P1.T2.504. Copulas (Hull)

Nicole Seaman

Director of CFA & FRM Operations
Staff member
Subscriber
Learning outcomes: Define copula, describe the key properties of copula and copula correlation. Explain one tail dependence. Describe Gaussian copula, Student t-copula, multivariate copula and one factor copula.

Questions:

504.1. In regard to copulas, each of the following is true EXCEPT which is false?

a. A copula is a way of defining the correlation between variables with known distributions.
b. Copulas cannot be used to define a correlation structure between more than two variables
c. The one-factor Gaussian copula model leads to very little tail dependence, which is a limitation of the model
d. The Gaussian copula is just one copula that can be used to define a correlation structure between marginal distributions; there are many other copulas leading to many other correlation structures.


504.2. Consider the following three statements about tail dependence:

I. Tail dependence is the tendency for extreme values for two or more variables to occur together
II. The choice of the copula affects tail dependence
III. The tail dependence is higher in a bivariate Student t-distribution than in a bivariate normal distribution.

Which of the above is (are) true?

a. None are true
b. Only I. is true
c. Only III. is true
d. All are true


504.3. Suppose that a bank has a total of $100.0 million of retail exposures of varying sizes with each exposure being small in relation to the total exposure. The one-year probability of default (PD) for each loan is 3.0% and the loss given default (LGD) for each loan is 60.0%. The copula correlation parameter, rho(ρ), is estimated as 0.250. Which is nearest to an estimate of the value at risk with a one-year time horizon and a 99.9% confidence level? (note: this is a variation on Hull's example 11.2)

a. $8.41 million
b. $12.57 million
c. $20.95 million
d. $36.72 million

Answers here:
 

Juun

New Member
Subscriber
Hi there,

I am a little confused here... is this AIM related to Part I or Part II of the exam ?!

Ok, my bad... I have just checked it was included in Part 1 of 2015 program...
 
Last edited:

ShaktiRathore

Well-Known Member
Subscriber
Hi all,

Could anyone elaborate on answer to 504.3?
Hi
Variance of each exposure=.03*.97=.0291=>std of each exposure=sqrt(.0291)=.1706
Variance of all portfolio of assets=corr*.0291=.25*.0291=>vol of portfolio=sqrt(.25*.0291)=.5*.1706=.0853
Var of portfolio=-z*vol of portfolio+El of portfolio=3*.0853-.018=.2546-.018=.2366
Var in value=.2366*100=23.66 mn $~20.95
Please tell if answer is correct
Thanks
 
Hi
Hi
Variance of each exposure=.03*.97=.0291=>std of each exposure=sqrt(.0291)=.1706
Variance of all portfolio of assets=corr*.0291=.25*.0291=>vol of portfolio=sqrt(.25*.0291)=.5*.1706=.0853
Var of portfolio=-z*vol of portfolio+El of portfolio=3*.0853-.018=.2546-.018=.2366
Var in value=.2366*100=23.66 mn $~20.95
Please tell if answer is correct
Thanks

Hi Shakti,
Thanks for your help buddy. You always help us out whenever we are stuck :) . Really appreciate that and BTW Happy Holi!!!! :)

I guess the question belongs to the Vasicek's model which i am a little confused about since, nowhere in the manual it is mentioned to be in course..

However, i guess the solution goes on by calculating the Worst Case Default rate which is=N{[N^-1(PD)+rho^0.5(0.999)]/(1-rho)^0.5}

so WCDR=0.3516, putting in the values given.

Losses when this worst case loss rate occurs are = 100*0.3516*0.6 or $21.09 million.

But i am afraid that the answer C is inaccurate.

David/Nicole pls help us on this..
 

ShaktiRathore

Well-Known Member
Subscriber
Hi happy holy,
Yes answer C seems inaccurate from the actual result u r getting,but questions asks for the nearest estimate of the Var not the exact please read the q again
Thanks
 

Nicole Seaman

Director of CFA & FRM Operations
Staff member
Subscriber
Hello @nonies,

We are currently working very hard to prepare the materials that are new to the 2015 curriculum. Please see our forum announcement HERE for more information on our process of updating materials.

Thank you,

Nicole
 

Shazam023

New Member
@Nicole Manley
i'm not able to open the answers link. its saying:-
Bionic Turtle - Error
You must be logged in and have the appropriate permissions to perform this action.

Note: If you can see a link in the top-right corner of the screen that says "Log in or Sign up" please click that to login.

and i m already logged in. so where to get correct answers???
 

Nicole Seaman

Director of CFA & FRM Operations
Staff member
Subscriber
@Nicole Manley
i'm not able to open the answers link. its saying:-
Bionic Turtle - Error
You must be logged in and have the appropriate permissions to perform this action.

Note: If you can see a link in the top-right corner of the screen that says "Log in or Sign up" please click that to login.

and i m already logged in. so where to get correct answers???

Hello @Shazam023

I looked up your account, and did not find a purchase associated with this account. The answers to our daily practice questions are available to paid members only. You can view all of our study packages HERE on our website. Once you are a paid member, you gain full access to the entire study planner, which includes the answers to all daily practice questions, plus you receive all of the benefits that your study materials have to offer :)

Thank you,

Nicole
 
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