Before revision:  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.
After revision:  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 99.6 \%) 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.