<<As the market, or a stock, goes down, generally speaking the option premium goes up as a percentage of the strike price to the stock price.>>
Yes, option decay with time or with decline in stock price is not linear. A good thing if you are selling calls and generally bad if you are a buyer. We are describing delta, the rate of change in the option for a given change in the stock, which is always less than one. Why is that a disadvantage? And could it be any other way? Short calls are acknowledged to be a less than a perfect hedge against a declining long stock position. If someone wants a hedge with a delta of 1.0, short the stock.
<<An example is that the VIX almost always increases as the market declines.>>
Yes, but the VIX is a ratio, not a vector. And a graph of VIX is not just the inverse of the market. If it was it would have no predictive value. Maybe it doesn't anyway, we just like to think so.(g)
Compare VIX:
stockcharts.com[w,a]dallyymy[d19970101,20010831][p][vc60]
with NASDAQ
stockcharts.com[w,a]dallyymy[d19970101,20010831][p][vc60]
VIX can be high for any value of the market.
Approx. Approx.
VIX peaks NASDAQ
end of Oct '97 1525
early Jan '98 1500
Sept 1 '98 1500 (VIX at highest peak in 4 years)
early Oct '98 1450
early March '00 3800
Oct '00 3100
end of Dec '00 2275
end of March '01 1600
VIX = or > 35 at all those times.
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