Is the risk really higher?...there are two kinds of risk in selling an option: 1 - frequency of it going into the money and 2 - the extent it goes into the money. Overpriced options are at less risk of going into the money, but tend to make larger moves when they do. Underpriced options are at greater risk of going into the money, but tend to make smaller moves when they do. On average, in a trendless market, these risks would balance out; and in a bull market, it should be the calls that have higher iv to reflect a volatility bias to the upside. I don't think that Black-Scholes take market trends into consideration, so this would be the only rational reason to accept a skew as fairly priced, but the skew is actually going against the trend. Iv should have nothing to do with the strike of an option; it's the same security reguardless of the strike. If there are two different iv's for one security, then at least one of them must be wrong.
You've got a couple of concepts conflated here, but here's something for your question about relative pricing on puts/bullish risk-reversals. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=375784
I wouldn't be able to judge the analysis in these books; are they saying that the model is correct?... and, if so, are they explaining the skew as an aberration of the market, where some options are permanently over/under-priced? I see mention of the skew changing after the '87 crash; in that case, the skew either didn't reflect reality before '87; it doesn't now; or as I'm inclined to believe, it never has as long as there's any skew other than making otm calls more expensive in an uptrend and otm puts more expensive in a down trend.
So, essentially then, the models are right and the market is persistently wrong; amazing - I never thought it could be that easy to profit with options. The book mentions that even atm puts have a negative return; to my thinking, this makes sense, because in an uptrending market atm calls should be priced higher than atm puts, but put-call parity prevents this, creating a distortion that can be exploited. The opposite distortion should also happen in a long term downtrend. I also noticed that the book mentioned that buying otm calls wasn't as consistently as profitable as selling the otm puts: what could be the reason for that?...is it possible that both the models and the market pricing have built in flaws? BTW, I appreciate constructive criticism - I'm here because most here know much more about options than I do: what concepts am I conflating?
The map is not the territory... Sorry I have not had enough time to post my thoughts..... Derman has a model called localized vol that accounts for skew... Because of the lower nominal amount of options otm it is cheap leverage and represents potiential rarer events in the distro of stock prices... Before 87 people didn't price otm higher.. After the crash prices went up... There is a convexity your paying for that you don't get with itm or ATM.... Meaning a rate of change of a higher order .... Anyone who has sold otm puts on leverage will tell you... The London whale was one.... These aren't my opinions I'm just telling you what's known and I don't think anyone would disagree... Although in my opinion it's better to sell the meat and buy the wings... A naked straddle I'd like better then a naked put...... Either way no strategy is better then the other it all depends on the market and your desired expression on it
There are a couple mistakes. Trending has almost nothing to to do with option prices. As you mentioned put call parity, there is really no practical difference between a put and a call. One can be converted to the other with ease. You are either long or short and above or below the market. As for the options model. Based on its assumptions it prices options correctly. One of the models assumptions is Geometric Brownian Motion. We have seen that over sized moves to the downside are more frequent and extreme than GBM predicts. Ergo those options are under priced by the model.
Trending is a good way to make money off options... Options typically never have long term trends priced in.... Hence the valve of buying leaps...
I'd be interested to know, on average, if most leaps are initiated from a buy or sell order. I never activity traded options going out longer than 6 months.