FRM II 全科目思维导图
2022-06-07 13:47:38 6 举报AI智能生成
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95% VAR is the (n*5%+1)th\u2029 highest observation.
Basic HS
定义：expected value of the loss when it exceeds VAR
A subadditive risk\u2029measure.
has only one correct answer
not ambiguous.
Expected Shortfall (Conditional VAR)
will often be more accurate than a 'raw' sample
estimate
Bootstrap Historical Simulation
Historical Simulation Approach
hybrid of EWMA & HS
Reduce distortions caused by events that are unlikely to\u2029 recur; helps to reduce ghost effects.
Gives us the option of letting our sample size grow over\u2029time.
Advantages
Age-weighted Historic Simulation
定义式
• Directly accounts for volatility changes
• Allows us to incorporate GARCH forecasts
• Can obtain VAR or ES estimates that can exceed maximum loss in actual datasets
• Empirical evidence to support superiority of estimates
Volatility-weighted Historical Simulation
Takes account of correlations as well as volatilities
More complex than volatility-weighted historical simulation but with the same principle.
特点
Correlation-weighted Historical Simulation
combine benefits of historical
simulation with power/flexibility of conditional volatility models (GARCH).
Semi-parametric bootstrap
Bootstrapping
Get VAR and ES estimates that exceed the maximum historical loss in data set.
Sensitive to changes of market conditions.
特点和优势
Filtered historical simulation
Weighted Historic Simulation Approaches
•Quiet period VAR (or ES) estimates will be low
•Difficult for in-sample shifts or regime changes
•Dominated by extreme losses unlikely to occur
•Most are subject to ghost effect (shadow effect)
•Plausible events that might occur but did not
•Constrained by largest loss in historical dataset
Disadvantages
Advantages And Disadvantages
Non-parametric Methods
VAR for returns that follows a normal distribution.
计算式
Normal VAR
VAR for asset prices follow a lognormal distribution.
Log Normal VAR
Parametric Estimation Approaches
More general than VAR or ES
If a portfolio has systematically lower values than another it must have greater risk. Standard deviation violates the monotonicity condition.
单调性
平移不变性
Increasing the size of a portfolio by a factor b should scale its risk measure by the same factor b. This property applies to the standard deviation.
同质性
The risk of a portfolio is less than the sum of separate risks. Merging portfolios not increase risk.
次可加性
特征
Estimated as a weighted average of the
quantiles (i.e.z the VaRs). The particulars of the weighting function are not important
Spectral measures
ES
Replace the equal weights in the with a more complicated weighting function.
More general Coherent Risk Measure
The presence of heavy tails might make ES estimators less accurate than VAR estimators.
L-estimator
Bootstrap
估计方法
Standard Errors Of Coherent Risk Measures
Method Of Estimating Coherent Risk
Coherent Risk Measures
QQ图
记忆：正S形是瘦尾
Quantile-Quantile Plots
参数
示意图
Block Maxima. Classical
Generalized Extreme Value Distribution (Block Maxima Method)
Generalized Pareto Distribution (Peaks over Threshold）
Models the tails of multivariate distributions
USE Copulas
Key issue is the (tail) dependence structure of the extreme events
It is important if extreme events are not independent
Multivariate EVT
三种主要理论
（1）Have the same goal
（2）Built on the same general principles
（3）They even share the same shape parameter: £ (Shape/Tail)
相同点
（1）GEV involves an additional parameter：location
（2）GEV can involve some loss of useful data as some blocks might have more than one extreme
POT better
POT requires to choosing the threshold
GEV better
优缺点
Extreme Value
Other Issues
Parametric And Non-parametric Methods Of Estimation
Compare the estimated loss from the calculated VAR with the actual losses realized at the end of the specified time horizon.
定义
Canot tell us with 100 % confidence whether our model is good or bad
Contamination（污染，混合） minimized in short horizons
Risk manager should track both the actual portfolio return and the hypothetical return
Sometimes a cleaned-return approximation is used: actual return minus fees/commissions/net income
怎么解决
VAR assumes a static portfolio（静态组合）
Backtesting的困难
ignores time variation，reflects the \"independence\" assumption
X：the proportion of times VAR is exceeded in a given sample.
f(x)
实例
流程
直接分布法
假设检验法
方法
Unconditional Coverage Model
considering whether exceptions come in clusters
H0: accurate model
统计量
Conditional Coverage Model
分类
10-days 99% VAR over 250 observations
标准区间
The penalty should apply
Basic integrity of the madel（模型基本面错误）
Model accuracy could be improved（模型精确度不足）
The penalty should be considered
Intraday（日内交易导致头寸变化）
Markets were particularly volatile or correlations changed
Bad luck
处理方法
The Basel Rules For Backtesting
Backtesting VAR
风险可归因：Positions can be simplified to smaller number of positions on set of primitive (elementary) risk factors
产品特征时变：Only solution when instrument characteristics change over time.
数据短缺：Sometimes only solution to data (shortage) problem
为什么要VAR Mapping
bond risk is associated with the maturity of the principal payment only
Principal mapping
the risk is associated with that of a zero-coupon bond withmaturity equal to the bond duration
Duration mapping
the risk of fixed-income instruments is decomposed into the risk of each of the bond cash flows
Cashflow mapping
Approaches to mapping（选哪个期限的y的问题）
公式
推导
Bond
Option
Delta-normal method
Delta-Gamma method
计算
选期限-定y的VAR-用公式计算资产的VAR
综合应用
过程
Stress Test
Relative VAR
VAR Mapping
Wrong-way risk: adverse correlation between a bond issuer and the bond insurer
Sovereign debt and currency value
Geopolitical tensions
Correlated markets and economies
nonfinancial variables
影响p因素
只有这个是ρ越小越好
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Multi-Asset Options
Protects an investor against currency risk
作用
举例：中国投资一家美国的进出口公司
原理
How deep in the money ( S和K的关系 )
Exchange rate
判断Option价值的两个要素
Quanto option
Fixed correlation <---> Realized/stochastic correlation
计算Realized/stochastic correlation
子主题
效果
Corelation Swap
直接对冲ρ
原因：波动率和ρ存在正相关关系
Buy Call On Index and Sell Call On Individual
-pay fixed in a variance swap on an index and-to receive fixed in variance swaps on individual components of the index.
Variance Swap
间接对冲sigma（波动率）
Hedge
解决方法
Equity Correlation
均值回归和趋势
一些结论
线性状况下
simplify statistical problems 简化统计过程
multiple univariate distributions —> single multivariate distribution
n-dimensional function \ightarrow unit-dimensional one
目的
推导过程
正态分布（高斯Copulas）
非正态分布（Mapping分布的思想）
计算方法（了解）
Copulas Function
非线性状况下
Correlation Risk Modeling and Management
取决于portfolio liquidity and purpose for risk measurement
accuracy of simple VAR measures diminish as time horizon lengthens
Time Horizon
less effective over longer time horizons
conditional backtests improve power of backtests
transaction costs ---> \"liquidity-adjusted VAR\" approach
Exogenous liquidity
price impact ---> depends on trade size(move market prices)
underlying asset is not very liquid
size of the position
small investors follow the same hedging strategy
asymmetric information→magnifies the sensitivity of prices to clusters of similar trade
外生流动性风险原因
Endogenous liquidity
Liquidity Risk
理论
Value at Risk(VAR)→not subadditive
Expected Shortfall→ subadditive
Spectral risk measures→generalization of expected shortal
Compare Risk Measures Methods
分解结构：compartmentalized approach
整体结构：unified approach
bank's risk assessment framework
top-down approach: risks are separable and can be aggregated in some way
bottom-up approach: better account for the interaction among risk factors
Top-down Vs. Bottom-up
实践
Academic Literature On Risk Measuring
VAR and Other Risk Measures
Cashflow是约定的，风险来自rate的变化 --> Duration衡量
Discounted Future CF
一般表达式
以现金流现值为权重
Mac. Duration
BV01: 当Δy=0.01%时的Dollar Duration
Mod. Duration
关联：通过求导关联
不含权，持有至到期不违约，CF确定
Effective Duration
所有情况，可含权
利率平行移动
Key rate Duration
利率非平行移动
Duration
可以为负值
Callable
More Convexity
Putable
含权债
正值
不含权债
正负
涨多跌少
Long Maturity（夜长梦多）
Low Coupon（钱少事多）
Low Yield（世道艰难）
影响因素（导致上涨）
当Duration相同时，CF越分散，Convexity越大
与 Duration关系：同涨同跌
短期+长期，中期少（Convexty）比较大
Barbell
集中于中期
Bullet
Portfoliop
Convexity
通过D和C求解的P和真实的P的关系（当Δy变化时）
Bond Valuation
Callable bond
Putable bond
call on bond
put on bond
不含权债期权
固守工具分类
二叉树求法
股票二叉树（一级内容）
结构
节点利率管后面的时间
每个节点现金流莫忘加入Coupon
注意点
运算过程
Pure Bond
Callable / Putable Bond
求的是期权费
除了最后一期求B的现值步骤，其他不需要理会Coupon
注意
欧式
每个节点还是要加入Coupon求解B现值，然后再用现值和执行价求出当下行权的情况下，期权价值C1
和欧式一样，用期权费直接折现，求出未来再行权的情况下，期权价值C0
美式
债券价格有上限
BSM要求价格正态分布，也就是无上限
债券要考虑利率变动
BSM要求无风险利率恒定
债券波动率随到期日临近而趋于稳定
BSM要求波动率恒定
为什么不用BSM求Option On Bond价值
Option On Bond
分债券种类运算
利率二叉树
二叉树定价法
Term Structure Models
F1是S1的函数
不能解释为什么利率时间曲线总是上扬，忽略了债券的投资风险
Pure Expectation
预期包含了liquidity premium
Liquidity Preference
shape of the yield curve→>preferences of borrowers and lenders
Yield at each maturity is determined independently
Market Segmentation
forward rates represent expected future spot rates plus a premium(not related to maturity)
explain almost any yield curve shape
Preferred habitat
Term Structure Thoerys
表达式
Model 1 : Model with no Drift
Ho-Lee Model
当λ时变时
当σ时变时
Model 2 : Model with Drift（有趋势项）
θ和λ的关系
k : 均值回归的速度
θ : long-run value of the short-term rate assuming risk neutrality
r : current interest rate level
参数含义
Vasicek Model
适用情景：σ与r是相关的
Cox-Ingersol-Ross(CIR)Model
Model 3 : Mean Reverting
表达式1
表达式2
变形表达式
原型表达式
Model 4 : Lognormal Model
Term Structure Art : Drift
Volatility of expected rates causes the future spot rates to be lower
Interest Rate Volatility
Convexity Effect(Jensen's inequality)
The value of convexity increases with maturity and volatility
The Science Of Term Structure Models
依赖利率平行移动假设：parallel assumption
DV01中性对冲
克服了DV01的假设：T-bond and the TIPS are perfectly co-dependent（y是1：1 move的）
estimate how much nominal yield changes given a change in TIPS yield
estimate of the volatility of the hedged portfolio
好处
一个对冲工具的推导
两个对冲工具的推导
改进方法：Regression Hege
sum of the variances of the principal components equals the sum of the variances of the individual rates
principal components are uncorrelated with one another
principal components are chosen to have the maximum possible variance
PCA
Empirical Approaches To Risk Metrics And Hedging
The volatility of the asset is constant
The price of the asset changes smoothly with no jumps
怎样的资产价格是服从lognormal分布的
距离到期时长
执行价格（波动率微笑刻画）
影响σ的因素
执行价格K和内涵波动率σ的函数
欧式期权Call和Put的波动率微笑相同
K/S0
Delta
Alternative ways of characterizing the volatility smile
波动率微笑
解决问题：BSM期权定价中，σ恒定的假设不满足
波动率微笑图像
价格分布图像（两边肥尾）
外汇
Firm's equity value decreases→leverageincreases→increases the riskness/volatility of the underlying assets
leverage
stock market crash→higher premiums for put prices when the strike prices lower
Crashophobia
产生原因
价格分布图像（左肥右瘦）
股票
没有Price Jump的波动率微笑
价格分布图像
有Price Jump的波动率微笑
Volatility Smiles
Risk Management Of Fixed Income and Option
Market Risk
已知且确定
Current Portfolio
α是回归出来的截距项
现实中，α受到constrains及其他因素限制，所以需要对回归出来的α进行调整
背景
Alpha = volitivity of α * Zα * IC（预测的准确程度）
Method 1:Scaling Technique
目的：把因数据问题导致的α不准排除
方法：分布尾部域直接去掉
Method 2: Trimming Technique
目的：去除数据问题导致的Benchmark的收益不准确
Benchmark Neutralization
目的：去除保留现金带来的α，这部分是择时收益
Cash-Neutral Alphas
目的：消除基金经理运气导致的alpha
Risk-Factor-NeutralAlphas
Method 3: Neutralization
Refine α
问题提出原因：Portfolio和Benchmark有部分重叠
benchmark weight of zero
P有B没有
Alphas can be inferred
B有P没有
Alpha Converge
Alphas
一级的内容
Covariance Estimates
α - 2λ * σα * Δσα（MCAR)
-(cost of selling)< MCVA<(cost of purchase)
MCVA
No-trade range for alpha
Transaction Costs
Active Risk Aversion（λ） = IR/(2*σ of α)
Active Risk Aversion（风险厌恶）
输入变量
方法：直接根据α大小选出最好的资产
lgnore all information
biases in the alphas
lgnore certain industry with low alpha
fails in addressing risk control purposes
缺陷
Method 1: Screens
方法：先分层，再取α最好的
优点：solved the problem of the possible exclusion of some categories of assets
缺点：Still suffers from possible errors in measuring alphas.
Method 2:Stratification（分层）
方法：多条件排序
优点：与Benchmark更接近
缺点：can be different from the benchmark with respect to the number of assets and risk characteristics.
Method 3: Linear Programming
● Ultimate approach（终极方法）
Method 4: Quadratic Programming
选资产的方法
Client Driven
PLack of attention to separate accounts
同一基金经理在不同的客户账户上的投资表现不同
表现
交易成本为0
消失条件
Dispersion问题
选资产
图示
马科维茨有效前沿
定权重
Portfolio Construction
Diversified VAR
Undiversified VAR
变形
常规的VAR
含义：多投入i资产一单位，VaR的变化量
MVaR
含义：多投入任意金额的i资产，VaR的变化量
IVaR = VaR(i + P) - VaR(P) = i( dollar) * MVaR(i)
Incremental VaR
CVaR = MVaR(i) * Pi = β * VaR(P) * w(i)
Pecentage Contribution = CVaR(i) / VaR(P) = β * w(i)
Component VaR
衍生VAR
Reducing positions with the highest marginal/ VAR.
Increase position with highest SR
Managing Portfolios Using VAR
Portfolio VAR
IPS决定的风险，是风险的主要构成
Policy-mix risk
执行偏差风险，相对较小
Active-management risk
Absolute Risk
Cash-flow risk
Economic risk
Types
相当于资产与负债的组合，形成了相对风险
Funding Risk
Relative Risk
Types Of Risk
VaR什么时候更有用
原则：Top-down allocation
maximize return at a targeted level of risk
Budgeting across Asset Classes
weight of porfolio managed by manager i
Budgeting across Active Managers
步骤
风险预算
VAR And Risk Budgeting
Portfolio Risk
机构：RMU
用途：衡量需要交易的资产在不影响市场的前提下，执行完毕需要的时间
Q：需要交易的资产总量
V：一天内该资产的市场总成交量
公式：LD = Q/（0.15V）
注意：Liquidity duration
Risk Monitoring And Performance Measurement
目的：看完风险，也看看收益
注意：T和切几段没有关系
not affected by cash inflows or outflows
计算思路：根据中间现金流时间切开时段
Time-Weighted
就是求IRR
现金流可以有效控制时适用
Dollar-Weighted
考虑外部现金流（基金购入或赎回）的Return计算
Sharp Ratio
注意：M Square 和 SR的排序是一样的，求M不方便可以直接求SR
M Square
Total Risk
Treynor Ratio
Jenson's Alpha
Systematic Risk
Information Ratio
Non-Systermatic Risk
基础指标
特征：P和M线性相关
No Market Timing Model
特征：二次凸性，C>0时，Good Timing
Treynor and Mazuy Model
特征：分段凸性，牛市D=1；熊市D=0
Henriksson and Merton Model
Value of appropriate fee for perfect foresight should equal to the price of the call option on the market index
Call Option Model
Market Timing（择时能力）
分类：Value vs Growth / Large vs Small
方法：四因子回归，系数大的是显性风格
Style Analysis（风格分析）
selection of the right asset classes(sectors)-选行业
selection of right securities within an asset class.-选个股
α来源分类
归因计算方法
Performance Attribution（归因）
高级计量
α假设检验
quickly change investment strategy
illiquid assets that are difficult to price
Survivorship bias
对冲基金的分析困难
附加话题
Risk-adjusted Performance Measures
Portfolio Performance Evaluation
Investment Risk Management
Infrequent Sampling
Selection Bias
Iliquid Assets Three key biases
Economic theory states that there should be a premium for bearing illiquidity risk
一个不全面的观点（flawed）
reduces optimal holdings（因为无法及时rebalance）
Rebalance lliquid Assets to Positions Below the Long-Run Average Holding
Consume Less with lliquid Assets
There Are No lliquidity \"Arbitrages\"
Investors Must Demand High lliquidity Hurdle Rates
major impacts of infrequent trading on asset allocation
Portfolio Choice With lliquid Assets（略）
Measurement Bias
Backfill Bias
Survivorship Bias
Selection Bias(self-reporting bias)
Biases Of Hedge Funds
CTA期货策略，CTAs tend not to have a particular bias towards being net long or net short in any particular market
Managed Futuress
盯住mis-pricing，top-down aproch，broad investment mandate，systematic or discretionary
Global Macro
做空收购者，做多被收购者，风险为deal risk
Risk Arbitrage (Merger Arbitrage)
Exploiting inefficiencies and price anomalies between related fixed income securities
Fixed Income Arbitrage
long可转债，short股票，因为债有凸性，irrespective of market moves.
Convertible Arbitrage
invest in both long and short sides of equity，flexibility to shift investment styles
Long/Short Equity
take more short positions than long positions focus on companies with weak cash flow
Dedicated Short Bias
投资新兴市场国家
Emerging Markets
Returns differ dramatically across months. not behave like a single niche strategy. with a similar goal of achieving almost zero beta
Equity Market Neutral strategy
Hedge Fund Strategies
Hedge Funds
Questions To Evaluate A Manager
Criteria To Assess Risk Management Process
Operational Due Diligence
Business Model Risk And Fraud Risk
尽职调查的四个方面
Performing Due Diligence On Specific Managers And Funds
Practical Topic（关于对冲基金）
Investment Risk
The Credit Decision （略）
The Credit Analyst （略）
Asymmetric information （信息不对称）
Principal-agent problems（委托代理问题）
Risk-Shifting （风险从股东转移给债权人）
Moral hazard（道德风险）
Adverse selection（逆向选择）
Externalities （外部性）
Collective action problems（共同行动问题）
Credit Contract Frictions
Credit Risky Securities
PD*LGD*Exposure
Expected Loss
1+r vs PD*RR + (1-PD)(1+r+z)
EL = PD(1-RR)
UEL = 1-RR-EL
比较风险债和无风险债
理解：EL是损失分布的均值，UEL是损失分布的σ，即偏离均值的程度，Economic Capital覆盖的是最坏损失超过EL的部分
Default and Recovery
1、由于downgrade导致的是CR
2、由于宏观环境导致的是MR
3、未说明是MR
Market Risk 和 Credit Risk 辨析
Introduction of Credit Risk
Introduction（识别）
EL
Worse Credit Loss
UL (Credit VaR)
Credit VaR 和 Market Risk VaR的对比
Step1 EL and UEL of of individual asset
Step2 EL and UEL of Portfolio
假设：每笔贷款有相同的规模和特征；ρ恒定
当n趋于无穷大时
一种简化变形
Step3 Risk Contribution
Step4 Economic Capital for Credit Risk
Risk Contribution
Credit VaR
K：正好在当年违约的概率【K2 = （1-d1）*d2】
Cumulative PD【C2 = d1 + (1-d1)d2】
Survival Rate【S2 = (1-d1)(1-d2) = 1-C2】
Average survival rate and average default rate
概念辨析
Marginal PD 随时间变大，Cumulative PD增长速度随时间变大
投资级别
Marginal PD 随时间变小，Cumulative PD增长速度随时间变小
投机级别
规律
Binomial Trees of PD
评级体系图
External Rating
两种评级方法图示
Internal Rating
信用转移矩阵计算
Credit Transition Matrices
Credit Ratings
5C法（不重要）
Point 1: Expert systems
思想：通过线性表达式把公式分为几组
典型例子：Altman's Z-Score models（了解）
Fisher Linear discriminant analysis
思想：因变量是个概率值
典型例子：logit and probit model
Parametric discrimination
Create an equation that does the best job of dividing the larger group into two subgroups.（两个超平面距离最大）
Linear and Non-Linear
Support vector machines
Parameter Method
K是决定看最近的几个邻居的超参数
已有正确分类的样本存在
K-nearest neighbor approach
Non-Parameter Method
Point 2: Quantitative methodologies
方法：利用贝叶斯公式判断
>时，出现C，则违约概率大；<时，出现C，则不违约概率大
1、Minimum error
Probabilities Method
减少错误分类的概率及因此带来的Loss
2、Minimum risk
minimizing the maximum error or risk.
3、Minimax
Type I ：误放
Type II ：误杀
错误类型
公式：满足时拒绝
减少错误的指标（拉格朗日乘数：似然比）
4、Neyman-Pearson
Optimization Method
Point 3: Decision Rules
Models
X轴：False Alert Rate: Type II error / Good-Ones
Y轴：Hit Rate: Correctly Predict / Bad-Ones
坐标系
图像
The receiver operating characteristic (Roc)
The cumulative accuracy profile (CAP GINI curve)
Model Performance
敞口小
风险主要是EL，可以treat this loss as a cost of doing business
零售银行特征
FICO
Credit bureau scores
Pooled model
created by the lender itself
Custom model
零售银行的Credit Models
Retail Credit Risk Management
Credit Scoring Models
Historical-based Approach
Risk-Neutral Probability of Default： YTM-Rf = PD（1-LGD）
Objective probability of default：YTM-Rf-RP = PD(1-LGD)
PD的计算
Bond 和 Benchmark的YTM的差
Yield spread
B和P期限不同时，P的YTM减去B的线性插值YTM（linearly interpolated YTM）或Swap rate
l-spead
不使用YTM，使用各自的Spot Rate计算
Z-spread
Z-spread adjusted for optionality of embedded options
Option adjusted spread(OASs)
Asset-swap spread
Market premium of CDS of issuer bond
CDS spread
浮动利率债券Fixed spread above current LIBOR needed to price bond correctly
Discount margin
类型
路径
宏观经济影响
含权影响
影响因素
计算公式
DV01
和DV01的对比
DVCS（Spread 01)
DVCS
Plotting the curve is further complicated by the choice of reference.
Credit Spread Curve
Credit Spread
Infer Credit Risk from Corporate Bond Prices
Value of equity = Call option on firm=value of firm's asset (V)-value of risky debt（执行价格是债务面值的看涨期权）
Value of risky debt = Risk free debt - put option on firm
思想
N(-d2)is the risk-neutral probability of default.
假设A的价值是可以在公开市场观测的，而E的价格在公开市场观察不准确
Credit Risk计量
σ公式推导
公式推导
基础理论
当Dt已知，根据简单折现方法获得Credit Spread
当Dt未知，根据莫顿模型推导Credit Spread
时间临近到期，Credit Spread扩大，但深度垃圾债除外
Rf上升，公司Value上升，Credit Spread减少
性质
Credit spread
次级债：好的时候是优先债， 差的时候是股，其实是一个Bull Spread期权组合（看推导）
Subordinate Debt in Merton Model
PD = N（-d2) = 1-N(d2)
LGD = EL/PD ; EL用莫顿模型基本理论求解
Calculate PD and LGD
模型推论
1、The value of the firm is observable and follows a lognormal diffusion process(geometric Brownian motion).
2、The risk-free interest rate is constant through time.
3、Debt consists of a single zero-coupon bond with a nominal payment of maturing at time T.
4、Firm can default only on the maturity date of the bond. 欧式期权
5、Equity consists of common shares only.
6、Debt-holders have limited liability and have no recourse to any other assets once equity is eliminated.
8、There are no cash flows prior to the maturity of the debt (including dividends).
假设
It could result in low default probability values and high recovery rates for firms with high leverage. Firms with high leverage in reality would typically have higher default probabilities and lower recovery rates.
缺点
假设和缺陷
Merton Model
1、企业只有一笔零息债券负债——假设有LT和ST负债
2、企业资产价格是可观察的——资产价格是一个概率分布
放宽了莫顿模型两个假设
模型示意图
若LT/ST<1.5
若LT/ST>1.5
Default Line的算法
DD计算公式
Step1 : 计算Asset到Default Line的距离DD
图中阴影部分违约概率
思想：就是求N(-d2）
Default Threshold: F（债务面值）
E（ROA）：收益率y
V: 底层资产价值（公司资产价值）
Maturity: T-t
违约概率公式
Step 2 : Report estimated default frequency (EDF)
Step 3 : 根据EDF确定Credit Rate
模型步骤
The KMV Approach
Infer Credit Risk from Equity Prices
Market Prices Approch
Agencies'ratings
Experts-based Internal Ratings Used by Banks
Experts-based Approaches
Structural approaches: based on economic and financial theoretical assumptions.
Reduced form approaches: use statistically suitable set of variables and disregarding the theoretical and conceptual causal relations: 如无监督学习
Cash Flow Simulations
Statistical-based Models
Heuristic methods：使用人工智能算法
Numerical methods：highly complex environments下的最优化训练算法
Heuristic and Numerical Approaches
Rating Assignment Methodologies
0/1分布
Bernouli Trail
N个独立贝努里分别的概率分布
Binomial Distribution 二项分布
λ 是1年平均违约概率
X = 0 的泊松概率是存活率
一个例题
泊松分布表达式
Poisson Distribution 泊松分布
描绘违约发生平均需要等待的时间
β = 1/λ
Exponential Distribution 指数分布
基础分布
Survival rate
Cumulative PD
思路：是对Cumulative PD求一阶导
Marginal PD
已知λ时计算
近似公式
根据风险中性原理求λ
Hazard Rates
思想：λ不是时变时，时间变量是λt，相当于是矩形面积，当λ时变时，就是λ(t)函数的积分面积或分段函数下面积
Hazard Rates Curve
Default Intensity Models
PD
影响RR的因素
Recover Rate 上升，LGD下降
LGD
未来某时间点Market Value的期望（均值）
MtM
EE (Expected Exposure)
The worst exposure that could occur at a given time in the future at a given confidence level.
PFE (Potential future exposure)
时间序列上最大的PFE
Maximum PFE
时间序列上EE的均值
Expected positive exposure(EPE)
对手方视角的EPE
ENE
对手方视角的EE
NEE
Negative exposure
单调不降的EE
Effecticve EE
时间序列上Effecticve EE的均值
Effective EPE
基本概念
Future uncertainty.
Periodic cash flows
When the credit exposure of a product results from the combination of multiple underlying risk factors.
Combination of profiles
Optionality / Exercise decisions
Collateral
Credit Exposure Metrics
Interest rate uncertainty 上升→DE上升
Diffusion effect（DE，扩散效应）
∶Bond's duration 上升→ AE上升
Amortization effect（AE，摊销效应）
两个效应
Exposure变化趋势
在此基础上再求极值
峰值的计算推导
Interest Rate Swaps
推演过程
Currency Swaps
敞口基本上确定，但固定利率债如果市场利率下降，敞口会上升
The increase in exposures in early years is the result of the CDS premium(or credit spread) widening. The maximum exposure for the CDS occurs at a credit event where the notional value is paid less the recovery value.
Credit Derivatives
The general exposure profile of a long option position tends to increase until exercise due to the increased possibility that can be highly in the money
Options
Other Security Types
不同合约的Exposure Profiles
Positive correlations have lower netting benefits
Negative correlations provide stronger netting benefits
The benefit of correlation
Netting benefit also depends on the initial MtM of transactions.
Netting Factor
Netting
Exposure could increase between margin calls.
Remargin period
Threshold
Minimum transfer amount
Independent amout（initial margin）
Rounding
影响效果的因素
Risk Mitigation Techniques
Credit Exposure
Credit migration
MtM=present value of all expected inflows less the present value of expected payments
Counterparty Risk Terminology
立刻关闭与之所有协议
Close-out
不再履行义务，亏损时有利
Walkaway feature
Mark-to-market
Diversification
Exchange and centralized clearinghouses
Hedging
缓释风险的手段
Expected value or price of counterparty credit risk. A positive value represents a cost to the counterparty that bears a greater propensity to default.
Risky value= risk-free value-CVA
This would be a charge to the weaker counterparty. CVA as a spread= Spread of CDX×EPE
CVA Spread
The CVA will most often increase given an increase in the credit spread.
Credit Value Adjustment (CVA)
Wrong-Way Risk
PD和EAD负相关 CVA下降
Right-Way Risk
Wrong-Way Risk Vs. Right-Way Risk
计算方法
Credit VaR with a single-factor model
Counterparty Risk
EAD
Key Parameter
思路：根据评级定利率和PD，根据利率定PV of Future Value，PD* PV* LGD就是EL
CreditMetrics (J.P. Morgan)
根据微观经济变化（企业股价变化）动态计量PD
假设只有违约是信用风险，评级下调不是，服从泊松分布，违约事件相互独立
CreditRisk+(Credit Suisse)
Moody's KMV
根据宏观经济因子动态计量PD，用Logit Model
CreditPortfolioView
四大实务模型
对比表
对比
Credit Risk Portfolio Models
The number of required calculations 计算太复杂
Certain characteristics of credit positions do not fit well in the default correlation credit potfolio model. 假设太简单
The limited data for estimating defults: Firm defaults are relatively rare events. 数据稀疏
缺点（Drawbacks）
Default corelation impacts the volatility and extreme quantiles of loss rather than the expected loss.
Credit VaR & Default Correlation
结论
Default Correlation for Credit Portfolios
目的：根据资产收益率的SFM推导ρ
βi相互独立
αi服从标准正态分布
资产之间的ρ等于βiβj
推论
假设和推论
Conditional Independence
Single Factor Model
Portfolio Credit Risk
Measurement（计量）
Credit Event
CDS原理：买保险，买Put Option
坏处：Delivery squeeze 购回交付债券的时候会抬升债券市场成本
好处：There is no need to determine the size of the loss
Physical delivery
算法：(100-z)%*the notional principal Z是企业残值的中间数（一般取违约发生后3个月值）
好处：There is no need to own or purchase the defaulted securities
问题：A problem arises because the market price is fluid（价格不稳定）
Cash delivery
CDS结算方式
First-to-default basket swap
定价模型：One-factor Gaussian copula model for time to default
Nth-to-default basket swap(N>=2)
Basket credit default swap
结构图
Senior basket CDS & Subordinated basket CDS
CDS的衍生形态
基本原则：买CDS的PV = CDS赔付的PV
CDS赔付的PV
买CDS的PV
CDS定价
Credit Default Swaps （CDS）
Total Return Swaps（TRS）
Vulnerable Option
Derivatives With Credit Risks-Swap
第一套思路
第二套思路
Credit-Linked Notes
信用衍生品
Senior
Junior / Mezzanine
有利息现金流分配上限（OC Trigger），剩下的进入信托账户，吸收未来损失
Equity
Waterfall Structure
insurance or wraps purchased from a third party
Externa
Overcollateralization (hard credit enhancement)
Excess spread (soft credit enhancement)
Subordinating note classes(tranches)
Internal
Credit Enhancements（信用增级）
pass-through structure.
Amortizing structure（摊销还款）
payments are not simply passed through.
Revolving structures（循环贷款）
Allows an SPV to make frequent issues or multiple securitizations.
Enables the SPV to issue multiple ABS through the single trust.
Sell multiple issues to investors that share excess spreads over these multiple series
Master trust structure（共享SPV池）
SPV Structures
典型结构
绩效工具
Performance Tools
Structured Products介绍
Mezzanine: 在低PD区像S，在高PD区像E
对Credit VaR的影响
Equity: ρ上升，Equity Value上升
Senior：ρ下降，Senior Value上升
对Value的影响
Correlation
Systematic risk: high systematic risk expressed in high correlations can still severely damage a portfolio.
Tranche thinness: The equity and mezzanine tranches are relatively thin.
Loan granularity:Loan granularity references the loan level diversjfication.
Other Factors
结构化产品Credit Risk的影响因素
计算
Default 01
Implied Correlation
几个概念
Structured Credit Risk
Cash-Flow CDOs
Synthetic CDOs
Collateralized Debt Obligations(CDOs)
结构化信用产品
Between Two Counterparties
Between Multiple Counterparties
Netting and Close-Out
Termination provisions 终止条款
Walkaway clauses
aims to reduce the gross notional amount and the number of trades
Trade compression
Termination Features
Collateral Management
损失补偿顺序
Central Counterparties(CCP)
Management（管理）
Credit Risk
People(human factor)
Internal processes
Systems
External events.
Strategic risk and Reputational risk
包含
Legal risk
不i包含
风险因子
Defining Operational Risk
注意：α = 15%
Basic Indicator Approach
注意：分母一直是3，与Basic方法有负值时分母同步缩小不同
根据不同业务性质确定β
Alternative Standardized Approach
Standardized Approach
Unexpected loss in a total loss distribution that corresponds to a confidence level of 99.9% over a 1-year time horizon.
Historical-based Loss Distribution
Loss Frequency: Poisson distribution
子分布
例题
离散时
Monte Carlo simulation Process.
连续时
卷积过程
Parametric-based LDA
LDA（Loss Distribution Approach）
Step 1: Group loss data into a business line/event type matrix
Step 3: Model an operational risk loss distribution in each cell of the business line/event type matrix
Step 4: Determine the operating risk capital requirements
Within-cell dependencies & Between-cell dependencies
Gaussian copulas are often used.
Modeling Dependence
The overall operational risk capital requirement would combine the results in each of the cells(no diversification benefit)
General Steps of LDA
分布确定方法
Internal Loss Data
Internal development
from media such as news or magazines.(reporting bias)
Subscription Databases
Operational Risk data exchange Association(ORX)
Consortium Data
数据供应商
Vendors
External Loss Data
Scenario Analysis
Risk Control Self-Assessment(RCSA)
Business Environment and Internal Control Factors
Data Framework
The advanced measurement approach(AMA)
计量方法
Assessing operational risk
Absorbed as an ongoing cost
Expected loss(EL)
Capital
Unexpected loss(ULl)
Insurance
The stress loss
Managing operational risk
较好的组织结构
Organizational Designs 组织机构
Operational Risk★★★
假设类错误
Common Model Errors
拟合类错误
Common Model Implementation Errors
Inaccurate data.
Incorrect sampling period length.
Liquidity and valuation problems.
Common Valuation and Estimation Errors
Sources of Model Risk
Challenge from model users may be weak if the model does not materially affect their results
USE
Outcomes analysis
Three core elements
Model Validation
Supervisory Guidance on Model Risk Management
Long-Term Capital Management
London Whale
Sell protection on the equity tranche of the CDX
Buy protection on the junior mezzanine tranche of the CDX.
操作
The 2005 Credit Correlation Episode
Subprime Default Models 次贷违约
Case Studies
Model Risk ★★★
Business line management
Functionally independent corporate operational risk function(CORF):
audit or by staff independent of the process or system
Independent review
Three Lines of Defense
Relationship Between ORMF and ORMS
Principles for the Sound Management of Operational Risk
Operational Risk and Model Risk Management
两个概念对比
Practitioners usually adopt a one-year time horizon.
RAROC Horizon
Default Probabilities
Confidence Level
RAROC Assumptions
RAROC
意义：投资者要求的回报率，分为普通股和优先股
决策规则：If RAROC>hurdle rate>value creation from the project and accepted.
The hurdle rate
Adjusted RAROC= RAROC-β(Rm - Rf)
决策规则
Adjusted RAROC
A business unit that are highly correlated to the overall firm need to be allocated more risk capital
Risk Capital and Diversification
Risk Capital Attribution and Risk-Adjusted Performance Measurement ★★★
Practices and Issues in Economic Capital Frameworks
Capital Management
Enterprise Risk Management
Risk Appetite Frameworks
Risk Culture
Stress Testing Banks
Capital Planning at Large Bank Holding Companies
Integrated Risk Management
Cyber Resilience
Operational Resilience
Resilience
Operational Risk
\"Liquidity black hole\" Phenomenon
Predatory trading掠夺性交易
Transparency is important for liquidity
Problems with liquidating a position
Transaction liquidity risk
Risk that creditors either withdraw credit or change the terms that the positions have to be unwound and/or are no longer profitable.
Funding Liquidity Risk（Balance Sheet Risk）
In situations of severe financial stress
Systemic Risk
Definition of Liquidity Risk
Bid-ask spread and brokers'commissions.
Tightness
Depth
The length of time for which a lumpy order moves the market away from the equilibrium price.
Resiliency （弹性）
Adverse price impact
The deterioration in the market price induced by the amount of time it takes to get a trade done
Slippage（滑点）
Characteristics used to measure market liquidity
VaR ＋ Liquidity Cost (LC)
思路
思路：外生价格影响就是Bid-Ask-Spread
常数情况下是一般市场状态，非常数情况下是压力市场状态
计算推导
LVaR大并不能说明流动性风险越大，因为里面还有VaR，因此可以剥离计算Liquidity Adjustment
Exogenous Price （外生价格影响）
E是弹性
Endogenous Price （内生价格影响）
两种效应相乘
Multiplying the effects
动机：因为每日逐步清仓，所以要对平方根法则进行调整
清仓时间调整
Liquidity-Adjusted VaR
Transaction Liquidity Risk
LIBOR（3个月）- Fed funds（1天）
Term Spread.
Eurodollor LIBOR（金融机构3个月） - Treasuries（政府3个月）
TED Spread
Indicators of Liquidity Risk
也叫Cash flow at risk
Borrowing or lending
Margin requirements
Collateral obligations
Unexpected cash flows
Changes in risk management policy
Factors that influence cash flow and LAR
Liquidity at Risk(LaR)
Funding Liquidity Risk
推导公式
Crash Metrics
Worst-case outcome
Crisis-scenario analyses
Approaches to Estimating Crisis Liquidity Risk（了解）
Measurement
bank run and rollover risk
Commercial Banking
Cash
Unpledged assets are assets not currently being used as collateral
Unused borrowing capacity. This is not an unfettered source of liquidity
管理流动性风险方法
Hedge Fund
The assets can still fluctuate in value
Money Market Mutual Funds(MMMFs)
不同机构流动性管理方法
Financing gap = average amount of loans- average amount of core deposits
一种流动性管理方法
Management
financing a security transaction in which the loan is collateralized by the security
Margin loans
Are matched pairs of the spot sale and forward repurchase of security
Repurchase agreements
The security lender continues to receive dividend and interest cash flows from the security
Securities lending
Total Return Swaps
The Collateral Market
Margin Leverage
Leverage ratio
Leverage
i 是内生于买卖价差的，而不是事先约定的
回购价格
Repos offer secured short-term financing; Repo financing is cheaper but less stable.
Repos offer relatively cheap sources of obtaining short-term funds.
Borrower
Lenders may also use repos(as the reverse repo side) to finance short positions in bonds.
Lender
Motivations for entering into repos
指定抵押债券的种类
收益比GC小
常见品种是OTR（On The Run 国债）
Special collateral
不指定抵押债券的种类
收益较大，但经济危机时，GC-Spread减少
General Collateral
Collateral类型
定义式：GC rate - Special rate
Spreads fluctuate over time （波动）
OTR special spreads are generally narrower immeditely after an auction but wider before auctions（流动性投放作用）
Special Spreads and the Auction Cycle（国债拍卖）
Special spreads move within a band that is capped at the GC rate and a floor of 0%
The special spread can also be smaller than the penalty for failed trades.
Special Spreads and Rate Levels
套利价值公式
用Special Spread套利
Special Spread
The Collateral Market and Leverage
Repurchase Agreements and Financing
This creates demand(supply) for the asset that restores the price to a more reasonable level.The result is that the market is liquid.
Negative feedback traders
Trend trading.
Stop-loss rules.
Dynamic hedging.
Creating options synthetically.
Margins. 强制平仓出现的卖单
Predatory trading.
LTCM(\"relative value fixed income\"trade). 长期资本管理公司采用的固收期限套利策略
形成Positive feedback traders的原因
Positive feedback traders
交易者类型
The Behavior of Traders
加杠杆和去杠杆周期
Leveraging and Deleveraging
Often the process is self-reinforcing.
Irrational Exuberance 非理性繁荣
The Importance of Diversity.
The Impact of Regulation
原因
Liquidity Black Hole
三个额外话题
Liquidity and Leverage
A leading indicator will provide information and signal potential stress prior to the occurrence of an actual event.
Sharpness （敏锐度）is the granularity and specificity of a particular indicator.
Forward Looking Bias
Banks should also strike a balance between external and internal measures
Normal and Stressed
Spanning Various Time Horizons:EWI coverage cannot be static and needs to reflect various time horizons
Measures
Escalation 升级上报
Reporting
Integrated Systems
Thresholds
Early Warning Indicators
主要原因：Diseconomies of Scope in Risk Management 规模不经济
Establishing lines of bank credit 获得其他银行的授信
Dedicating a buffer stock of cash and liquid securities
Laddering the maturities of its liabilities
Access to secured financing from central bank facilities.
缓释信用风险的方法
the linkages via counterparty chains 有对手方风险
dealer banks have no default insurance
too big to fail
和传统商业银行的区别
The Failure Mechanics of Dealer Banks
Foundations of Liquidity and Treasury Risk
Outgoing wire transfers(the largest use) 对外电汇
Funding of nostro accounts 往来账
Collateral pledging. 保证金和抵押金
Asset purchases/funding. 购买资产
日内流动性用途
Cash balances.
Incoming funds flow（最主要）
Intraday credit.
Central banks: as a large source of intraday credit.
FMUs and other banks may also provide intraday credit.
Liquid assets
Overnight borrowings.
Other term funding: Similar to overnight borrowing.
日内流动性来源
Treasury is the first line of defense
Corporate Risk Management is the second line of defense
Internal Audit is the third line of defense
three lines of defense model
Governance of Intraday LRM
Measures for Understanding Intraday Flows
Daily Maximum Intraday Liquidity Usage
Intraday Credit Relative to Tier 1 Capital
Client Intraday Credit Usage
Payment Throughput 支付吞吐量
Measures for Quantifying and Monitoring Risk Levels
Help identify key vulnerabilities and their sensitivity to external factors.
Help in formulating contingency plans for how a bank might respond to an event.
Developing the technology infrastructure
Role of Stress Testing
For Financial Institutions
The first line of defense is membership criteria 会员准入标准
Net Debit Caps 对单一借款方的头寸限制
Liquidity Savings Mechanism
staggered multiple settlement windows throughout the day. 错开结算时间窗口
Settlement Windows
Contingent Liquidity
工具
Monitoring the risks of their participants is the second line of defense
A mechanism to facilitate settlement in the event of a participant failure: mutualizing the default risk
防线
For FMUs
日内流动性管理
Intraday Liquidity Risk Management
目的：对现金流根据时间和规模两个维度进行分类
A Taxonomy of Cash Flows
传统的只关心赚钱不赚钱，赚钱也有可能流出现金流（实物交付）
Liquility Option 只关心现金流
和传统Option区别
量的维度
成本维度（融资或投资成本）
现金流与预期有差别（不管高低），就是Risk
流动性风险的新定义
Liquidity Options
TSECF：时间序列上的预期现金流序列
TSECCF：时间序列上的累计预期现金流序列
includes the cash flows from all existing contracts that comprise the assets and liabilities
CFs are adjusted to consider credit risks and liquidity options
CFs originated by new business increasing the assets should be included
The rollover of maturing liabilities and new bond issuances
The temporal distribution could produce periods of negative cumulated cash flows
TSECF & TSECCF
Balance sheet expansion with secured or unsecured funding. 依赖外部条件
Balance sheet shrinkage by selling assets 依赖内部条件
Repo can also be considered separately and labelled as\"balance sheet neutral\". 依赖内部条件
第一种分类法
Selling of assets （AS）
Secured funding using assets as collateral and via repo （RP)
Balance sheet liquidity(BSL)
Unsecured funding via withdrawals of committed credit lines available （USF）
第二种分类法
All the bonds available for sale(AFS) and other assets that can be sold and/or Repoed relatively easily.
In the banking book
Add stocks and some structured products to generate liquidity
In the trading book
第三种分类法
TSLGC : 时间序列
TSCLGC：累计时间序列
The term structure of LGC
Liquidity Generation Capacity 流动性创造能力
银行业务种类的影响结构
原则：有占有权的就是Available Assets
The Term Structure of Available Assets
目的：汇总现金流和创造现金流的能力
The TSL must always be positive if the financial institution has to be solvent all the time.
The Term Structure of Expected Liquidity
定义：一定置信区间下极端现金流偏离TSECF的距离
方法：蒙特卡洛模拟
Cash Flows at Risk （CFaR）
Term Structure of Liquidity-at-Risk (TSLaR)
Quantitative Liquidity Risk Measures
Monitoring Liquidity
应急流动性，压力测试对象，是liquid asset buffer
Contingent liquidity
日常运营流动性，无法满足压力状况下需求
Operational liquidity
特定用途流动性，无法满足压力状况下需求
Restricted liquidity
Not primarily aimed at supporting the bank during times of stress. But may be redirected to meet contingent liquidity requirement needs.
Strategic liquidity
流动性分类
Contingent liquidity that is currently in place.
Liquid asset buffer.
They are those assumed to occur under stress scenarios.
Stressed outflows.
They are assumed to partially offset the stressed outflows.
Stressed inflows.
Normal Liquid Asset Buffer-Stressed Cash Outflow +Stressed Cash Inflows
Stressed liquid asset buffer.
压力测试模型的要素
目的：确定压力测试范围
Liquidity transfer restrictions. 转移支付限制区域
Currency. 货币域
Regulatory jurisdiction. 监管区域
业务单元划分维度
Organizational Scope
至少12个月时间窗口
现金流测算频率：初期需要每日预测
Planning Horizon
Historical statistical techniques(E.g. CFaR)
Deterministic models(E.g. hypothetical liquidity stress scenarios)
Monte Carlo simulation(A statistical technique)
Testing Techniques
Historical Scenarios
Distinguish between systemic and idiosyncratic risk;
Distinguish between levels of severity; 区分严重程度
Clearly define the scenarios;
Consider more holistic approaches. 更全面的方法
Hypothetical Scenarios
Scenario Development
要细分每一种情况
Development of Assumptions
输出内容： Stress testing assumptions; Liquidity position metrics; Prospective liquidity position metrics; Capital and performance metrics
Outputs of the Model
The specific roles should consist of ：Asset-liability committee;Treasury; Risk management; Internal audit; Model risk management.
Governance and Controls
Liquidity vs. Yield
Liquidity vs. Capital
liquidity optimization opportunity
An incentive for banks to favor\"sticky\"funding sources 关注粘性融资渠道
Funding optimization.
Optimization
IT基础设施
Establishment a Sustainable Infrastructure
与capital stress testing整合
与asset liability management整合
Integration with Other Models
压力测试模型建立过程
Liquidity Stress Testing
报告内容
Liquidity Risk Reporting
Liquidity Stress Testing and Liquidity Risk Reporting
Governance and Oversight
Scenarios and Liquidity Gap Analysis
Contingent Actions
Market Signals and Reputational Impact
指向EWI
Monitoring
风险级别逐步升级管理
Escalation Levels
Data and Reporting
Contingency Funding Planning（了解）
Holistic Liquidity Risk Management Framework
The Investment Function in Financial-Services Management
Risk Management for Changing Interest Rates: ALM and Duration
Liquidity and Reserves Management: Strategies and Policies
Managing Deposit and Non-deposit Liabilities
Liquidity Transfer Pricing: A Guide to Better Practice
Day-to-day Techniques of Liquidity and Treasury Risk Management
US Dollar Shortage in Global Banking and International Policy Response
Covered Interest Parity Lost: Understanding the Cross-Currency Basis
International Perspective to Liquidity Risk Management
Liquidity and Treasury Risk
计算方法：RWA=RW*NP
Risk-Weighted Assets (RWA)
Expected Loss and Unexpected Loss
Basic Terms
Evolution of Basel Accord
Introduction of Basel Accord
Total assets to capital ratio had to be less than 20
Cooke ratio must exceed 8%.
Two capital requirements
风险加权资产的计算
all corporate loans were treated the same regardless of the creditworthiness of the borrower
ignored the benefits of diversijfication.
Major limitations of Basel I
Basel I
Total capital=0.08x(credit risk RWA＋market risk RWA+ operational risk RWA).
概要
三级资本划分
资本结构
资本充足率计算方法
基础要求
At least 50% of capital must be Tier1.This means there is 4% .
Half of the Tier1 requirement has to be met with common equity.
进阶要求
资本要求
Bank Aseet
资产分类
评级-权重对应表
Risk weights based on external credit rating assessments.
· The simple approach（改变RW）: The risk weight of the collateral replaces the risk weight of the counterparty.
· The comprehensive approach（改变NP）: Adjust the size of the exposure upward and the value of the collateral downward
Collateral Adjustment
EL的计算框架
ρ的计算（了解）
WCDR计算（Asymptotic Single Risk Factor(ASRF) Model）
MA（Maturity Adjustment计算）
模型推导
1-year 的99.9% VaR
计算UL的VaR参数
All systematic risks are modeled by a single risk factor; allidiosyncratic(unsystematic) risks tend to cancel out.
公司规模越大，ρ越大；PD越大，ρ越小（坏人千人千面，系统性风险小）
Maturity Adjustment：FIRB下确定2.5年，AIRP下各自计算
参数说明
Internal Rating-Based(IRB) Approaches
only a treatment like the Advanced IRB approach is used
No maturity adjustment.
ρ=0.15 for residential mortgages;
ρ=0.04 for qualifying revolving assets (mostly credit card balances)；
other
ρ分三种情况
ρ are lower for retail than for wholesale exposures
特殊规定
特例：Retail exposures
Credit
It ignores correlations between the instruments.
Standardized Measurement Method
VaR的参数是99%的10天VaR，因此daliy VaR已知，要乘以根号10
SRC是The specific risk charge(SRC)
m定值方法：基底是3，根据规则调增
m是根据回测得到的模型准确性调整参数
Internal Models Approach
Market
Operational（详见操作风险章节）
三类资产的风险计量
Pillar 1: Minimum Capital Requirements
概要： Allow regulators from different countries some discretion in how they apply the rules.
Concentration risk
Risk of Credit risk mitigation(CRM)
Credit Risk
第一支柱虽涉及但未完全涵盖的风险
Interest rate risk of banking
book Liquidity risk
Reputation risk
Strategic risk
Business risk
第一支柱未涉及的风险
Business bycle
外部因素
涵盖的风险
Pillar 2: Supervisory
Increase transparency
Disclose more information about the risks
要求
Pillar 3: Market Discipline
FrameWork
Basel Il
用压力情境下数据计算，99% confidence level over a 10-day period
250-day period of stressed market conditions.
k就是巴II里面的m
SVaR
default risk
credit migration risk for debt instruments.
覆盖风险（内含信用风险部分）
IRC
CRM is a single capital charge for correlation-dependent instruments that replaces the specific risk charge(SRC) and the IRC.
发展：Comprehensive Risk Measure
Stressed Value-at-Risk(SVaR)& Incremental Risk Capital Charge
proposed an alternate measure using expected shortfall(ES)
every risk factor is assigned a liquidity horizon for capital calculations.
Fundamental Review of The Trading Book
Basel II.5
Strengthen the risk coverage of the capital for trading books and complex off-balance sheet exposures.
Requiring a leverage ratio
Promoting countercyclical buffers
Instituting policies to address systemic risk
Instituting a global liquidity standard
改革总述
1. Common equity including retained earnings(Core Tier 1 capital)
2. Non-cumulative perpetual preferred stock(additional Tier 1 capital)
3. Tier 1 capital is adjusted downward to reflect defined benefit pension plan deficits 养老金赤字减项
Tier 1 Capital
1. Debt subordinated to depositors with an original maturity of five years or more
Tier 2 Capital
取消了 Tier 3 capital.
1、Capital Definition
Capital Conservation Buffer(CCB) 资本留存超额资本
Countercyclical Buffer 反周期超额资本
2、资本金比例要求
Selecting Internal Loss Reference Dates
operational risk management framework(ORMF)& operational risk measurement system (ORMS)
3、Operational Risk
The Committee will test a Tier 1 leverage ratio of 3%
4、Leverage Ratios
systemically important institutions
5、Systematic Risk Management
目的：Promote short-term resilience of a bank's liquidity profile
Level I assets
Level2A assets: A minimum 15% haircut is applied to the current marketvalue of each Level 2A asset
Level2 assets
分子：High-Quality Liquid Assets(HQLA)
分母：Net Cash Outflows
Liquidity Coverage Ratio
目的：Promote resilience over a longer time frame
赋权方法
Net Stable Funding Ratio(NSFR)
Contractual maturity mismatch
Concentration of funding
Available unencumbered assets
Liquidity coverage ratio by significant currency
Market-related monitoring tools
Liquidity Monitoring Tools
6、Liquidity Requirements
7、Risk Coverage
Basel III
使之颗粒度更细，更敏感的具体方法
1. Standardised Approach for Credit Risk
具体移除标准
(1) Removing the use of the advanced IRB approach for certain asset classes
(2) Specification of input floors: introduce minimum\"floor\"values for bank-estimated IRB parameters（PD，LGD，EAD）
(3) Additional enhancements
2. Internal Ratings-based Approaches for Credit Risk
The exposure component of CVA is directly related to the price of the transactions. These prices are sensitive to variability in underlying market risk factors
enhance its risk sensitivity
strengthen its robustness
CVA risk is a form of market risk.The standardized and basic approaches of the revised CVA framework have been designed and calibrated to be consistent with the approaches used in the revised market risk framework.
improve its consistency
3. CVA Risk Framework
Operational risk increases at an increasing rate with a bank's income;
Banks which have experienced greater operational risk losses historically are assumed to be more likely to experience operational risk losses in the future.
BIC
ILM
ORC(Minimum operational risk capital)=BIC*ILM
A bank with losses that are high relative to its BIC is required to hold higher capital
Operationalloss events related to credit risk and that are accounted for in credit risk RWAs should not be included in the loss data set.
Operational risk losses related to market risk are treated as operational risk
4. Operational Risk Framework
系统重要性银行的杠杆率要求增加0.5%
A G-SIB that does not meet one of these requirements will be subject to the associated minimum capital conservation requirement (expressed as a percentage of earnings).
如果不能满足整个指标体系中任意一项
5. Leverage Ratio Framework
IRP计算的RWA须在（RWA，72.5%标准法计算的RWA）中取孰大
6. Output Floor
2017 Basel III
三大支柱一模一样
In Basel/II there is a stronger emphasis on the stability of the financial system(systemic risk)
Solvency ll focuses on individual policyholders.
MR：99% 10天
CR/OR：99.9% 1年
巴塞尔协议
99.5% 1年
Solvency
VaR Parameters
Risk Classes
· Solvency capital requirements(SCR)
· Minimum capital requirement (MCR):capital requirement is between 25-45% of the SCR.
Solvency lI capital requirements use a two-level approach
Minimum Capital Requirements
风险分层
Diversification（在什么层次做diversification）
与巴塞尔协议的区别
Standardized approach: Analogous to Basel Il
· Underwriting risk
· Operational risk
· Investment risk: divided into market risk and credit risk
Internal Models Approach: A VaR is calculated with a one-year time horizon and a 99.5% confidence level.
Solvency lI Framework
Solvency ll
Basel Accord
Current Issue
FRM II
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