mathematical_finance

Financial contagion — the cascading failure of interconnected institutions through bilateral exposures — is the central mechanism behind systemic crises from Lehman Brothers (2008) to Silicon Valley Bank (2023).

Expected Shortfall (ES) replaced Value-at-Risk as the primary risk measure in Basel III's Fundamental Review of the Trading Book, yet its estimation by Monte Carlo simulation converges at rate $O(1/\sqrt{M})$ — requiring $10^6$ paths for three-digit accuracy.