I'm trying to understand option pricing better.
Let's say security ABC is \$40, and a 38 PUT option with 40% implied volatility (and 90 days till expiration) is priced at X. If security ABC then drops to \$30, should the price of a $28 PUT option with 40% implied volatility (and 90 days till expiration), now have a price of:
30 ----- * price of $38 PUT? 40
Similarly, do stocks at around \$100 / share, have options whose time value is twice as much as a stock trading at \$50 a share, everything else (e.g. volatility) being equal?
P.S. Another similar area of this question is selling covered calls. For the static return, one of course divides the sale price of the option against the cost of the underlying security, and one is often seeking to maximize that return. So, I guess one could say/ask, will a stock trading at \$40 a share, generate the same return ratio as a stock trading at \$30 a share, if those options have the same implied volatility?