Combinatorial implications of nonlinear uncertain volatility models: the case of barrier options

Abstract

Extensions to the Black-Scholes model have been suggested recently that permit one to calculate worst-case prices for a portfolio of vanilla options or for exotic options when no a priori distribution for the forward volatility is known. The Uncertain Volatility Model (UVM) by Avellaneda and Parás finds a one-sided worstcase volatility scenario for the buy resp. sell side within a specified volatility range. A key feature of this approach is the possibility of hedging with options:...