Publication: The relationship between the volatility of returns and the number of jumps in financial markets
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2009-12
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Abstract
The contribution of this paper is two-fold. First we show how to estimate the volatility of high
frequency log-returns where the estimates are not a affected by microstructure noise and the
presence of Lévy-type jumps in prices. The second contribution focuses on the relationship
between the number of jumps and the volatility of log-returns of the SPY, which is the fund that
tracks the S&P 500. We employ SPY high frequency data (minute-by-minute) to obtain estimates
of the volatility of the SPY log-returns to show that: (i) The number of jumps in the SPY is an
important variable in explaining the daily volatility of the SPY log-returns; (ii) The number of
jumps in the SPY prices has more explanatory power with respect to daily volatility than other
variables based on: volume, number of trades, open and close, and other jump activity measures
based on Bipower Variation; (iii) The number of jumps in the SPY prices has a similar
explanatory power to that of the VIX, and slightly less explanatory power than measures based on
high and low prices, when it comes to explaining volatility; (iv) Forecasts of the average number
of jumps are important variables when producing monthly volatility forecasts and, furthermore,
they contain information that is not impounded in the VIX.
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Volatility forecasts, High-frequency data, Implied volatility, VIX, Jumps, Microstructure noise