Comment on "Are nancial crashes predictable?"

as a predict ive tool for the detect ion of periods of large declines in the nancial markets as rst suggested in [2]. The crit icism was based on a rather primit ive \ eye−balling analysis" lacking the consistent methodology used in the ident i cat ion of more than twenty crashes on the US, Ho ng−Kong and FX markets alone which all were preceded by a market bubble parameterised by eq. (1) [3]. Speci cally, a well−de ned opt imisat ion algorithm was used t t ing eq. (1) as well as spect ral analysis and analy sis of synthet ic data [3]. They furthermore wrote \ We want to publicly disclose here the fact that on the basis of a log−periodic analysis, a crash on the J GB market for the end of May 1995 was predicted. On this basis, one of us (J PA) bought for $1:000:000 of put opt ions ... The crash did not occur and only a delicate t rading back allowed to avoid losses". This represents a severely distorted picture of a scient i c experiment . First , the ana lysis (performed by the author and Didier Sornet te) and experiment was not done in May 1995, but in J uly 1995. In g. 1 we see eq. (1) t ted t o the J apanese bond price in the correct t ime period of the experiment . Note that the values obtained for the parameters ! and (see capt ion) are on the border of what has since been ident i ed prior to over twenty crashes on the US, Hong−Kong and FX markets alone [3]. The result that was borne out of the analysis of J uly 1995 was that J GB might crash around tc 1995:63 19 Aug. 1995. In g. 1, we see that the market peaked on Wednesd ay 16 Aug. 1995 at a price 3:96 only to decline over 35 t rading days later to a price of 3:36 on 4 Oct . 1995, i.e., a total decline of 15:2%. Admit tedly, this does not t the convent ional picture of a m arket crash, as it is too slow in its unfolding. However, considering the lesser volat ility generally seen in the bond markets, this is not very surprising. In [4] it has been shown that a st retched exponent ial f (x) = a exp ( bxz) (2)