Suhas Nayak (Stanford University)

Abstract: We study the calibration of volatility surfaces in a stochastic volatility environment. Starting with a stochastic volatility model for asset prices, we cast the volatility estimation problem as a variational one and we derive an HJB equation for the volatility surface. We incorporate uncertainty in market prices and we study the asymptotics of the resulting HJB equation in the fast mean-reversion regime. We present numerical solutions from our estimation scheme and find certain parameters of the volatility surface to be both stable in time and stable with respect to our iteration procedure.