1. Credit Risk Analysis信用风险分析

Fundamentals of Credit Risk

• Define Credit Risk:
  • The possibility of losing money due to the inability, unwillingness or no timeliness of a counterparty to honor a financial obligation.
• Entities are Exposed to Credit Risk
  • Bank
  • Asset managers
  • Hedge funds
  • Insurance company
  • Pension Fund
• Classifications:
  • Default Risk
  • Recovery Risk
  • Exposure Risk
• CAMEL system
  • Capital
  • Asset
  • Management
  • Earning
  • Liquidity
  • Disadvantage:
    • management不好分析
    • Asset可能有水分，表外asset

Governance

• Three Lines of Defenses
  • First Line: Business owners who primarily own and manage risk
  • Second line:
  • Third line:

Credit Risk Management

• Three drivers
  • PD Probability Default
  • EAD Exposure at Default
  • LGD Loss given Default
• Credit Var: 非预期损失 Unexpected loss as the worst case portfolio loss at a given confidence level over a specific holding period
  • $EL = PD*(1-RR)*EAD = PD*LGD*EAD$
  • 一定置信水平下的worst case loss.
  • Credit →loss distribution →有偏的分布
• Default correlation

  • 两个资产的违约相关性

    原始笔记这里引用了信用风险资本结构示意图，但图片文件没有随 organise 一起提供；后续可补一张“银行资本结构/清偿顺序”图。

  • 4中情况 $\pi$几代表哪个会违约

  • $\rho = \frac{Cov(x_1,x_2)}{\sigma_1\sigma_2}$

  • ρ等于零的时候， 及$\pi_{1,2} = \pi_1\pi_2$ 可以视为独立事件

  • 违约发生次数可以用二项分布建模（违约，不违约）

Capital Structure in Banks

• steps to derive Economic Capital for Credit Risk
  • EL expected loss
  • Unexpected Loss 就是credit Var
  • Unexpected Loss Contribution
  • Economic Capital
• $UL = EA*\sqrt{PD*\sigma^2_LR+LR^2*LR_{PD}^2 * \sigma^2}$
• 非预期损失某一个资产的贡献：ULMCi
  • $ULMC_i = \frac{\delta UL_p}{\delta UL_i}$
• 债券法计算违约概率
  • 精确式：$\frac{1}{(1+YTM)^T} =\frac{PD*RR+1*(1-PD)}{1+R_f}$
  • $PD = \frac{1}{LR}(1-\frac{1+Rf}{1+YTM})$
  • 近似式：$PD*LD = YTM - R_f = CS$
• 股票法计算违约概率
  • Merton Model:
    • 股东方：
      • V<K 资不抵债，股东方拿0
      • V>K 股东拿V-K
      • 想象是一个执行价格为K的Call
      • $E=VN(d_1)-Ke^{rT}N(d_2)$
    • 债券人：
      • V>K 债券人拿K
      • V<K 债券人拿V
      • K-min(V,K) 想象成是标的资产是V(资产价值), 执行价格K(债务面值)
      • $D=VN(-d_1)-Ke^{-rT}N(d_2)$
  • 莫顿模型用了BSM的假设
    • V~lognormal，不服从估计不准确
    • 欧式，不能提前
    • 连续，不能解释突发的
  • PD= P(V<K) = N(-d2)
    • K: default point
    • d_2: distance to default
    • $d_2 = \frac{ln(V/{Ke^{rT})}}{\sigma \sqrt{T}}$ 近似式只能在T=1 时候使用 $d_2 = \frac{ln(V)-ln(K)}{\sigma }$
  • Credit Spread: Merton → Debt Value = D Face Value = F
    • $CS = -(\frac{1}{T-t})ln(\frac{D}{F})-r$
  • Moody's KMV model 对莫顿模型补充，有时候莫顿模型需要的条件没办法满足
    • 1， 计算Distance to Default (DD)
      • K可确认分短期和长期 （对于长短期限的债券需要调整权重）
        • Long Term > Short Term: ST + 1/2LT
        • Long Term < Short Term: 0.7 ST + 0.7 LT
      • 把DD带入到历史数据中
        1. 直接用d2
        2. Moody’s $DD = \frac{V-K}{\sigma_V}$
  • 指数分布：建模时间（发生在这个时间段之内的概率）
    • Hazard Rate: the Rate at which default will arrive (*看到hazard rate大概率是指数分布）
    • $P(t^*<t) = 1-P(x=0) = 1-e^{\lambda t}$
    • 存活率+违约概率=1
    • 联合概率：Marginal default probability
    • 条件概率 ： given， conditional on； 前期不违约，后期违约，无记忆性
    • λ通常需要估计，根据risk-neutral 估计，用市场价格，债券法估计
• Single Factor Model单因素模型
  • 主要解决计算相关性的问题

Introduction to Credit Risk Modeling and Assessment

• 建模分析
  • Experts-Based
  • Statistical-Based
  • Heuristic and Numerical Approach (AI) 模型训练集
• Rating System评级系统
  • 直接使用
  • 借鉴计算
  • Good Rating System
    • 可测量性Measurability，可验证性 Verifiability
    • 客观性Objective，同质性Homogeneity
    • Specificity
  • Moody‘s(穆迪), S&P(issuer), FITCH （AAA）
    • 累积PD违约概率
    • Transition Matrix: 对于未来评级变化进行估计，每次评级变化是独立的
• 借鉴计算Measurement of PD in Rating System
  • Cumulative Default probability
    • probability that a borrower will default over a specified multi-year period.
  • Marginal Default probability(联合概率，前期不违约，后期违约）
  • Survival Rate: 第一期不违约，第二期不违约…

Credit Scoring and Rating

Credit Scoring and Retail Credit Risk Management

Country Risk: Determinants, Measures, and Implications

• 交易对手风险，主要：OTC derivatives
  • 交易对手风险量化（counterparty Risk CVA and DVA)
    • CVA，BCVA对风险中性的价格进行调整，用历史违约来计算，直接在value上进行调整
    • Exit price. Market implied (risk-neutral) parameters.
    • Market-implied default probability 是通常比历史数据要高的
    • Value adjustment 对未来预期损失的定价
      • $C V A= \sum PV EL_i = LR*\sum EE_i*PD_i$
      • 组合需要知道总的价格和单个价格
        • incremental CVA: 加入一笔资产对CVA的影响
        • Marginal CVA：每一笔交易对于组合的贡献程度
  • wrong way risk 敞口和PD之间的关系，导致CVA变化：PD 上升，exposure上升
    • CVA 的假设没有
    • 如果有的话需要考虑相关性
    • 常见模型：
      • Intensity Approach: 指数分布simulation
      • Structure Approach: 建立PD和敞口的分布，得到联合的2元分布
      • Parametric Approach
      • Jump Approaches

2. Credit Risk Estimation信用风险估计

Estimating Default Probabilities

Credit Value at Risk

Portfolio Credit Risk

Structured Credit Risk

Credit Derivatives

3. Counterparty Risk Management对手风险管理

Derivatives

Counterparty Risk, CVA, Stress Testing

Netting, Close-Out, (Collateral) and Settlement

Structured Credit Risk and Securitization

• Mitigating Approaches

贡献者: kai

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