Risk Management and Financial Institution Chapter 18 —— Fundamental Review of the Trading Book

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Risk Management and Financial Institution Chapter 18 —— Fundamental Review of the Trading Book

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• “Fundamental Review of the Trading Book” (FRTB)，针对市场风险资本的计算

• 比之前的方式更加复杂

18.1 基本背景

• FRTB 使用 ES expected shortfall with a 97.5% confidence，测量的标准是出于压力状态下的ES
• 通常情况下，97.5%的ES 与 99% 的VaR基本相等
• 如果损失分布存在厚尾，那么ES 将比VaR大得多
• 巴塞尔I 和 II.5使用的展期更改为了体现流动性
  • market variables change shocks
  • market variables risk factors
  • 展期 liquidity horizons，总共明确的五种，10、20、40、60、120

• 银行被要求使用IMA以及SA方式计算市场风险资本

• FRTB与之前计算方法的区别：

  • 基于trading book
  • IMA方法在银行内可以部分分割，某些部门使用IMA 有些使用SA
  • 目标是防止监管套利
  • FRTB对于trading book and banking book 定义更加明确

18.2 Standardized Approach 标准法

• Under the standardized approach, the capital requirement is the sum of three components:
  • a risk charge calculated using a risk sensitivity approach
    • 七种风险资产种类
    • 每个资产种类需要计算delta 风险，vega风险，曲率风险（curvature）
      • delta risk charge for a risk class is calculated using the risk weights and weighted sensitivity approach
      • 
      • W_i以及ρ由巴塞尔委员会给予，δ，由银行自行给出
      • In practice, the Wi are set equal to multiples of the stressed daily volatility to reflect the liquidity horizon and the confidence level that regulators wish to consider
      • Suppose that the stressed daily volatility of risk factor i is estimated as 2% and that the risk factor has a 20-day liquidity horizon，则risk weight equals to
      • Vega risk 的测算方法和delta 相同
      • 资产与资产之间没有分散化的优势
      • 最终结果是delta risk 7大类 + vega risk 7 大类
  • a default risk charge
  • a residual risk add-on

18.2.1 Term Structures期限结构

• 期限结构的不同顶点是不同的风险因子

• The Basel Committee defines risk weights for each vertex of the term structure and correlations between the vertices of the same term structure

• A simplification is used when correlations between points on different term structures are defined. The correlations between point A on term structure 1 and point B on term structure 2 are assumed to be the same for all A and B

18.2.2 Curvature Risk Charge

• Charge a capital for a bank’s gamma risk exposure
• To evaluate the impact of curvature net of the delta effect, the standardized approach therefore calculates:
  • Wiδi minus the impact of a increase of Wi in the risk factor
  • − Wiδi minus the impact of a decrease in the risk factor of Wi.

• The curvature risk charges for different risk factors are combined to determine a total curvature risk charge

18.2.3 Default Risk Charge

• 交易对手风险spread 更改也被FRTB考虑进去了

• 又被称作为JTD risks，jump to default

• 计算方法：This is calculated by multiplying each exposure by a loss given default (LGD) and a default risk weight

• Both the LGD and the risk weight are specified by the Basel Committee

18.2.4 Residual Risk Add on

• The residual risk add-on considers risks that cannot be handled by the delta/ vega/curvature approach described earlier

• exotic options when they cannot be considered as linear combinations of plain vanilla options

• 计算方式：The add-on is calculated by multiplying the notional amount of the transaction by a risk weight that is specified by the Basel Committee

18.2.5 A simplified Approach

• For smaller banks 简单标准法
• vega and gamma risk do not have to be considered

18.3 Internal Models Approach

• Estimate stressed ES with a 97.5% confidence

• 一般来说ES的计算使用historical simulation approach

• 

• In FRTB, banks are required to consider changes over periods of 10 days that occurred during a stressed period in the past

• 先计算ES1，10-days changes are made to all risk factors

• 以ES1 为参数，计算categories 2 ES2，以此类推，计算ES4，ES5，ES3

• LHj is the liquidity horizon for category j

• 例如：suppose first that all risk factors are in category 1 or 2 so that only ES1 and ES2 are calculated

• 如果有3个资产：

• What we will refer to as the weighted expected shortfall (WES) is a weighted average of (a) the ES for the whole portfolio and (b) the sum of the partial expected shortfalls. Specifically:

• The parameter λ is set by the Basel Committee to be 0.5

• if there are less than 24 observations on a risk factor in a year or more than one month between successive observations, the risk factor is classified as non-modelable
  

• where WESt − 1 is the WES for day t − 1, NMCt − 1 is the capital charge calculated for non-modelable risk factors on day t − 1, WESavg is the average WES for the previous 60 days, and NMCavg is the average capital charge calculated for the non-modelable risk factors over the previous 60 days. The parameter mc is at minimum 1.5

18.3.1 Back - Testing

• FRTB back-tests a bank’s models by asking each trading desk to back-test a VaR measure calculated over a one-day horizon and the most recent 12 months of data. Both 99% and 97.5% confidence levels are to be used.

18.3.2 Profit and Loss Attribution

• 另外一个测试方法：profit and loss attribution
• Two measures must be calculated：

• U denotes the difference between the actual and model profit/loss in a day and V denotes the actual profit/loss in a day

• Regulators expect the first measure to be between –10% and +10% and the second measure to be less than 20%.

18.3.3 Credit Risk

• FRTB定义了两种credit risk：

  • Credit spread risk is the risk that the company’s credit spread will change, causing the mark-to-market value of the instrument to change.
  • Jump-to-default risk is the risk that there will be a default by the company

• 在IMA方法下，信用溢差风险依照其它市场风险因子计算

• jump to default 风险按照banking book 的default风险计算

18.3.4 Securitization 证券化

• CRM rules allow a bank (with regulatory approval) to use its own models in Basel II.5
• under FRTB the standardized approach must be used for securitizations

18.4 Trading book vs Banking Book

• Roughly speaking, the trading book consists of instruments that the bank intends to trade

• The banking book consists of instruments that are expected to be held to maturity

• intended to trade 不足以归类为 trading book

• there are strict rules preventing them from being subsequently moved between the two books