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Quantitative Risk Management / Operational Risk and Insurance Analytics

Overview

Market risk and credit risk have well-developed data infrastructures: daily P&L streams for market risk, credit ratings and CDS spreads for credit risk. Operational risk — losses from failed processes, fraud, IT failures, legal settlements, and external events — has neither. A bank that experienced a rogue trading loss last Tuesday has one data point; and it can pool data from industry consortia (ORX, Federal Reserve Bank of Boston), but even these are sparse in the tail. Yet regulators demand a 99.9% VaR for operational risk — the same confidence level as the Basel IRB formula for credit.
This scarcity is the defining challenge of operational risk modelling. The actuarial tools from non-life insurance, developed over a century of modelling rare catastrophic losses (floods, earthquakes, third-party liability), are the natural methodological toolkit. The loss distribution approach (LDA) — estimating frequency and severity distributions separately, then computing the aggregate loss distribution — is the standard in both insurance and operational risk.
The main technical question: given NN losses of random sizes X1,X2,…X_1, X_2, \ldots, what is the distribution of the total loss SN=∑k=1NXkS_N = \sum_{k=1}^N X_k? This is the compound distribution problem, solved analytically only in special cases, but tractable by recursion (Panjer), moment approximation (normal, translated-gamma), and Monte Carlo with EVT tail fitting.

By the end of this topic you should be able to:

  • define operational risk according to Basel II and identify the seven event types and eight business lines;
  • explain the basic indicator (BI) and standardized approaches and write their capital formulas;
  • describe the loss distribution approach (LDA) under the Advanced Measurement Approach (AMA);
  • state the three empirical stylized facts about operational loss data: heavy tails, random timing, non-stationary frequency;
  • define a compound distribution SNS_N and compute its mean and variance (Proposition 13.8);
  • state the Panjer recursion condition and apply it for N∼Poi(λ)N \sim \text{Poi}(\lambda);
  • explain why a normal approximation fails for heavy-tailed operational losses and describe the GPD alternative;
  • define Poisson mixture models, show that a Poisson-gamma mixture is a negative binomial, and interpret the gamma-distributed rate parameter.

In this lesson

  1. Contents
  2. The big picture

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