The Swiss franc remained pinned at sky-high levels Monday, hovering around one-to-one against the euro after last week's shock decision by the Swiss National Bank to allow its currency to climb.

"Around parity the Swiss franc appears more overvalued versus the euro than at any other time in the last 30 years, and the strength of the Swiss franc is likely to put significant strain on the Swiss economy," said Beat Siegenthaler, a currency strategist at UBS, adding that he nonetheless assumes that the exchange rate will "fluctuate around parity for the coming months."

Swiss stocks regained some stability Monday, with the main Swiss SMI up 1.8%. Stocks took a beating on the announcement last week, as investors feared that foreign buyers would shun expensive exports.

Having last week been among the biggest losers, shares in Swiss banks Julius Baer Gruppe AG and UBS Group AG were among the biggest gainers on the pan-European all-sector index, as were shares in Zurich Insurance Group AG, Swiss Re AG, Nestlé SA and Novartis AG.

Head of the Swiss finance department Eveline Widmer-Schlumpf told local press over the weekend that the country "can cope" with the decision by the SNB to let the euro fall below its previous limit of CHF1.20 against the franc.

Elsewhere Monday, expectations that the European Central Bank later this week will announce plans to aggressively ramp up its asset purchase program continued to shape markets.

Barclays economists wrote that expectations of the ECB embarking on sovereign quantitative easing were now so high that "without decisive actions, the ECB risks failing on its mandate to deliver on the inflation target and financial stability."

"Deflation and market stress, in turn, would deteriorate fiscal dynamics in the euro area and possibly precipitate default or breakup scenarios," they added.

Yields on sovereign bonds issued by countries including Italy, Spain and Portugal slumped to new all-time lows. The euro hovered around $1.1570, taking its losses against the dollar so far in 2015 to almost 4.5%.

"Given what we know about the impact of QE programs on currencies it seems reasonable to suppose that the start of this week will see the euro come under significant pressure against a wide range of currencies, " said Simon Derrick, chief market strategist at BNY Mellon.

The Stoxx Europe 600 and London's FTSE 100 were broadly steady on the day while Germany's DAX added 0.3% and France's CAC declined 0.2%.

Brent crude slumped 1.5% to around $49.45 a barrel while gold edged 0.2% lower to $1,1275 a troy ounce.

Write to Josie Cox at josie.cox@wsj.com

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