Operational Risk - LDA

LDA (Loss Distribution Approach)

總論：

• Basel II Accord 允許數種方法來量話 operational risk，LDA 為其中之一。
• LDA  亦可用於計算 economic capital needed for unexpected operational risk losses.

步驟：

1. Organize and group loss data into a business line/event type matrix.
   
   (Loss data is "backward-looking")
   
   
   
2. Assign every data point in the matrix an equal weight with exceptions.
3. Modeling operational risk loss distirbution in each cell, including
1. frequency
2. severity.
4. Determine operational risk capital requirement for each business line.

優點：

•  Loss estimates 考慮機構特性
• 依據數學及統計原則
• 可與其他 capital charge 合併
• 反映 loss estimate 可隨時間改變

缺點：

• 需要大量的資料，但通常有困難
• 是根據過去經驗
• 只有 direct losses 被列入考量
• 缺乏 robust operational risk sensitivity measure

資料採用原則：

• 所有相關資料都要採用
• 只反映 inflation
• 使用 gross losses
• 要 mapped to 目前的組織架構
• 外幣損失金融換成本幣
• 減少 double counting 的可能性

資料加權原則 :

• 一般是每個資料都等權值，但有三例外
• Split losses
• Old losses (會分配較低的權重)
• External data and scenarios

Frequency distribution :

• 通常用
• Poisson distribution
• Negative binomial distribution
• Binomial distribution
• Calibration 用 time serires of internal frequency data

Severity distribution :

• 問題 : 近期的 internal data 資料不足以用來 calibrating tails of severity distributions

Dependencies in LDA models :

• Within-cell dependencies (frequency 和 severity 通常是獨立的)
• Occurence of loss events
• Frequency distribution and severity distribution
• Severity samples in a cell
• Between-cell dependencies
• frequency distribution between cells (通常是 dependent)
• severity distribution between cells

Economic capital :

• 目的：吸收 unexpected losses with a high degree certainty
• degree of certainty : depends on credit rating
• economic capital = (operational value at risk) - (expected loss) = unexpected loss

Validation :

• Review 的項目含
• data inputs
• model methodology: (assumed frequencies, severities, dependence structure)
• model outputs
• Sensitivity analysis
• 對 frequency insensitive
• 對 severity distribution 比較重要
• Stress testing