Calibrating volatility function bounds for an uncertain volatility model

ABSTRACT It is widely acknowledged that the Black-Scholes constant volatility model is inadequate in modeling the underlying asset price, as evidenced by the observed volatility smile. Based on the relative-entropy minimization method in Avellaneda et al (1997), we propose a method to calibrate, from market bids and asks, a pair of volatility functions for an uncertain volatility model. The mid-prices are used to ensure separation of the lower and upper volatility functions. We show that the calibrated uncertain volatility model produces more realistic bid and ask prices, when compared with prices obtained from an uncertain volatility model with constant volatility bounds set to extreme market implied volatilities.