In risk management, estimating Expected Shortfall (ES), though important and indispensable, is difficult when a sample size is small. This paper makes efforts to create a recipe for such challenge. A tail-based normal approximation with explicit formulas is derived by matching a specific...

Monte Carlo methods are widely-used simulation tools for market practitioners from trading to risk management. When pricing complex instruments, like mortgage-backed securities (MBS), strong path-dependency and high dimensionality make the Monte Carlo method the most suitable, if not the only,...