We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum–stability assumption or the max–stability assumption,...

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model...