IEOR 4731 Credit Risk and Credit Derivatives (Spring 2012)
Solutions to Assignment 2
Instructor: Xuedong He
TA: Juan Li
Answer 1
B (t, T ) = E Q [e
EQ[
T
t
r (u)du
|Ft ]. For 0 < s < t
t (H )
B (t, T )E Q [H |Ft ]
s (H )
|Fs ] = E Q [
|Fs ] = E Q [E Q [H
IEOR E4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2012
Homework Set 2
(Due Feb. 23)
Reading
Textbook: Sections 3-4 in Chapter 3.
Suggested Reading
Reference book: Chapter 2.
Assignment
Let r(s), s 0 be the spot short interest rate and Q be t
IEOR E4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2012
Suggested Solution to Midterm Exam
1. Using Merton model, we obtain the current price of the debt
D0 = V0 N (d1 ) + LerT N (d2 ),
where
d1 =
1
ln(V0 /L) + (r + 2 2 )T
,
T
d2 = d1 T .
It
IEOR 4731: Credit Risk/Derivatives (Spring 2011)
Solutions to Assignment 5
Columbia University
Instructor: Xuedong He
TA: Jinbeom (JB) Kim
Answer 1
This problem is similar to Question 6, and 7 in Homework 4. We can easily get the result just by changing
m
IEOR E4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2012
Midterm Exam: Part I
Duration: 1 hour and 15 minutes
Return this problem sheet with your solutions. Please explain the reasoning behind
your responses: answers will not be considered suc
IEOR E4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2011
Final Exam
Duration: 2 hour and 30 minutes
Return this problem sheet with your solutions. Please explain the reasoning behind
your responses: answers will not be considered sucient if th
Columbia University
M.S. in Financial Engineering
Spring 2007
IEOR 4731: Credit Derivatives
Instructor: Rama CONT
MIDTERM Exam: Solution
We shall use a constant interest rate r and a constant nominal recovery rate of
R. All spreads/rates are annualized an
Suggested Solution to HW 4
1. See m-le: HW4.m. The risk-neutral default intensity = 2%.
2. See m-le: HW4.m. The risk-neutral expected tranche loss is 0.61485% of the
portfolio notional value.
3. See m-le: HW4.m. The risk-neutral expected tranche loss is 0
IEOR 4731 Credit Risk and Credit Derivatives (Spring 2012)
Solutions to Assignment 3
Instructor: Xuedong He
TA: Juan Li
Answer 1
B (t, T ) = er(T t) , Q(t, T ) = e(T t) , N = 1, t = 1/4, n = 4T , Ti = it, i = 1, 2, . . . , n.
The value of premium leg is:
IEOR E4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2012
Midterm Exam: Part II
Duration: 1 hour and 15 minutes
Return this problem sheet with your solutions. Please explain the reasoning behind
your responses: answers will not be considered su
IEOR E4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2012
Homework Set 5
(Due Apr. 26)
Reading
Textbook: Sections 16 in Chapter 14; Sections 14 in Chapter 19; Sections 14 in
Chapter 20.
Assignment
1. Compute the coecients of tail dependence for
IEOR E4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2012
Homework Set 3
(Q1-5 are due Mar 1 and Q6-8 are due Mar 22)
Reading
Textbook: Sections 5-10 in Chapter 3; Sections 1-3 in Chapter5; Sections 1-8 in
Chapter 6; Chapter 7
Assignment
A CDS
IE4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2011
Suggested Solution to Midterm Exam
1. Using Merton model, we obtain the current price of the debt
D0 = V0 N (d1 ) + LerT N (d2 ),
where
d1 =
1
ln(V0 /L) + (r + 2 2 )T
,
T
d2 = d1 T .
It is e
IE4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2011
Midterm Exam, Part II
Duration: 1 hour and 15 minutes
Return this problem sheet with your solutions. Please explain the reasoning behind
your responses: answers will not be considered sucien
IE4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2011
Midterm Exam, Part I
Duration: 1 hour and 15 minutes
Return this problem sheet with your solutions. Please explain the reasoning behind
your responses: answers will not be considered sucient
IEOR E4731 Credit Risk and Credit Derivative
Xuedong He, Spring 2011
Suggested Solution to Final Exam
1. (a) The portfolio loss is
L(t) = (1 R)
1 (F (t)
1
Z
(b)
M
1
E [L(t)] =
lim E
M +
M
Q
Q
= lim E
M +
1
= lim
M + M
j =1
M
1
M
Q
1
= lim
M + M
1j t
1j t
Columbia University
IEOR 4731: Credit Derivatives
Instructor: Rama CONT
M.S. in Financial Engineering
Spring 2007
TA: Romain DEGUEST and KAN Yu Hang.
MIDTERM Exam.
Duration: 2 hours 15 minutes. No documents allowed.
Please explain the reasoning behind you