I'd be a bit wary of any data source that had quite as wide a range as that for 2017...
Nothing about European banks has been any kind of "normal" for well over a decade now; but <0.5 and >2, let alone both in quick succession, still represents a "hardcore" variety of financial pornography (such sadly are EU banks). Normally you could blame pretty much anything in this sector on Deutsche Bank (DBK), the financial slo-mo train-wreck that just keeps on giving; but 2017 was actually one of the calm periods here (DBK only down 25% that year).
Basic fundamentals - banks are levered. Call it 100 assets; 90 deposits/debt and 10 equity capital. Net Interest Margins are 1%. In broad strokes, plus or minus loose change. So if 1% of the assets become doubtful (or more doubtful than the usual provisions for expected usual loan losses), the hit from provisioning will be ~100% of profits, or ~10% to book value.
Which is a two-way street. If things don't turn out as bad as feared, writing back provisions can boost EPS and book - without any actual change in the bank's profitability. This is a very normal process, into early cyclical recoveries. I don't recall the exact timings of the last round of NPL write-ups but from memory, the US saw this in 2012-3; and Europe in 2015-6 (obviously delayed post-GFC by the Eurocrisis).
Making the simple point - "book" might be a balance sheet item; but for banks, it's hugely levered to swings in loan deliquency.
But your real problem here isn't the fact that book is thus quite a flexible concept (for banks). It's the valuation swings. Book might wang around; but bank stock prices normally wang around in the same direction for the same reasons that book moves. Earnings collapse -> book declines & stock price down -> much less of a change in PBV ratios (or vice versa). The problem here is the valuation mismatches (more than the volatility of stock prices, earnings or book). Hence the caveat about data quality here. 20% even 50% swings no problem (for EU banks!!!)... but 400% (ie 0.5x to 2.0x) smells a little "off".
See eg the BIS: "The ABCs of Bank PBRs"
This version of this captures some 2017 re-rating (before Italy blew it in 2018!!!)... but nothing like the scale/volatility suggested.
The only theoretical way I could see that kind of thing happening would be quite convoluted, playing to a mismatch of capital raising. Imagine a hypothetical bank with 100 assets and 10 equity. Fair value is 1.0 PBV, unchanged by the capital raising (RoE down = bad, balance sheet stronger = good). Their friendly neighbourhood regulator phones them up and tells them to raise 5 new capital; but their friendly investment bank says they'll only underwrite this issuance, by offering the shares at a 50% discount. So you have a bank worth 10 becoming a bank worth 15; but with double the share-count. The market smells a rat; and knows this is coming, so it values the bank at 7.5 today (half the shares exist today for half ultimate fair value). Against a pre-issuance book of 10, that's a PBV of 0.75. When the shares are issued, you have 15 equity worth 15 equals 1.00 PBV overnight. Et voila, a timing mismatch.
Except I don't recall any such stories in Europe in 2017 ;-( Suspect the data source has a time-series "funny" in it...