Please help me understand this. Theoretically, VIX is supposed to reflect high volatility in both directions. But it seems that VIX only goes up mostly when there is fear of market drops, not when there is anticipation of large market rises. What gives? Thanks.
Ya gotcha theory, and then, ya gotcha fact. Congratulations on having noticed they're not the same. In fact, whenever the market goes up, the VIX drops. When the market goes down, the VIX goes up. You can look at a one-minute chart, a daily chart, a weekly chart or a monthly chart and you will find that the negative correlation is almost perfect. Below is an example of a one-minute chart comparing the S&P 500 and the VIX. Why is that? Because the VIX really charts complacency (low VIX) vs nervousness (higher VIX), not volatility. Puts, after all, are essentially insurance policies against a crash, so the VIX represents the price of crash insurance. Every time the market ticks down, nervousness goes up a little, and so does the VIX. Every time the market ticks up, nervousness goes down a little, and so does the VIX. Why do I only mention puts and not calls? Because the stock market is different from other markets in that the vast majority of participants are long. The overall need for downside insurance is far greater than the need for upside insurance. In commodities (crude for example), the market is two-sided - you have your shorts (consumers) and your longs (producers), so the need to hedge against crude going up is overall about equal to the need to hedge against crude going down. Not so in stocks, where the overall concern about the market going down is far greater than the concern by those who would be hurt by the market going up.
Too much call buying drives up both calls and puts IV. Same for puts. There can't be different IV for calls and puts because it would be removed by a simple, risk-free conversion arbitrage. High IV and thus high VIX only means option buyers are paying more and nothing else. If this high IV can actually predict sudden movements is a debatable topic.
When I wrote "puts" in my previous post, I meant "out-of-the-money puts." By "calls" I meant "out of the money calls." As you say, puts and calls at the same strike trade at the same IV.
Most of the daily movement in VIX is movement of spot across strikes and only a small fraction is actual change in vols (reset of implied higher or lower). You can easily prove it to you yourself by looking at changes in fixed strike volatility (e.g. look at IV for Dec 1225 strike) vs changes in VIX. For more insight into this, go and look at how VIX is calculated and how it reflects different implied vol of various strikes. A super-simple calc of what "skew-adjusted" VIX would be is VIX - (SPX(current) / SPX(ref) - 1) * Skew10% * 100
How then would you explain the almost-perfect negative correlation between SPX and VIX, as charted on the previous page?
Dude, did you actually read what I wrote? Most of the "correlation" you are seeing is due to VIX being calculated off different ATM strike. Go make an index that is skew adjusted and you will see that for yourself. Or look at implied volatility at a single strike and see that it's far less volatile then VIX itself. VIX is a calculated index where you take quadratic-weighted options across all strikes starting from ATM. Each options contribution to the vix price is equal to PriceOfOption * 2/TimeToExpiry * StrikeStep / Strike^2. Now, there is an inherent fixed strike negative skew in the market, lower strikes have higher implied volatility. The calculation of VIX blends these implieds in such way that as S&P moves, you will see more contribution of options at higher strikes when S&P moves up (lowering the VIX number) and options at lower strikes when S&P moves down (increasing VIX number). Does that make sense?