Stocks in Japan fell 2.0% Friday morning after a volatile session overseas and concerns about an oil glut still weighing on the market.

Tokyo's Nikkei Stock Average was down 2%, leading the region mostly lower, even as the Japanese yen weakened. Stocks were falling after swings in the U.S. market, where investors were rattled overnight after Switzerland's central bank scrapped its policy of capping the Swiss franc at 1.20 to the euro.

"The unfavorable currency and crude price effects on the market are naturally causing capital flight from Japanese risk assets and toward bonds," said Norihiro Fujito, senior investment strategist at Mitsubishi UFJ Morgan Stanley Securities.

The U.S. dollar strengthened, trading at Yen116.35, from Yen116.21 late Thursday in Asia, while the euro was at Yen135.28, from Yen134.97 yesterday.

Elsewhere, Hong Kong was off 0.6% and Australia lost 0.5%.

In New Zealand, currency trading house Global Brokers NZ Ltd. said it would close its doors, a casualty of the unexpected decision by the Swiss National Bank to cease capping its currency. The majority of the company's clients in Swiss franc positions were on the losing side and sustained losses far greater than their account equity, the statement said.

The region's weakness also came after oil prices erased gains from Wednesday's rally. Light, sweet crude for February delivery, the U.S. benchmark, settled down $2.23, or 4.6%, at $46.25 a barrel on the New York Mercantile Exchange, continuing to fall in Asia.

Bradford Frischkorn contributed to this article.

Write to Chao Deng at Chao.Deng@wsj.com

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