And holding a naked put seems logical and natural.
2. Can IV be really considered as a Standard Deviation for a stock price? Same reasons to ask – why would a stock probability to be at a certain price range shrink just because the market moved higher? Why would it widen in case of a fall?
1.You are correct. A rising stock price usually means that IV is falling. Thus, any gains resulting from positive delta are diminished by losses from declining vega. Most novice call buyers miss that point.
You believe that it feels 'natural' to be short the put option and collect time decay. I also prefer to be short options (as a spread, never a naked option) because of time decay. However, I don't see anything 'natural' about being exposed to huge losses by selling naked options. There is nothing natural about that. [In further correspondence, you admit to having a big appetite for risk – and under those circumstances, selling options would feel natural]. Hedging that risk feels more natural to me – and that means we can each participate in the options world, trading in a way that feels comfortable.
However, the majority of individual investors – especially rookies – find that owning long calls feels natural: Limited losses and large gains are possible. That combination appeals to those who don't understand how difficult it is to make money consistently when buying options. The chances of winning are not good when the stock must not only move your way, but must do so quickly.
More experienced traders believe it makes sense to sell option premium, rather than own it. Please understand: that is not a blanket statement. There are many good reasons (hedging risk is primary) for owning options, but in my opinion, speculating on market direction is not one of them.
The problem with holding a naked (short) put option is that profit potential is limited and potential losses can be very large. In addition, when the stock falls and you are losing money because of delta – IV is increasing and the negative vega is going to increase those losses. Although positive theta helps reduce losses – the effects of theta are often less than those from vega and delta.
Even though long calls and short puts are both bullish plays, they really serve different purposes. Traders who want to own calls are playing for a significant move higher, while put sellers can be happy if the stock doesn't fall. Put sellers have a much greater chance to earn a profit, but that profit is limited. Selling puts is not for the trader who is looking for a big move or who wants to own insurance that protects a portfolio.
2. Standard deviation is a number calculated from data – and one of the pieces of data required is an estimate of the future volatility of the stock.
Yes, it appears that a rising market results in a smaller value for the standard deviation move, but in reality, SD decreases because the marketplace (and that is the summary of the opinions of all participants – the people who determine option prices) estimates (as determined by the prices and IV of options) that future volatility will be less than it is now. You are not forced to accept that. You may use any volatility number that suits to calculate a standard deviation move.
If you argue that it doesn't make sense for a mathematical calculation to depend on human emotions and decisions, I cannot disagree. However, to calculate a standard deviation, it just makes sense to use the best available estimate for future volatility. Most traders accept current IV as that 'best' estimate. That does not make it the best, it's just a consensus opinion.
If you prefer to use your own estimate to calculate a one standard deviation move, you can do that – as long as you have some reason to believe that your estimate is reasonable.