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 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
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
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
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 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