开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

梦梦 · 2025年05月17日

有三个地方不明白

NO.PZ2024042601000100

问题如下:

A CRO at an investment bank has asked the risk department to evaluate the bank’s 3-year derivative exposure position with a counterparty. The 1-year CDS on the counterparty is currently trading at a spread of 180 bps. The table below presents trade and forecast data on the CDS spread, the expected exposure, and the recovery rate on the counterparty:

Additionally, the CRO has presented the risk team with the following set of assumptions to use in conducting the analysis:

Counterparty’s default probabilities follow a constant hazard rate process

The investment bank and the counterparty have signed a credit support annex (CSA) to cover this exposure, which requires collateral posting of AUD 13 million over the life of the contract

The current risk-free rate of interest is 2% and the term structure of interest rates will remain flat over the 3-year horizon

Collateral and exposure values will remain stable over the life of the contract

Given the information and the assumptions above, what is the correct estimate for the credit valuation adjustment for this position?

选项:

A.

AUD 0.140 million

B.

AUD 0.863 million

C.

AUD 1.291 million

D.

AUD 2.514 million

解释:

To derive the credit valuation adjustment (CVA), we use the standard formula:


Where (at any time t),

• The discount factor (DFt) is determined from the risk-free rate of 2%; and

• The hazard rate = Spread/(1 – RR) = (180/10,000)/(1 – 0.85) = 12% (true for years 2 and 3);

• The probability of default is derived from its relationship with the constant hazard rate (λ) ,

PD(t)=1-exp(-λt).

For instance, PD(1)=1-exp(-0.12*1)=11.31% (Marginal probability (PD1))

PD(2)=1-exp(-0.12*2) = 21.34%; Marginal probability (PD2)=21.34%-11.31%=10.03%

PD(3)=1-exp(-0.12*3) = 30.23%; Marginal probability (PD3)=30.23%-21.34%=8.89%

• Collateral amounts of AUD 13 million for year 2 and AUD 13 million for year 3 are considered.

Hence, the rest of the derivation becomes:

(Expected Exposure, Collateral, and CVA in AUD million)

1、听经典题视频,答案应该是0.33,这里没有

2、给的条件有cds,有EE,有rf可以把EE折现

为什么不能用cva=cds*pv(EE)?

3、为什么每一年的pd是用1-e^(-入*1),而不是用非条件概率,也就是第一年的违约概率,不管第一年是否违约,第二年的违约概率e^(-入*1)—e^(-入*2)这种?1-e^(-入*2)既不是条件违约概率也不是非条件违约概率吧?就是指第二年末之前的违约概率?

1 个答案

pzqa27 · 2025年05月19日

嗨,努力学习的PZer你好:


1、听经典题视频,答案应该是0.33,这里没有

视频那个解析算法是对的,但是计算结果错了,请按讲义和题目来,这里已经修复过了。


2、给的条件有cds,有EE,有rf可以把EE折现 为什么不能用cva=cds*pv(EE)?

因为这个算法计算出来更精确一些,cds spread x EPE算出来是一个近似的结果,解析这个算法是按照CVA的定义进行计算的。


3、为什么每一年的pd是用1-e^(-入*1),而不是用非条件概率,也就是第一年的违约概率,不管第一年是否违约,第二年的违约概率e^(-入*1)—e^(-入*2)这种?1-e^(-入*2)既不是条件违约概率也不是非条件违约概率吧?就是指第二年末之前的违约概率?

这里肯定用的是边际违约率,而不应该用条件违约率, 根据讲义上的定义,这里计算CVA的PD应该是j-1和j之间的违约率,没有任何条件,所以是边际违约率。

----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

梦梦 · 2025年05月19日

“e^(-入*1)—e^(-入*2)”是条件违约概率?条件违约概率不应该是e^(-入*1)—e^(-入*2)除以e^(-入*1)吗?

  • 1

    回答
  • 0

    关注
  • 8

    浏览
相关问题

NO.PZ2024042601000100 问题如下 A CRO investment bank haskethe risk partment to evaluate the bank’s 3-yerivative exposure position with a counterparty. The 1-yeC on the counterparty is currently trang a spreof 180 bps. The table below presents tra anforecast ta on the C sprea the expecteexposure, anthe recovery rate on the counterparty:Aitionally, the CRO hpresentethe risk tewith the following set of assumptions to use in concting the analysis:• Counterparty’s fault probabilities follow a constant hazarrate process• The investment bank anthe counterparty have signea cret support annex (CSto cover this exposure, whirequires collaterposting of AU13 million over the life of the contract• The current risk-free rate of interest is 2% anthe term structure of interest rates will remain flover the 3-yehorizon• Collateranexposure values will remain stable over the life of the contractGiven the information anthe assumptions above, whis the correestimate for the cret valuation austment for this position? A.AU0.140 million B.AU0.863 million C.AU1.291 million AU2.514 million To rive the cret valuation austment (CVA), we use the stanrformula:Where (any time t),• The scount factor (t) is terminefrom the risk-free rate of 2%; an• The hazarrate = Sprea(1 – RR) = (180/10,000)/(1 – 0.85) = 12% (true for years 2 an3);• The probability of fault is rivefrom its relationship with the constant hazarrate (λ) ,Pt)=1-exp(-λt). For instance, P1)=1-exp(-0.12*1)=11.31% (Marginprobability (P))P2)=1-exp(-0.12*2) = 21.34%; Marginprobability (P)=21.34%-11.31%=10.03%P3)=1-exp(-0.12*3) = 30.23%; Marginprobability (P)=30.23%-21.34%=8.89%• Collateramounts of AU13 million for ye2 anAU13 million for ye3 are consireHence, the rest of the rivation becomes: (ExpecteExposure, Collateral, anCVA in AUmillion) 为什么不能用CVA的另一个计算方法 CVc sprex EPE, 然后再折现

2024-11-02 19:26 1 · 回答

NO.PZ2024042601000100 问题如下 A CRO investment bank haskethe risk partment to evaluate the bank’s 3-yerivative exposure position with a counterparty. The 1-yeC on the counterparty is currently trang a spreof 180 bps. The table below presents tra anforecast ta on the C sprea the expecteexposure, anthe recovery rate on the counterparty:Aitionally, the CRO hpresentethe risk tewith the following set of assumptions to use in concting the analysis:• Counterparty’s fault probabilities follow a constant hazarrate process• The investment bank anthe counterparty have signea cret support annex (CSto cover this exposure, whirequires collaterposting of AU13 million over the life of the contract• The current risk-free rate of interest is 2% anthe term structure of interest rates will remain flover the 3-yehorizon• Collateranexposure values will remain stable over the life of the contractGiven the information anthe assumptions above, whis the correestimate for the cret valuation austment for this position? A.AU0.140 million B.AU0.863 million C.AU1.291 million AU2.514 million To rive the cret valuation austment (CVA), we use the stanrformula:Where (any time t),• The scount factor (t) is terminefrom the risk-free rate of 2%; an• The hazarrate = Sprea(1 – RR) = (180/10,000)/(1 – 0.85) = 12% (true for years 2 an3);• The probability of fault is rivefrom its relationship with the constant hazarrate (λ) ,Pt)=1-exp(-λt). For instance, P1)=1-exp(-0.12*1)=11.31% (Marginprobability (P))P2)=1-exp(-0.12*2) = 21.34%; Marginprobability (P)=21.34%-11.31%=10.03%P3)=1-exp(-0.12*3) = 30.23%; Marginprobability (P)=30.23%-21.34%=8.89%• Collateramounts of AU13 million for ye2 anAU13 million for ye3 are consireHence, the rest of the rivation becomes: (ExpecteExposure, Collateral, anCVA in AUmillion) 这里的折现因子公式和计算过程可以列举下嘛跟我算的折现因子不一样

2024-11-02 16:47 2 · 回答