Volkov took part in the European Cup from March 2004 and achieved the first podium in January 2005. At the Junior World Championships in 2006 he was fifth. In March 2008 he won his first European Cup. He made his debut in the Freestyle World Cup on December 11, 2009 in Suomu, Finland, where he was 21st in the Moguls competition. In December 2010 he made it into the top ten for the first time, but top positions were rare for the time being. On January 14, 2012 he stood Mont Gabriel for the first time on the podium of a World Cup competition, as third in the dual moguls discipline. In Deer Valley he won his first World Cup on February 4, 2012.