Volkov took part in the European Cup from February 2003 and achieved the first podium in November of the same year. He made his debut in the Freestyle World Cup on December 19, 2003 in Madonna di Campiglio , where he was 57th in the Mughal competition. He won his first World Cup points on December 16, 2004 with 14th place in Tignes . At the Junior World Championship in 2006 he won the gold medal in both the Moguls and Dual Moguls competitions, and in January 2006 he made it into the top ten for the first time in the World Cup.
In the winter of 2006/07 Volkov won the European Cup twice. A fourth place on March 1, 2008 in Mariánské Lázně remained his best World Cup result for almost years. In 2010 he took part in the Winter Olympics. He had to take a break for almost the entire 2010/11 season due to an injury. After a somewhat subdued start to the season, he achieved the first World Cup podium finish on February 4, 2012 with third place in the Dual Moguls competition in Deer Valley .