Asaf received his master's degree in piano performance from The Juilliard School in New York, and his bachelor's degree from the Mannes School of Music, New York. His teachers include Jerome Lowenthal, Jerome Rose, Sara Davis Buechner, and Lucille Straub. He began playing the piano at age four, and at ten, he started composing. At age 11, he had the honor of playing a commissioned work written by Richard Felciano for the Music Teachers Association of California (MTAC) at the state convention in Los Angeles. Asaf was the first prize winner in the Piano Performance category of the Orange County Musicians' Association. He has taken first place awards in the Glendale McGaughey Competition, the California Association of Professional Music Teachers Bartok Festival, the Southern California Junior Bach Festival, the West Los Angeles Branch Scholarship Competition, and in the Southwestern Youth Music Festival at California State University, Dominguez Hills, Young Pianist Category.

Asaf was a semifinalist of the 1997 Naumburg International Piano Competition and a prizewinner of the International Keyboard Institute and Festival Dorothy MacKenzie Artist Recognition Scholarship Awards in 1999 and 2000 held in New York City. He performed at the Tilles Center on Long Island, NY with the Gemini Youth Symphony Orchestra under the baton of Kimbo Ishii-Eto in March 1999. In 2002, Asaf performed twice at Alice Tully Hall, Lincoln Center, New York.

Asaf performed his New York recital debut at Weill Recital Hall, Carnegie Hall, New York on April 25, 2004. He also performed the complete Schumann piano sonatas as well as the Schubert posthumous sonatas at Steinway Hall, New York in the 2004-2005 season.