We perform wavelet decomposition of high frequency financial time series into high and low-energy spectral sectors . Taking the FTSE100 index as a case study, and working with the Haar basis, it turns out , very unsuspectedly, that the high-energy component and a fraction of the low-energy contribution, defined by most (\simeq 98 \%) of the wavelet coefficients , can be neglected for the purpose of option premium evaluation with expiration times in the range of a few days to one month. The relevant low-energy component, which has attenuated volatility (reduction by a factor \simeq 1/10), is (i) normally distributed, (ii) long-range correlated for intraday prices and volatility, and (iii) time-reversal asymmetric. Our results indicate that the usual non-gaussian profiles of log-return distributions contain much more information than needed for option pricing, which is essentially dependent on hidden self-correlation properties of the underlying asset fluctuations .
We perform wavelet decomposition of high frequency financial time series into large and small time scale components . Taking the FTSE100 index as a case study, and working with the Haar basis, it turns out that the small scale component defined by most (\simeq 99.6 \%) of the wavelet coefficients can be neglected for the purpose of option premium evaluation . The relevance of the hugely compressed information provided by low-pass wavelet-filtering is related to the fact that the non-gaussian statistical structure of the original financial time series is essentially preserved for expiration times which are larger than just one trading day .
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high and low-energy spectral sectors
large and small time scale components
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, very unsuspectedly, that the high-energy component and a fraction of the low-energy contribution, defined
that the small scale component defined
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98
99.6
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,
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with expiration times in the range of a few days to one month. The relevant low-energy component, which has attenuated volatility (reduction by a factor \simeq 1/10), is (i) normally distributed, (ii) long-range correlated for intraday prices and volatility, and (iii) time-reversal asymmetric. Our results indicate that the usual
. The relevance of the hugely compressed information provided by low-pass wavelet-filtering is related to the fact that the
R
profiles of log-return distributions contain much more information than needed for option pricing, which is essentially dependent on hidden self-correlation properties of the underlying asset fluctuations
statistical structure of the original financial time series is essentially preserved for expiration times which are larger than just one trading day