FRM II 全科目思维导图
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Market Risk
VAR and Other Risk Measures
Parametric And Non-parametric Methods Of Estimation
Non-parametric Methods
Historical Simulation Approach
Basic HS
95% VAR is the (n*5%+1)th
highest observation.
Expected Shortfall (Conditional VAR)
定义:expected value of the loss when it exceeds VAR
A subadditive risk
measure.
not ambiguous.
has only one correct answer
Bootstrap Historical Simulation
will often be more accurate than a 'raw' sample
estimate
Weighted Historic Simulation Approaches
Age-weighted Historic Simulation
hybrid of EWMA & HS
Advantages
Generalizes standard HS,
traditional HS is a special case with zero decay, or lambda --> 1
More responsive to large losses, also better
at handling clusters of large losses.
Reduce distortions caused by events that are unlikely to
recur; helps to reduce ghost effects.
Gives us the option of letting our sample size grow over
time.
Volatility-weighted Historical Simulation
定义式
Advantages
• 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
Correlation-weighted Historical Simulation
特点
Takes account of correlations as well as volatilities
More complex than volatility-weighted historical simulation but with the same principle.
定义式
Filtered historical simulation
特点和优势
Semi-parametric bootstrap
combine benefits of historical
simulation with power/flexibility of conditional volatility models (GARCH).
Bootstrapping
keeps the non-parametric nature of HS, while volatility model gives
a sophisticated treatment of volatility.
Get VAR and ES estimates that exceed the maximum historical loss in data set.
Sensitive to changes of market conditions.
Advantages And Disadvantages
Advantages
•Handle non-normal returns (skew and kurtosis)
•Handle any position type including derivatives
•Relatively easy to implement
•No "curse of dimensionality"
•Uses readily available data (returns, volatility)
•Easy to generate confidence intervals
•Can be combined with parametric "add-ons”
Disadvantages
•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
Parametric Estimation Approaches
Normal VAR
VAR for returns that follows a normal distribution.
计算式
Log Normal VAR
VAR for asset prices follow a lognormal distribution.
计算式
Other Issues
Coherent Risk Measures
More general than VAR or ES
特征
单调性
If a portfolio has systematically lower values than another it must have greater risk. Standard deviation violates the monotonicity condition.
平移不变性
Adding cash k to a portfolio should reduce its risk by k. This reduces the lowest portfolio value. As with X, k is measured in dollars.
同质性
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.
次可加性
The risk of a portfolio is less than the sum of separate risks. Merging portfolios not increase risk.
VAR is not sub-additive. Therefore, VAR is not a coherent risk measure.
Method Of Estimating Coherent Risk
Spectral measures
Estimated as a weighted average of the
quantiles (i.e.z the VaRs). The particulars of the weighting function are not important
ES
The easiest case of coherent risk measure. It gives all tail-loss quantiles an equal weight, and other quantiles a weight of 0.
More general Coherent Risk Measure
Replace the equal weights in the with a more complicated weighting function.
The estimated risk measure rises with n, and eventually converges to the true value.
More sensitive to the value of n than ES because if n becomes larger the quantiles will be more concentrated in the tail, which represent a more weighted-average extreme value of the distribution.
Standard Errors Of Coherent Risk Measures
The presence of heavy tails might make ES estimators less accurate than VAR estimators.
估计方法
L-estimator
Bootstrap
Quantile-Quantile Plots
QQ图
记忆:正S形是瘦尾
Extreme Value
三种主要理论
Generalized Extreme Value Distribution (Block Maxima Method)
参数
示意图
According to Fisher-Tippett theorem, as the sample size n gets large, the distribution of extremes converges to the generalized extreme value (GEV) distribution
Block Maxima. Classical
Generalized Pareto Distribution (Peaks over Threshold)
参数
计算式
示意图
Multivariate EVT
Models the tails of multivariate distributions
Key issue is the (tail) dependence structure of the extreme events
USE Copulas
It is important if extreme events are not independent
相同点
(1)Have the same goal
(2)Built on the same general principles
(3)They even share the same shape parameter: £ (Shape/Tail)
优缺点
POT better
(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
GEV better
POT requires to choosing the threshold
Backtesting VAR
定义
Compare the estimated loss from the calculated VAR with the actual losses realized at the end of the specified time horizon.
Backtesting的困难
Canot tell us with 100 % confidence whether our model is good or bad
VAR assumes a static portfolio(静态组合)
怎么解决
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
分类
Unconditional Coverage Model
ignores time variation,reflects the "independence" assumption
方法
直接分布法
X:the proportion of times VAR is exceeded in a given sample.
f(x)
流程
实例
假设检验法
Conditional Coverage Model
considering whether exceptions come in clusters
方法
H0: accurate model
统计量
If LR>3.84, we would reject the hypothesis that the model is correct.
The Basel Rules For Backtesting
10-days 99% VAR over 250 observations
标准区间
处理方法
Basic integrity of the madel(模型基本面错误)
The penalty should apply
Model accuracy could be improved(模型精确度不足)
The penalty should apply
Intraday(日内交易导致头寸变化)
The penalty should be considered
Bad luck
Markets were particularly volatile or correlations changed
VAR Mapping
为什么要VAR Mapping
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
Approaches to mapping(选哪个期限的y的问题)
Principal mapping
bond risk is associated with the maturity of the principal payment only
Duration mapping
the risk is associated with that of a zero-coupon bond with
maturity equal to the bond duration
maturity equal to the bond duration
Cashflow mapping
the risk of fixed-income instruments is decomposed into the
risk of each of the bond cash flows
risk of each of the bond cash flows
计算
Delta-normal method
Bond
公式
推导
Option
公式
推导
Delta-Gamma method
Bond
公式
推导
Option
公式
推导
综合应用
选期限-定y的VAR-用公式计算资产的VAR
Other Issues
Stress Test
过程
Relative VAR
公式
Correlation Risk Modeling and Management
线性状况下
定义
Wrong-way risk: adverse correlation between a bond issuer and the bond insurer
影响p因素
nonfinancial variables
Sovereign debt and currency value
Geopolitical tensions
Correlated markets and economies
解决方法
Hedge
Multi-Asset Options
Option on the better of two. Payoff =max (S1, S2)
Option on the worse of two. Payoff =min (S1, S2)
只有这个是ρ越小越好
Call on the maximum of two. Payoff =max [0, max (S1, S2)-K]
Exchange option (as a convertible bond). Payoff =max (0, (S2-S1))
Spread call option. Payoff =max [0, (S2-S1) - K]
BulletOption on the better of two or cash. Payoff =max (S1, S2, cash )
Dual-strike call option. Payoff =max (0, S1-K1, S2-K2)
Quanto option
作用
Protects an investor against currency risk
原理
举例:中国投资一家美国的进出口公司
判断Option价值的两个要素
How deep in the money ( S和K的关系 )
Exchange rate
直接对冲ρ
Corelation Swap
方法
Fixed correlation <---> Realized/stochastic correlation
计算Realized/stochastic correlation
效果
子主题
间接对冲sigma(波动率)
原因:波动率和ρ存在正相关关系
方法
Buy Call On Index and Sell Call On Individual
Variance Swap
-pay fixed in a variance swap on an index and
-to receive fixed in variance swaps on individual components of the index.
-to receive fixed in variance swaps on individual components of the index.
一些结论
Equity Correlation
均值回归和趋势
非线性状况下
Copulas Function
目的
simplify statistical problems 简化统计过程
multiple univariate distributions —> single multivariate distribution
n-dimensional function \rightarrow unit-dimensional one
定义式
计算方法(了解)
正态分布(高斯Copulas)
推导过程
非正态分布(Mapping分布的思想)
推导过程
Academic Literature On Risk Measuring
理论
Time Horizon
取决于portfolio liquidity and purpose for risk measurement
accuracy of simple VAR measures diminish as time horizon lengthens
Backtesting VAR
less effective over longer time horizons
conditional backtests improve power of backtests
Liquidity Risk
Exogenous liquidity
transaction costs ---> "liquidity-adjusted VAR" approach
Endogenous liquidity
price impact ---> depends on trade size(move market prices)
外生流动性风险原因
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
实践
Compare Risk Measures Methods
Value at Risk(VAR)→not subadditive
Expected Shortfall→ subadditive
Spectral risk measures→generalization of expected shortal
bank's risk assessment framework
分解结构:compartmentalized approach
整体结构:unified approach
Top-down Vs. Bottom-up
top-down approach: risks are separable and can be aggregated in some way
bottom-up approach: better account for the interaction among risk factors
Risk Management Of Fixed Income and Option
The Science Of Term Structure Models
Bond Valuation
Discounted Future CF
计算
Cashflow是约定的,风险来自rate的变化 --> Duration衡量
Duration
利率平行移动
不含权,持有至到期不违约,CF确定
Mac. Duration
以现金流现值为权重
一般表达式
Mod. Duration
计算
BV01: 当Δy=0.01%时的Dollar Duration
关联:通过求导关联
推导过程
所有情况,可含权
Effective Duration
利率非平行移动
Key rate Duration
Convexity
特征
正负
含权债
Callable
可以为负值
Putable
More Convexity
不含权债
正值
涨多跌少
与 Duration关系:同涨同跌
影响因素(导致上涨)
Long Maturity(夜长梦多)
Low Coupon(钱少事多)
Low Yield(世道艰难)
当Duration相同时,CF越分散,Convexity越大
Portfoliop
Barbell
短期+长期,中期少(Convexty)比较大
Bullet
集中于中期
通过D和C求解的P和真实的P的关系(当Δy变化时)
Term Structure Models
固守工具分类
不含权债
含权债
Callable bond
Putable bond
不含权债期权
call on bond
put on bond
二叉树定价法
股票二叉树(一级内容)
二叉树求法
利率二叉树
结构
注意点
节点利率管后面的时间
每个节点现金流莫忘加入Coupon
分债券种类运算
Pure Bond
运算过程
运算过程
Callable / Putable Bond
运算过程
Option On Bond
分类
欧式
运算过程
注意
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
美式
运算过程
注意
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
取max(C0,C1),作为当前节点的期权价值,往前折现
为什么不用BSM求Option On Bond价值
BSM要求价格正态分布,也就是无上限
债券价格有上限
BSM要求无风险利率恒定
债券要考虑利率变动
BSM要求波动率恒定
债券波动率随到期日临近而趋于稳定
Term Structure Thoerys
Pure Expectation
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
Liquidity Preference
预期包含了liquidity premium
Market Segmentation
shape of the yield curve→>preferences of borrowers and lenders
Yield at each maturity is determined independently
Preferred habitat
forward rates represent expected future spot rates plus a premium(not related to maturity)
explain almost any yield curve shape
Term Structure Art : Drift
Model 1 : Model with no Drift
表达式
Model 2 : Model with Drift(有趋势项)
一般表达式
当λ时变时
Ho-Lee Model
表达式
当σ时变时
表达式
Model 3 : Mean Reverting
Vasicek Model
表达式
θ和λ的关系
参数含义
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
Cox-Ingersol-Ross(CIR)Model
适用情景:σ与r是相关的
表达式
Model 4 : Lognormal Model
原型表达式
变形表达式
表达式1
表达式2
注意点
Ho-Lee model, the drift terms are additive
Lognormal model, the drift terms are multiplicative
一些结论
Interest Rate Volatility
Volatility of expected rates causes the future spot rates to be lower
Convexity Effect(Jensen's inequality)
表达式
The value of convexity increases with maturity and volatility
Empirical Approaches To Risk Metrics And Hedging
DV01中性对冲
依赖利率平行移动假设:parallel assumption
改进方法:Regression Hege
好处
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
方法
一个对冲工具的推导
两个对冲工具的推导
PCA
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
Volatility Smiles
解决问题:BSM期权定价中,σ恒定的假设不满足
推导
怎样的资产价格是服从lognormal分布的
The volatility of the asset is constant
The price of the asset changes smoothly with no jumps
影响σ的因素
距离到期时长
执行价格(波动率微笑刻画)
波动率微笑
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
Alternative ways of characterizing the volatility smile
K/S0
Delta
没有Price Jump的波动率微笑
外汇
波动率微笑图像
价格分布图像(两边肥尾)
股票
波动率微笑图像
产生原因
leverage
Firm's equity value decreases→leverage
increases→increases the riskness/volatility of the underlying assets
increases→increases the riskness/volatility of the underlying assets
Crashophobia
stock market crash→higher premiums for put prices when the strike prices lower
价格分布图像(左肥右瘦)
有Price Jump的波动率微笑
波动率微笑图像
价格分布图像
Investment Risk
Investment Risk Management
Portfolio Construction
选资产
输入变量
Current Portfolio
已知且确定
Alphas
背景
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
Refine α
Method 1:Scaling Technique
Alpha = volitivity of α * Zα * IC(预测的准确程度)
推导过程
Method 2: Trimming 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 3: Neutralization
Benchmark Neutralization
目的:去除数据问题导致的Benchmark的收益不准确
Cash-Neutral Alphas
目的:去除保留现金带来的α,这部分是择时收益
Risk-Factor-NeutralAlphas
目的:消除基金经理运气导致的alpha
Alpha Converge
问题提出原因:Portfolio和Benchmark有部分重叠
处理方法
P有B没有
benchmark weight of zero
B有P没有
Alphas can be inferred
Covariance Estimates
一级的内容
Transaction Costs
MCVA
α - 2λ * σα * Δσα(MCAR)
-(cost of selling)< MCVA<(cost of purchase)
No-trade range for alpha
推导过程
Active Risk Aversion(风险厌恶)
Active Risk Aversion(λ) = IR/(2*σ of α)
推导过程
选资产的方法
Method 1: Screens
方法:直接根据α大小选出最好的资产
缺陷
lgnore all information
biases in the alphas
lgnore certain industry with low alpha
fails in addressing risk control purposes
Method 2:Stratification(分层)
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 3: Linear Programming
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 4: Quadratic Programming
Explicitly considers alpha, risk, and transactions costs.
● Ultimate approach(终极方法)
Dispersion问题
产生原因
Client Driven
PLack of attention to separate accounts
表现
同一基金经理在不同的客户账户上的投资表现不同
消失条件
交易成本为0
定权重
马科维茨有效前沿
图示
推导
Portfolio Risk
Portfolio VAR
常规的VAR
公式
变形
Diversified VAR
Undiversified VAR
衍生VAR
MVaR
含义:多投入i资产一单位,VaR的变化量
推导过程
Incremental VaR
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)
Component VaR
含义:i资产变化确定金额的数量Pi, VaR的变化
CVaR = MVaR(i) * Pi = β * VaR(P) * w(i)
Pecentage Contribution = CVaR(i) / VaR(P) = β * w(i)
Managing Portfolios Using VAR
Reducing positions with the highest marginal/ VAR.
Increase position with highest SR
Types Of Risk
Absolute Risk
Policy-mix risk
IPS决定的风险,是风险的主要构成
Active-management risk
执行偏差风险,相对较小
Relative Risk
Types
Cash-flow risk
Economic risk
Funding Risk
相当于资产与负债的组合,形成了相对风险
VAR And Risk Budgeting
VaR什么时候更有用
the horizon is short, turnover rapid, and leverage high
风险预算
原则:Top-down allocation
步骤
Budgeting across Asset Classes
maximize return at a targeted level of risk
Budgeting across Active Managers
weight of porfolio managed by manager i
Risk Monitoring And Performance Measurement
步骤
机构:RMU
注意:Liquidity duration
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
公式:LD = Q/(0.15V)
Q:需要交易的资产总量
V:一天内该资产的市场总成交量
Portfolio Performance Evaluation
目的:看完风险,也看看收益
考虑外部现金流(基金购入或赎回)的Return计算
Time-Weighted
计算思路:根据中间现金流时间切开时段
注意:T和切几段没有关系
not affected by cash inflows or outflows
Dollar-Weighted
就是求IRR
现金流可以有效控制时适用
Risk-adjusted Performance Measures
基础指标
Total Risk
Sharp Ratio
公式
M Square
公式
注意:M Square 和 SR的排序是一样的,求M不方便可以直接求SR
Systematic Risk
Treynor Ratio
公式
Jenson's Alpha
公式
Non-Systermatic Risk
Information Ratio
公式
高级计量
Market Timing(择时能力)
No Market Timing Model
表达式
特征:P和M线性相关
Treynor and Mazuy Model
表达式
特征:二次凸性,C>0时,Good Timing
Henriksson and Merton Model
表达式
特征:分段凸性,牛市D=1;熊市D=0
Call Option Model
Value of appropriate fee for perfect foresight should equal to the price of the call option on the market index
Style Analysis(风格分析)
分类:Value vs Growth / Large vs Small
方法:四因子回归,系数大的是显性风格
Performance Attribution(归因)
α来源分类
selection of the right asset classes(sectors)-选行业
selection of right securities within an asset class.-选个股
归因计算方法
附加话题
α假设检验
方法
对冲基金的分析困难
quickly change investment strategy
illiquid assets that are difficult to price
provide profits over a long period of time, but expose the fund to infrequent losses
Survivorship bias
Practical Topic(关于对冲基金)
Portfolio Choice With lliquid Assets(略)
Iliquid Assets Three key biases
Survivorship bias
Infrequent Sampling
Selection Bias
一个不全面的观点(flawed)
Economic theory states that there should be a premium for bearing illiquidity risk
major impacts of infrequent trading on asset allocation
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
Hedge Funds
Biases Of Hedge Funds
Measurement Bias
Backfill Bias
Survivorship Bias
Selection Bias(self-reporting bias)
Hedge Fund Strategies
Managed Futuress
CTA期货策略,CTAs tend not to have a particular bias towards being net long or net short in any particular market
Global Macro
盯住mis-pricing,top-down aproch,broad investment mandate,systematic or discretionary
Risk Arbitrage (Merger Arbitrage)
做空收购者,做多被收购者,风险为deal risk
Fixed Income Arbitrage
Exploiting inefficiencies and price anomalies between related fixed income securities
Convertible Arbitrage
long可转债,short股票,因为债有凸性,irrespective of market moves.
Long/Short Equity
invest in both long and short sides of equity,flexibility to shift investment styles
Dedicated Short Bias
take more short positions than long positions focus on companies with weak cash flow
Emerging Markets
投资新兴市场国家
Equity Market Neutral strategy
Returns differ dramatically across months. not behave like a single niche strategy. with a similar goal of achieving almost zero beta
Performing Due Diligence On Specific Managers And Funds
尽职调查的四个方面
Questions To Evaluate A Manager
Criteria To Assess Risk Management Process
Operational Due Diligence
Business Model Risk And Fraud Risk
Credit Risk
Introduction(识别)
The Credit Decision (略)
The Credit Analyst (略)
Introduction of Credit Risk
Credit Risky Securities
Credit Contract Frictions
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)
Default and Recovery
Expected Loss
PD*LGD*Exposure
比较风险债和无风险债
1+r vs PD*RR + (1-PD)(1+r+z)
EL = PD(1-RR)
UEL = 1-RR-EL
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
Market Risk 和 Credit Risk 辨析
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
4、Market to Market Risk 是中间地带,没有downgrade, 但市场其他债券也没有变化,是日间小变化导致的
Measurement(计量)
Credit VaR
定义
示意图
定义式
EL
Worse Credit Loss
UL (Credit VaR)
Credit VaR 和 Market Risk VaR的对比
Risk Contribution
Step1 EL and UEL of of individual asset
Step2 EL and UEL of Portfolio
Step3 Risk Contribution
一种简化变形
假设:每笔贷款有相同的规模和特征;ρ恒定
推导过程
当n趋于无穷大时
Step4 Economic Capital for Credit Risk
注意:Credit Loss分布是highly left skew, 实务中用Beta Distribution描绘
Key Parameter
PD
Historical-based Approach
Binomial Trees of PD
概念辨析
Marginal PD: 单年的违约率【d1, d2……】
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
规律
投资级别
Marginal PD 随时间变大,Cumulative PD增长速度随时间变大
投机级别
Marginal PD 随时间变小,Cumulative PD增长速度随时间变小
Credit Ratings
External Rating
评级体系图
Internal Rating
两种评级方法图示
Credit Transition Matrices
信用转移矩阵计算
Credit Scoring Models
Models
Point 1: Expert systems
5C法(不重要)
Point 2: Quantitative methodologies
Parameter Method
Fisher Linear discriminant analysis
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)
Parametric discrimination
思想:因变量是个概率值
典型例子:logit and probit model
Support vector machines
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
Non-Parameter Method
K-nearest neighbor approach
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
Point 3: Decision Rules
Probabilities Method
1、Minimum error
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
Optimization Method
2、Minimum risk
减少错误分类的概率及因此带来的Loss
3、Minimax
minimizing the maximum error or risk.
4、Neyman-Pearson
错误类型
Type I :误放
Type II :误杀
减少错误的指标(拉格朗日乘数:似然比)
公式:满足时拒绝
Model Performance
The receiver operating characteristic (Roc)
坐标系
X轴:False Alert Rate: Type II error / Good-Ones
Y轴:Hit Rate: Correctly Predict / Bad-Ones
图像
The cumulative accuracy profile (CAP GINI curve)
图像
决策规则:The accuracy ratio(AR) is defined as AR/(AR+AP), with a ratio close to 1 implying a more accurate model.
Retail Credit Risk Management
零售银行特征
敞口小
风险主要是EL,可以treat this loss as a cost of doing business
零售银行的Credit Models
Credit bureau scores
FICO
Pooled model
built by outside parties, is more costly than implementing a credit bureau score model; offers more flexibility to specific industry.
Custom model
created by the lender itself
Market Prices Approch
Infer Credit Risk from Corporate Bond Prices
PD的计算
Risk-Neutral Probability of Default: YTM-Rf = PD(1-LGD)
Objective probability of default:YTM-Rf-RP = PD(1-LGD)
推导过程
Credit Spread
类型
Yield spread
Bond 和 Benchmark的YTM的差
l-spead
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
Z-spread
不使用YTM,使用各自的Spot Rate计算
Option adjusted spread(OASs)
Z-spread adjusted for optionality of embedded options
Asset-swap spread
Float Notes, 支付Float收到Fix,因此产生的spread
CDS spread
Market premium of CDS of issuer bond
Discount margin
浮动利率债券Fixed spread above current LIBOR needed to price bond correctly
影响因素
宏观经济影响
路径
含权影响
路径
DVCS
DV01
定义:利率变动1个Bp, 价格变动的幅度ΔP
计算公式
DVCS(Spread 01)
定义:spread变动1个Bp, 价格变动的幅度ΔP
和DV01的对比
Credit Spread Curve
The first step to creating the curve is to plot the most liquid credit spreads observable in the market,generally from CDS premiums or bond spreads.
Plotting the curve is further complicated by the choice of reference.
An alternative method uses the credit spread around a single, liquid observation(e.g, credit spread with five years to maturity) to map the entire curve.
Infer Credit Risk from Equity Prices
Merton Model
基础理论
思想
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
公式推导
Credit Risk计量
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
σ公式推导
模型推论
Credit spread
计算
当Dt已知,根据简单折现方法获得Credit Spread
推导
当Dt未知,根据莫顿模型推导Credit Spread
推导
性质
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
Subordinate Debt in Merton Model
推导
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)
Calculate PD and LGD
PD = N(-d2) = 1-N(d2)
LGD = EL/PD ; EL用莫顿模型基本理论求解
假设和缺陷
假设
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.
7、Trading in markets occurs not only for the firm's equity and debt securities, but also for its assets.
8、There are no cash flows prior to the maturity of the debt (including dividends).
缺点
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.
The KMV Approach
放宽了莫顿模型两个假设
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
模型示意图
模型步骤
Step1 : 计算Asset到Default Line的距离DD
Default Line的算法
若LT/ST<1.5
若LT/ST>1.5
DD计算公式
Step 2 : Report estimated default frequency (EDF)
图中阴影部分违约概率
违约概率公式
思想:就是求N(-d2)
公式
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
Step 3 : 根据EDF确定Credit Rate
Other Issues
Rating Assignment Methodologies
Experts-based Approaches
Structured Experts-based System: 如4C, CAMPLS
Agencies'ratings
Experts-based Internal Ratings Used by Banks
Statistical-based Models
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
Heuristic and Numerical Approaches
Heuristic methods:使用人工智能算法
Numerical methods:highly complex environments下的最优化训练算法
Default Intensity Models
基础分布
Bernouli Trail
0/1分布
Binomial Distribution 二项分布
N个独立贝努里分别的概率分布
Poisson Distribution 泊松分布
λ 是1年平均违约概率
X = 0 的泊松概率是存活率
泊松分布表达式
一个例题
Exponential Distribution 指数分布
描绘违约发生平均需要等待的时间
表达式
β = 1/λ
λ就是Harzard Rate, β称为Sacle Parameter
Hazard Rates
定义
The hazard rate(i.e., default intensity )is represented by the(constant) parameter λ and the probability of default over the next small time interval, dt, is λdt.
已知λ时计算
Survival rate
Cumulative PD
Marginal PD
思路:是对Cumulative PD求一阶导
根据风险中性原理求λ
公式推导
近似公式
其中,z是CDS risk spread, 是可观察量
Hazard Rates Curve
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
LGD
Recover Rate 上升,LGD下降
影响RR的因素
EAD
Credit Exposure
Credit Exposure Metrics
基本概念
MtM
未来某时间点Market Value的期望(均值)
EE (Expected Exposure)
MAX (0, MtM)
PFE (Potential future exposure)
The worst exposure that could occur at a given time in the future at a given confidence level.
Maximum PFE
时间序列上最大的PFE
Expected positive exposure(EPE)
时间序列上EE的均值
Negative exposure
ENE
对手方视角的EPE
NEE
对手方视角的EE
Effecticve EE
单调不降的EE
Effective EPE
时间序列上Effecticve EE的均值
影响因素
Future uncertainty.
In situations where there is a single payout at the end of the life of a contract, uncertainty regarding the value of the final exchange increases over time.
Periodic cash flows
When cash flows occur regularly, the negative impact of the future uncertainty factor is reduced.
Combination of profiles
When the credit exposure of a product results from the combination of multiple underlying risk factors.
Optionality / Exercise decisions
Collateral
不同合约的Exposure Profiles
Interest Rate Swaps
两个效应
Diffusion effect(DE,扩散效应)
Interest rate uncertainty 上升→DE上升
Amortization effect(AE,摊销效应)
∶Bond's duration 上升→ AE上升
Exposure变化趋势
峰值的计算推导
在此基础上再求极值
Currency Swaps
推演过程
Other Security Types
Loans, Bonds and Repos
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
Credit Derivatives
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.
Options
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
Risk Mitigation Techniques
Netting
The benefit of correlation
Positive correlations have lower netting benefits
Negative correlations provide stronger netting benefits
Netting Factor
计算
Netting benefit improves(i.e, netting factor declines)with a larger number of exposures and a lower correlation.
Netting benefit also depends on the initial MtM of transactions.
Collateral
影响效果的因素
Remargin period
Exposure could increase between margin calls.
Threshold
Minimum transfer amount
Independent amout(initial margin)
Rounding
Counterparty Risk
Counterparty Risk Terminology
Credit migration
There is mean reversion in credit quality, so the implication is that counterparties with strong credit ratings tend to deteriorate and those with weak credit ratings tend to improve.
MtM
MtM=present value of all expected inflows less the present value of expected payments
缓释风险的手段
Close-out
立刻关闭与之所有协议
Collateralization (i.e., margining)
Walkaway feature
不再履行义务,亏损时有利
Mark-to-market
Diversification
Exchange and centralized clearinghouses
Netting
Hedging
Credit Value Adjustment (CVA)
定义
Expected value or price of counterparty credit risk. A positive value represents a cost to the counterparty that bears a greater propensity to default.
计算
Risky value= risk-free value-CVA
CVA Spread
This would be a charge to the weaker counterparty. CVA as a spread= Spread of CDX×EPE
影响因素
The CVA will most often increase given an increase in the credit spread.
However, the impact will not be linear because default probabilities are limited to 100% Ifa counterparty is very close to default, the CVA will actually decrease slightly and in default the CVA will fall to zero.
The CVA will be lower for an upward-sloping curve compared to a flat and a downward-sloping curve, and the CVA will be higher for a downward-sloping curve compared to a flat and an upward-sloping curve.
- Wrong-Way Risk Vs. Right-Way Risk
Wrong-Way Risk
PD和EAD正相关, CVA上升
Right-Way Risk
PD和EAD负相关 CVA下降
Credit VaR with a single-factor model
计算方法
Portfolio Credit Risk
Credit Risk Portfolio Models
四大实务模型
CreditMetrics (J.P. Morgan)
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
Moody's KMV
根据微观经济变化(企业股价变化)动态计量PD
CreditRisk+(Credit Suisse)
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
CreditPortfolioView
根据宏观经济因子动态计量PD,用Logit Model
对比
对比表
Default Correlation for Credit Portfolios
公式
推导过程
结论
缺点(Drawbacks)
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
Credit VaR & Default Correlation
Default corelation impacts the volatility and extreme quantiles of loss rather than the expected loss.
As a credit portfolio becomes more granular, the credit VaR decreases. However, when the default probability is low,the credit VaR is not impacted as much when the portfolio becomes more granular
Single Factor Model
目的:根据资产收益率的SFM推导ρ
公式
假设和推论
Assuming that each e, is not correlated with other credits, each return on asset, a, is a standard normal variate. The correlation between pairs of individual asset returns between two firm's i andj is β.B;
假设
βi相互独立
αi服从标准正态分布
推论
资产之间的ρ等于βiβj
Conditional Independence
Management(管理)
信用衍生品
Credit Default Swaps (CDS)
Credit Event
CDS原理:买保险,买Put Option
CDS结算方式
Physical delivery
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
Cash 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)
CDS的衍生形态
Basket credit default swap
First-to-default basket swap
Nth-to-default basket swap(N>=2)
定价模型:One-factor Gaussian copula model for time to default
Senior basket CDS & Subordinated basket CDS
结构图
CDS定价
基本原则:买CDS的PV = CDS赔付的PV
推导
CDS赔付的PV
买CDS的PV
Total Return Swaps(TRS)
结构
Vulnerable Option
Option holder receives the promised payment only if the value of the counterparty firm, V, is greater than the required payment on the option.
The payoff : Max[Min(V, S-X),0]
If ρ(V, s)is strongly negative then vulnerable option has little value. If ρ(V, S) is strongly positive then there is no credit risk.
Derivatives With Credit Risks-Swap
结构
Credit-Linked Notes
第一套思路
第二套思路
结构化信用产品
Structured Products介绍
Types
流程
典型结构
Waterfall Structure
Senior
Junior / Mezzanine
Equity
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
Credit Enhancements(信用增级)
Externa
insurance or wraps purchased from a third party
Internal
Overcollateralization (hard credit enhancement)
Excess spread (soft credit enhancement)
Subordinating note classes(tranches)
SPV Structures
Amortizing structure(摊销还款)
pass-through structure.
Revolving structures(循环贷款)
payments are not simply passed through.
Master trust structure(共享SPV池)
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
Performance Tools
绩效工具
Structured Credit Risk
结构化产品Credit Risk的影响因素
PD
Convexity
Senior: Negtive Convexity, 在低PD区不敏感,凹离原点
Equity: Positive Convexity, 凸向原点,在高PD区不敏感
Mezzanine: 在低PD区像S,在高PD区像E
对Credit VaR的影响
Correlation
对Value的影响
Equity: ρ上升,Equity Value上升
Senior:ρ下降,Senior Value上升
Mezzanine:ρ在低区像Senior, ρ在高区像Equity
对Credit VaR的影响
Other Factors
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.
几个概念
Default 01
计算
Implied Correlation
For securitized tranches, starting with observed market prices and a pricing function for the tranches, it is possible to back out the unique implied correlation to calibrate the model price with the market price.
Collateralized Debt Obligations(CDOs)
Cash-Flow CDOs
Synthetic CDOs
Risk Mitigation Techniques
Netting and Close-Out
Between Two Counterparties
Between Multiple Counterparties
Termination Features
Termination provisions 终止条款
Walkaway clauses
Trade compression
aims to reduce the gross notional amount and the number of trades
Collateral Management
Central Counterparties(CCP)
损失补偿顺序
Operational Risk
Operational Risk and Model Risk Management
Operational Risk★★★
Defining Operational Risk
风险因子
分类
People(human factor)
Internal processes
Systems
External events.
包含
Strategic risk and Reputational risk
不i包含
Legal risk
Assessing operational risk
计量方法
Basic Indicator Approach
公式
注意:α = 15%
Standardized Approach
计算公式
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
The advanced measurement approach(AMA)
计算方法
Unexpected loss in a total loss distribution that corresponds to a confidence level of 99.9% over a 1-year time horizon.
分布确定方法
LDA(Loss Distribution Approach)
Historical-based Loss Distribution
Parametric-based LDA
子分布
Loss Frequency: Poisson distribution
Loss Severity: lognormal distribution (asymmetrical, fat-tailed)
卷积过程
离散时
例题
连续时
Monte Carlo simulation Process.
General Steps of LDA
Step 1: Group loss data into a business line/event type matrix
Step 2: Assign every data point in the matrix an equal weight (except for split, old, and external losses and scenarios)
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
The overall operational risk capital requirement would combine the results in each of the cells(no diversification benefit)
Modeling Dependence
Within-cell dependencies & Between-cell dependencies
Gaussian copulas are often used.
Data Framework
Internal Loss Data
External Loss Data
Subscription Databases
Internal development
from media such as news or magazines.(reporting bias)
Consortium Data
Operational Risk data exchange Association(ORX)
Vendors
数据供应商
Scenario Analysis
Biases and Challenges: Presentation bias, Availability bias, Confidence bias, Huddle bias,Gaming and Inexpert opinion
Business Environment and Internal Control Factors
Risk Control Self-Assessment(RCSA)
Managing operational risk
Expected loss(EL)
Absorbed as an ongoing cost
Unexpected loss(ULl)
Capital
The stress loss
Insurance
Organizational Designs 组织机构
较好的组织结构
Model Risk ★★★
Sources of Model Risk
Common Model Errors
假设类错误
Common Model Implementation Errors
拟合类错误
Common Valuation and Estimation Errors
Inaccurate data.
Incorrect sampling period length.
Liquidity and valuation problems.
Supervisory Guidance on Model Risk Management
USE
Challenge from model users may be weak if the model does not materially affect their results
Such challenges tend to be asymmetric, because users are less likely to challenge an outcome that results in an advantage for them.
Model Validation
Three core elements
Evaluation of conceptual soundness, including developmental evidence.
Ongoing monitoring, including process verification and benchmarking.
Outcomes analysis
Case Studies
Long-Term Capital Management
London Whale
The 2005 Credit Correlation Episode
操作
Sell protection on the equity tranche of the CDX
Buy protection on the junior mezzanine tranche of the CDX.
Subprime Default Models 次贷违约
Principles for the Sound Management of Operational Risk
Three Lines of Defense
Business line management
Functionally independent corporate operational risk function(CORF):
Independent review
audit or by staff independent of the process or system
Relationship Between ORMF and ORMS
Capital Management
Risk Capital Attribution and Risk-Adjusted Performance Measurement ★★★
两个概念对比
RAROC
计算方法
RAROC Assumptions
RAROC Horizon
Practitioners usually adopt a one-year time horizon.
Default Probabilities
A through-the-cycle(TTC) probability of default is more commonly used for computations involving economic capital, profitability,and strategic decisions.
Confidence Level
The hurdle rate
意义:投资者要求的回报率,分为普通股和优先股
计算方法
决策规则:If RAROC>hurdle rate>value creation from the project and accepted.
Adjusted RAROC
计算方法
Adjusted RAROC= RAROC-β(Rm - Rf)
决策规则
If adjusted RAROC>Rf, then accept the project
Risk Capital and Diversification
A business unit that are highly correlated to the overall firm need to be allocated more risk capital
Practices and Issues in Economic Capital Frameworks
Integrated Risk Management
Enterprise Risk Management
Risk Appetite Frameworks
Risk Culture
Stress Testing Banks
Capital Planning at Large Bank Holding Companies
Resilience
Cyber Resilience
Operational Resilience
Liquidity and Treasury Risk
Foundations of Liquidity and Treasury Risk
Liquidity and Leverage
Definition of Liquidity Risk
Transaction liquidity risk
Problems with liquidating a position
"Liquidity black hole" Phenomenon
Predatory trading掠夺性交易
Transparency is important for liquidity
Funding Liquidity Risk(Balance Sheet Risk)
Risk that creditors either withdraw credit or change the terms that the positions have to be unwound and/or are no longer profitable.
Systemic Risk
In situations of severe financial stress
Measurement
Transaction Liquidity Risk
Characteristics used to measure market liquidity
Tightness
Bid-ask spread and brokers'commissions.
Depth
Resiliency (弹性)
The length of time for which a lumpy order moves the market away from the equilibrium price.
Adverse price impact
Slippage(滑点)
The deterioration in the market price induced by the amount of time it takes to get a trade done
Liquidity-Adjusted VaR
思路
VaR + Liquidity Cost (LC)
计算
Exogenous Price (外生价格影响)
思路:外生价格影响就是Bid-Ask-Spread
计算推导
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
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
the liquidity adjustment will increase(decrease)when there is an increase(decrease) in the spread, a decrease (increase) in the confidence level, and a decrease(increase) in the holding period
Endogenous Price (内生价格影响)
公式推导
E是弹性
Multiplying the effects
两种效应相乘
清仓时间调整
动机:因为每日逐步清仓,所以要对平方根法则进行调整
Funding Liquidity Risk
Indicators of Liquidity Risk
Term Spread.
LIBOR(3个月)- Fed funds(1天)
TED Spread
Eurodollor LIBOR(金融机构3个月) - Treasuries(政府3个月)
Liquidity at Risk(LaR)
也叫Cash flow at risk
VaR is concerned with a loss in value, LaR is concerned with a cash flow shortfall.
For example, a bond hedged with a futures contract has low VAR but high LAR
Factors that influence cash flow and LAR
Borrowing or lending
Margin requirements
Collateral obligations
Unexpected cash flows
Changes in risk management policy
Systemic Risk
Approaches to Estimating Crisis Liquidity Risk(了解)
Crash Metrics
推导公式
Worst-case outcome
Crisis-scenario analyses
Management
不同机构流动性管理方法
Commercial Banking
bank run and rollover risk
Hedge Fund
管理流动性风险方法
Cash
Unpledged assets are assets not currently being used as collateral
Unused borrowing capacity. This is not an unfettered source of liquidity
Money Market Mutual Funds(MMMFs)
The assets can still fluctuate in value
一种流动性管理方法
Financing gap = average amount of loans- average amount of core deposits
三个额外话题
Leverage
The Collateral Market
Margin loans
financing a security transaction in which the loan is collateralized by the security
Repurchase agreements
Are matched pairs of the spot sale and forward repurchase of security
Reverse repo transactions: finance long positions in securities, typically bonds
Securities lending
One party lends a security to another in exchange for a fee, called a rebate
The security lender continues to receive dividend and interest cash flows from the security
Total Return Swaps
Leverage ratio
推导过程
Margin Leverage
Repurchase Agreements and Financing
回购价格
i 是内生于买卖价差的,而不是事先约定的
Motivations for entering into repos
Borrower
Repos offer secured short-term financing; Repo financing is cheaper but less stable.
Repos offer relatively cheap sources of obtaining short-term funds.
Lender
Repos offer a low risk, collateral-secured investment opportunity
Lenders may also use repos(as the reverse repo side) to finance short positions in bonds.
The Collateral Market and Leverage
Collateral类型
Special collateral
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)
General 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
Special Spread
定义式:GC rate - Special rate
Special Spreads and the Auction Cycle(国债拍卖)
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 Rate Levels
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.
用Special Spread套利
套利价值公式
Liquidity Black Hole
定义
Liquidity black hole describes a situation where liquidity has dried up →As everyone wants to sell and no one wants to buy, or vice versa.
原因
The Behavior of Traders
交易者类型
Negative feedback traders
This creates demand(supply) for the asset that restores the price to a more reasonable level.The result is that the market is liquid.
Positive feedback traders
When positive feedback traders dominate the trading, market prices are liable to be unstable and the market may become one-sided and illiquid.
形成Positive feedback traders的原因
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
Leveraging and Deleveraging
加杠杆和去杠杆周期
Irrational Exuberance 非理性繁荣
Often the process is self-reinforcing.
The Impact of Regulation
A uniform regulatory environment comes with costs. All banks tend to respond in the same way to external events,
The Importance of Diversity.
Early Warning Indicators
Measures
Forward Looking Bias
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.
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
Escalation 升级上报
Reporting
Integrated Systems
Thresholds
The Failure Mechanics of Dealer Banks
主要原因:Diseconomies of Scope in Risk Management 规模不经济
缓释信用风险的方法
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.
和传统商业银行的区别
the linkages via counterparty chains 有对手方风险
dealer banks have no default insurance
too big to fail
Holistic Liquidity Risk Management Framework
Intraday Liquidity Risk Management
日内流动性用途
Outgoing wire transfers(the largest use) 对外电汇
Settlements, at PCS systems. 支付、清算、结算系统
Funding of nostro accounts 往来账
Collateral pledging. 保证金和抵押金
Asset purchases/funding. 购买资产
日内流动性来源
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.
Fed funds, London Interbank Offered Rate (LIBOR), and Eurodollar deposits.
Other term funding: Similar to overnight borrowing.
日内流动性管理
For Financial Institutions
Governance of Intraday LRM
three lines of defense model
Treasury is the first line of defense
Corporate Risk Management is the second line of defense
Internal Audit is the third line of defense
Measures for Understanding Intraday Flows
Measures for Quantifying and Monitoring Risk Levels
Daily Maximum Intraday Liquidity Usage
Intraday Credit Relative to Tier 1 Capital
Client Intraday Credit Usage
Payment Throughput 支付吞吐量
Role of Stress Testing
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
For FMUs
防线
The first line of defense is membership criteria 会员准入标准
Monitoring the risks of their participants is the second line of defense
工具
Net Debit Caps 对单一借款方的头寸限制
Collateral
Liquidity Savings Mechanism
Settlement Windows
staggered multiple settlement windows throughout the day. 错开结算时间窗口
Contingent Liquidity
A mechanism to facilitate settlement in the event of a participant failure: mutualizing the default risk
Monitoring Liquidity
A Taxonomy of Cash Flows
目的:对现金流根据时间和规模两个维度进行分类
结构图
Liquidity Options
定义
The right of a holder to receive cash from, or to give cash to, the bank at predefined times and terms.
和传统Option区别
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
流动性风险的新定义
现金流与预期有差别(不管高低),就是Risk
量的维度
成本维度(融资或投资成本)
Quantitative Liquidity Risk Measures
TSECF & TSECCF
定义
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
特点
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
缺点
Many of the CFs are stochastic, such that the TSECF always forecasts just the expected value of a distribution offlows
The temporal distribution could produce periods of negative cumulated cash flows
Liquidity Generation Capacity 流动性创造能力
分类
第一种分类法
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
第二种分类法
Balance sheet liquidity(BSL)
Selling of assets (AS)
Secured funding using assets as collateral and via repo (RP)
Remaining liquidity, relates to balance sheet expansion (security-unlinked non-BSL)
Unsecured funding via withdrawals of committed credit lines available (USF)
第三种分类法
In the banking book
All the bonds available for sale(AFS) and other assets that can be sold and/or Repoed relatively easily.
In the trading book
Add stocks and some structured products to generate liquidity
The term structure of LGC
TSLGC : 时间序列
TSCLGC:累计时间序列
The Term Structure of Available Assets
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 Expected Liquidity
目的:汇总现金流和创造现金流的能力
定义式
The TSL must always be positive if the financial institution has to be solvent all the time.
Cash Flows at Risk (CFaR)
定义:一定置信区间下极端现金流偏离TSECF的距离
定义式
方法:蒙特卡洛模拟
Term Structure of Liquidity-at-Risk (TSLaR)
定义:Collection of unexpected cash flows at each date, calculated as the difference between the minimum and the average level of cash flows
定义式
Liquidity Stress Testing and Liquidity Risk Reporting
Liquidity Stress Testing
流动性分类
Contingent liquidity
应急流动性,压力测试对象,是liquid asset buffer
Operational liquidity
日常运营流动性,无法满足压力状况下需求
Restricted liquidity
特定用途流动性,无法满足压力状况下需求
Strategic liquidity
Not primarily aimed at supporting the bank during times of stress. But may be redirected to meet contingent liquidity requirement needs.
压力测试模型的要素
Liquid asset buffer.
Contingent liquidity that is currently in place.
Stressed outflows.
They are those assumed to occur under stress scenarios.
Stressed inflows.
They are assumed to partially offset the stressed outflows.
Stressed liquid asset buffer.
Normal Liquid Asset Buffer-Stressed Cash Outflow +Stressed Cash Inflows
压力测试模型建立过程
Organizational Scope
目的:确定压力测试范围
业务单元划分维度
Liquidity transfer restrictions. 转移支付限制区域
Currency. 货币域
Regulatory jurisdiction. 监管区域
Planning Horizon
至少12个月时间窗口
现金流测算频率:初期需要每日预测
Testing Techniques
Historical statistical techniques(E.g. CFaR)
Deterministic models(E.g. hypothetical liquidity stress scenarios)
Monte Carlo simulation(A statistical technique)
Scenario Development
Historical Scenarios
Hypothetical 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
Development of Assumptions
要细分每一种情况
Outputs of the Model
输出内容: Stress testing assumptions; Liquidity position metrics; Prospective liquidity position metrics; Capital and performance metrics
Governance and Controls
The specific roles should consist of :Asset-liability committee;Treasury; Risk management; Internal audit; Model risk management.
Optimization
liquidity optimization opportunity
Liquidity vs. Yield
Liquidity vs. Capital
Funding optimization.
An incentive for banks to favor"sticky"funding sources 关注粘性融资渠道
Establishment a Sustainable Infrastructure
IT基础设施
Integration with Other Models
与capital stress testing整合
与asset liability management整合
Liquidity Risk Reporting
报告内容
Contingency Funding Planning(了解)
Governance and Oversight
Scenarios and Liquidity Gap Analysis
Contingent Actions
Market Signals and Reputational Impact
Monitoring
指向EWI
Escalation Levels
风险级别逐步升级管理
Data and Reporting
Day-to-day Techniques of Liquidity and Treasury Risk Management
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
International Perspective to Liquidity Risk Management
US Dollar Shortage in Global Banking and International Policy Response
Covered Interest Parity Lost: Understanding the Cross-Currency Basis
Basel Accord
Introduction of Basel Accord
Basic Terms
Risk-Weighted Assets (RWA)
计算方法:RWA=RW*NP
Expected Loss and Unexpected Loss
Evolution of Basel Accord
Basel I
Two capital requirements
Total assets to capital ratio had to be less than 20
Cooke ratio must exceed 8%.
风险加权资产的计算
Major limitations of Basel I
all corporate loans were treated the same regardless of the creditworthiness of the borrower
ignored the benefits of diversijfication.
Basel Il
FrameWork
Pillar 1: Minimum Capital Requirements
概要
Total capital=0.08x(credit risk RWA+market risk RWA+ operational risk RWA).
资本结构
三级资本划分
资本要求
基础要求
资本充足率计算方法
进阶要求
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.
资产分类
Bank Aseet
三类资产的风险计量
Credit
Standardized Approach
Risk weights based on external credit rating assessments.
评级-权重对应表
Collateral Adjustment
· 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
Internal Rating-Based(IRB) Approaches
EL的计算框架
模型推导
WCDR计算(Asymptotic Single Risk Factor(ASRF) Model)
ρ的计算(了解)
MA(Maturity Adjustment计算)
参数说明
计算UL的VaR参数
1-year 的99.9% VaR
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
LGD:FIRB下45%for senior claims and 75%for subordinated claims. If there is collateral, the LGD is reduced using the comprehensive approach
特例:Retail exposures
only a treatment like the Advanced IRB approach is used
特殊规定
Banks provide internal estimates of PD, LGD and EAD.
No maturity adjustment.
ρ分三种情况
ρ=0.15 for residential mortgages;
ρ=0.04 for qualifying revolving assets (mostly credit card balances);
other
ρ are lower for retail than for wholesale exposures
Market
Standardized Measurement Method
计算方法
缺点
It ignores correlations between the instruments.
Internal Models Approach
计算方法
参数
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是根据回测得到的模型准确性调整参数
m定值方法:基底是3,根据规则调增
Operational(详见操作风险章节)
Basic Indicator Approach
Standardized Approach
The advanced measurement approach(AMA)
Pillar 2: Supervisory
概要: Allow regulators from different countries some discretion in how they apply the rules.
涵盖的风险
第一支柱虽涉及但未完全涵盖的风险
Credit Risk
Concentration risk
Risk of Credit risk mitigation(CRM)
第一支柱未涉及的风险
Interest rate risk of banking
book Liquidity risk
Reputation risk
Strategic risk
Business risk
外部因素
Business bycle
Pillar 3: Market Discipline
要求
Increase transparency
Disclose more information about the risks
Basel II.5
Stressed Value-at-Risk(SVaR)& Incremental Risk Capital Charge
计算公式
参数
SVaR
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
IRC
计算方法
覆盖风险(内含信用风险部分)
default risk
credit migration risk for debt instruments.
99.9% confidence level over one year, computed on at least a weekly basis.(参考的是信用风险的方法)
发展:Comprehensive Risk Measure
CRM is a single capital charge for correlation-dependent instruments that replaces the specific risk charge(SRC) and the IRC.
Fundamental Review of The Trading Book
proposed an alternate measure using expected shortfall(ES)
every risk factor is assigned a liquidity horizon for capital calculations.
计算方法
To be allocated to the trading book, the bank must prove more than an intent to trade.
Basel III
改革总述
Raising capital standards, both in terms of quality and quantity.
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
1、Capital Definition
Tier 1 Capital
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 2 Capital
1. Debt subordinated to depositors with an original maturity of five years or more
2. Some preferred stock, such as cumulative perpetual preferred
取消了 Tier 3 capital.
2、资本金比例要求
Capital Conservation Buffer(CCB) 资本留存超额资本
Countercyclical Buffer 反周期超额资本
3、Operational Risk
Selecting Internal Loss Reference Dates
the date of the event's occurrence, the date of discovery, the date of contingent liability, the date of the first financial impact, and the date of the settlement.
operational risk management framework(ORMF)& operational risk measurement system (ORMS)
4、Leverage Ratios
The Committee will test a Tier 1 leverage ratio of 3%
5、Systematic Risk Management
systemically important institutions
6、Liquidity Requirements
Liquidity Coverage Ratio
目的:Promote short-term resilience of a bank's liquidity profile
计算公式
分子:High-Quality Liquid Assets(HQLA)
Level I assets
Cash, Central bank reserves, Marketable securities, Non-0% risk weightedsovereign or central bank securities.
Level2 assets
Level2A assets: A minimum 15% haircut is applied to the current marketvalue of each Level 2A asset
Level2B assets: Residential mortgage-backed securities, Corporate debt securities, Common equity. A greater haircut than Level 2A assets is applied
分母:Net Cash Outflows
net cash outflows=ouflows over the next 30 calendar days-min(inflows,75% of outflows)
Net Stable Funding Ratio(NSFR)
目的:Promote resilience over a longer time frame
计算公式
赋权方法
Liquidity Monitoring Tools
Contractual maturity mismatch
Concentration of funding
Available unencumbered assets
Liquidity coverage ratio by significant currency
Market-related monitoring tools
7、Risk Coverage
Reforms are intended to address CCR (counterparty credit risk), credit value adjustments(CVA) and wrong-way risk.
2017 Basel III
1. Standardised Approach for Credit Risk
使之颗粒度更细,更敏感的具体方法
2. Internal Ratings-based Approaches for Credit Risk
(1) Removing the use of the advanced IRB approach for certain asset classes
具体移除标准
(2) Specification of input floors: introduce minimum"floor"values for bank-estimated IRB parameters(PD,LGD,EAD)
(3) Additional enhancements
· for exposures secured by non-financial collateral, reducing the LGD parameters
· for unsecured exposures, reducing the LGD parameter from 45% to 40% for exposures to non-financial corporates
3. CVA Risk Framework
enhance its risk sensitivity
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
strengthen its robustness
Removes the use of an internally modelled approach, and consists of:(i) a standardized approach; and (il a basic approach.
improve its consistency
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.
4. Operational Risk Framework
假设
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.
计算方法
ORC(Minimum operational risk capital)=BIC*ILM
BIC
ILM
注意
A bank's internal loss data must be comprehensive and capture all material activities and exposures. The minimum threshold is set at E20,000.
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
5. Leverage Ratio Framework
系统重要性银行的杠杆率要求增加0.5%
如果不能满足整个指标体系中任意一项
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).
6. Output Floor
IRP计算的RWA须在(RWA,72.5%标准法计算的RWA)中取孰大
Solvency ll
与巴塞尔协议的区别
FrameWork
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.
VaR Parameters
巴塞尔协议
MR:99% 10天
CR/OR:99.9% 1年
Solvency
99.5% 1年
Risk Classes
So/vency II comprehensively assesses all quantitatively measurable risk types, all related to underwriting risk.
Minimum Capital Requirements
With Basel I/II, there is only one minimum equity capital ratio requirement
Solvency lI capital requirements use a two-level approach
· Solvency capital requirements(SCR)
· Minimum capital requirement (MCR):capital requirement is between 25-45% of the SCR.
Diversification(在什么层次做diversification)
Basel I/lll only considers LevelI diversification,Solvency I considers Level1,Level 2 and Level3 diversification
风险分层
Solvency lI Framework
Standardized approach: Analogous to Basel Il
Internal Models Approach: A VaR is calculated with a one-year time horizon and a 99.5% confidence level.
· Underwriting risk
· Operational risk
· Investment risk: divided into market risk and credit risk
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