If US starts offering negative interest rate, is it possible that there is an increase in market volatility without the stock market correcting?
In general can volatility spike without stock market correcting? If so how?
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Sure. Volatility is a measure of price movements in any direction, not necessarily levels. Actual volatility is measured by the magnitude of periodic changes of prices (how big the swings are). Imagine a calm sea where the tide is rising. There are no waves (volatility) but the level (price) is rising smoothly. Now imaging a turbulent sea. There are many crashing waves but the average level is not changing. The market could swing wildly from one day to the next without being in a "correction" state.
Implied volatility (how volatile investors think the market will be) is measured by various option prices (the higher the expected volatility, the higher the prices of options). This too can be high without a market correction, since market expectations could be different than what actually happens.