making market in all strikes and months. I only had to adjust for DOTM options when I was long/short a lot of them. I don't like hedging a lot of <5 delta options with stock and prefer to look for other options to hedge.
So being off by 5% is acceptable? That's more than one option on a 1000 share hedge. Plus it only gets worse the longer-dated you go. Cox Ross is a bulletproof model, but it gets adjusted for Leaps.