We present a multiscale stochastic analysis of foreign exchange rates using the H-theory formalism, which provides a hierarchical intermittency model for the information cascade in the currency market. We examine the distributions of returns and volatilities for the three most traded currency pairs: euro-U.S. dollar, U.S. dollar-Japanese yen, and British pound-U.S. dollar. We find that these markets have a hierarchy of timescales, with larger markets exhibiting more hierarchy levels. We provide a theoretical framework for understanding why the number of levels in the information cascade increases with market size, in analogy with similar behavior for the energy cascade in turbulence as a function of Reynolds number. We briefly argue that using turbulence-like models for financial markets can also provide valuable insights for developing efficient algorithmic trading strategies.