Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives Jean-Pierre Fouque 1 George Papanicolaou 2 Ronnie Sircar 3 Knut Sølna 4 February 3, 2011 1 Department of Statistics & Applied Probability, University of California, Santa Barbara, CA 93106-3110, fouque@pstat.ucsb.edu. Work supported by NSF grants DMS-0806461, DMS-0455982 and DMS-0071744. 2 Department of Mathematics, Stanford University, Stanford CA 94305, papanico@math.stanford.edu. 3 Department of Operations Research & Financial Engineering, Princeton University, Sherrerd Hall, Princeton, NJ 08544, sircar@princeton.edu. Work supported by NSF grants DMS-0807440, DMS-0739195, DMS-0456195 and DMS-0306357. 4 Department of Mathematics, University of California, Irvine, CA 92697, ksolna@math.uci.edu.