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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

Cashflow mapping

the risk of fixed-income instruments is decomposed into the 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.

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

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

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.

<ol><li>Wrong-Way Risk Vs. Right-Way Risk</li></ol>

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