typora-copy-images-to: Risk Management and Financial Institution
文章目录
- Risk Management and Financial Institution Chapter 18 —— Fundamental Review of the Trading Book
- 18.1 基本背景
- 18.2 Standardized Approach 标准法
- 18.2.1 Term Structures期限结构
- 18.2.2 Curvature Risk Charge
- 18.2.3 Default Risk Charge
- 18.2.4 Residual Risk Add on
- 18.2.5 A simplified Approach
- 18.3 Internal Models Approach
- 18.3.1 Back - Testing
- 18.3.2 Profit and Loss Attribution
- 18.3.3 Credit Risk
- 18.3.4 Securitization 证券化
- 18.4 Trading book vs Banking Book
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
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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
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银行被要求使用IMA以及SA方式计算市场风险资本
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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
- Wi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
- a risk charge calculated using a risk sensitivity approach
18.2.1 Term Structures期限结构
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期限结构的不同顶点是不同的风险因子
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The Basel Committee defines risk weights for each vertex of the term structure and correlations between the vertices of the same term structure
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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
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交易对手风险spread 更改也被FRTB考虑进去了
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又被称作为JTD risks,jump to default
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计算方法:This is calculated by multiplying each exposure by a loss given default (LGD) and a default risk weight
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Both the LGD and the risk weight are specified by the Basel Committee
18.2.4 Residual Risk Add on
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The residual risk add-on considers risks that cannot be handled by the delta/ vega/curvature approach described earlier
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exotic options when they cannot be considered as linear combinations of plain vanilla options
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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
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Estimate stressed ES with a 97.5% confidence
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一般来说ES的计算使用historical simulation approach
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In FRTB, banks are required to consider changes over periods of 10 days that occurred during a stressed period in the past
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先计算ES1,10-days changes are made to all risk factors
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以ES1 为参数,计算categories 2 ES2,以此类推,计算ES4,ES5,ES3
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LHj is the liquidity horizon for category j
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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:
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The parameter λ is set by the Basel Committee to be 0.5
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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
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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:
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U denotes the difference between the actual and model profit/loss in a day and V denotes the actual profit/loss in a day
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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
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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
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在IMA方法下,信用溢差风险依照其它市场风险因子计算
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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
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Roughly speaking, the trading book consists of instruments that the bank intends to trade
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The banking book consists of instruments that are expected to be held to maturity
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intended to trade 不足以归类为 trading book
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there are strict rules preventing them from being subsequently moved between the two books