operational_risk.rmd

---
title: "FRM Operational and Integrated Risk Management"
author: "Alex Dou"
date: "October 13, 2019"
output: html_document
---

## OpRisk Data an Governance

### Event Category
#### Execution, Delivery and Process Management
* High frequency and low loss

#### Clients, products, and business practices
* Low frequency and high loss

#### Business disruption and system failures

#### Exteranl fraud

#### Internal fraud

#### Employment practices and workplace safety

#### Damage to physial assets

## Modelling Approaches

### Basel II Models
* BIA
* SA
* AMA

#### Basic Indicator Approach (BIA)


$$ K_{BIA} = \frac{\sum{GI_i \alpha}}{n}  $$

* GI=annual positive gross income
* n= number of years with positive income
* alpha=0.15


#### Standardized Aproach (SA)

$$ \frac{\sum{GI_{1-8}\beta_{1-8}}}{3}  $$

##### Alternative Standardized Approach

$$ K_{RB} = \beta_{RB} \times  LA_{RB} \times m  $$

* m=0.035

#### Advanced Measurement Approache (AMA)
* 1-year, 99.9% conficence level
* 4 elements: Internal loss data, external loss data, Scenario analysis, business environment internal control factors

##### Loss Distribution Approach(LDA)
* Rely on internal losses
* At least 3 years of loss data
* Prons: Real historical data
* Crons: Maybe to short to capture fat-tail event, data does not reflect the future
* Modeling frequency: **Poisson distrubtion**
* Modeling severity: **Lognormal distribution**
* Combining 2 distrubutions: **Convolution, 99.9% certainty**

### Extrme Value
#### Generalized Extreme-Value Theory (GEV)
* 块最大直方法，消除聚集效应
* 3 Parameters: **xi** tail, **mu**, **sigma** 
* Xi>0, **fat tail**, **Frechet distribution**
* Xi=0, normal tail, Gumbel distribution
* Xi<0, thin tail, Weibull distribtuion

#### Peaks-over-threshold Approach (POT)
* 2 parameters: **xi** tail, **beta** range
* Needs to choose a threshold **u**
* **u** 太低不能体现极值特征；太高则数据太少


### Source of model risks
* Distrubtion of underlying asset is stationary
* Rate of return are normally distributed
* Oversimplified models
* Asuming pefect capital markets
* Liquidity is assumed to be ample
* Misapplied to a situation

## Capital Planning and Framework
### RAROC: Risk-adjusted return on capital
#### Hurdle rate
#### ARAROC

## Liquidity and Leverage
### Repo
### Liquidity Risks
#### Exogenous
##### Constant Spread Approach
##### Exogenous Spread Approach

#### Endogenous
##### Price elasticity
##### Endogenous pricess approach

#### Exogenous and Endogenous

#### Liquidity Discount Approach

#### Liquidity at Risk

#### Sources of liquidity risks