LONDON—The Russian rouble tumbled to a record low and European currencies including the euro bore the brunt of selling on Thursday after Russia launched an invasion of Ukraine, sparking dramatic moves across foreign exchange markets. Investors dashed for safe-haven currencies including the dollar, which jumped 0.9 percent, as well as the Swiss franc and Japanese yen. Aside from the rouble, it was the currencies of European countries such as the Swedish crown, Hungarian forint, and Polish zloty that were hammered the most—all losing more than 1 percent as traders braced for the fallout from a war in Europe’s east and more Western sanctions on Russian assets. Volatility across FX markets soared, with one commonly followed measure hitting its highest since December 2020. MUFG analyst Lee Hardman said risk-off sentiment would “dominate in the near-term favoring further U.S. dollar, yen and Swiss franc strength. “In contrast, risks remain heavily tilted to …