IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2012
Suggested Solutions to Assignment 2
1. [L] Chapter 3: Exercise 10
We have = 10%, c = 8%, m = 2, and n = 10 2 = 20. Using the duration
formula in the lecture notes, we have
D=
%
1 + 1
IEOR 4700: Homework 3
Chap 6.
problem 2. (Dice product)
Let a and b be the outcomes of two die rolls. Then z = ab.
By independence, we know
E [z ] = E [a]E [b] = 12.25
V ar[z ] = E [a2 ]E [b2 ] (E [a]E [b])2 79.97
=
problem 3. (Two correlated assets)
2
2
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2012
Final Examination
(150 minutes)
Return this problem sheet with your solutions. The number in the round bracket
at the end of each question is the points assigned to it. Please explai
IEOR 4700: Homework 2
Chap 3.
problem 10. (Duration)
Use the formula to obtain 6.84 years
problem 11. (Annuity duration)
Using P V = A we have
r
(1 + r) dP V
PV
dr
r(1 + r)
A2
=
A
r
D=
Hence
DM =
=
1+r
r
D
1
=
1+r
r
problem 12. (Bond Selection)
(a)PA = 88
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2012
Midterm Examination: Part I
(75 minutes)
Return this problem sheet with your solutions. The number in the round bracket
at the end of each problem is the points assigned to this prob
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2012
Suggested Solutions to Assignment 3
1. [L] Chapter 6: Exercise 2
Let X and Y be the random variables representing the resulting values of the
rst dice and second dice respectively. T
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2012
Suggested Solutions to Assignment 7
1. Let T T be the maturity of the futures contact and let F (t) be the future
price. Then F (t) = S (t)er(T t) . Suppose the number of shares of t
IEOR4700 Introduction to Financial Engineering
David D. Yao
Sample Final Examination
(150 minutes)
All problems are equally weighted.
1. Consider delta-hedging, applied to a European call option. Explain why at maturity T , the
value is always equal to 1
IEOR4700 Introduction to Financial Engineering
David D. Yao
Practice Midterm Examination
(150 minutes)
All problems are equally weighted.
1. Recall the relationship between the change in bond price (P ) and the change in yield ()
can be approximated as: P
IEOR4700 Introduction to Financial Engineering
David D. Yao, Fall 2009
Final Examination
(150 minutes)
Return this problem sheet with your solutions. All problems are equally weighted.
1. From the stock-price model (GBM), dStt = dt + dBt , we know dSt , t
IEOR4700 Introduction to Financial Engineering
David D. Yao
Practice Midterm Examination
(150 minutes)
All problems are equally weighted.
1. Recall the relationship between the change in bond price (P ) and the change in yield ()
can be approximated as: P
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Fall 2014
Suggested Solutions to Assignment 3
1. [L] Chapter 6: Exercise 2
Let X and Y be the random variables representing the resulting values of the
rst dice and second dice respectively. The
T70 Chapter 6 MEAN~VAR|ANCE PORTFOLEO THEORY
EXERCISES
The single efcient fund of risky assets F can be found by solving a system of
12 linear equations and n unknowns. When the soiution to this system is normaiized
so that its components sum to 1, the re
IEOR 4700: Homework 1
Chap 2.
problem 6. (Sunk cost)
The payment stream for apartment A is 1,000, 1,000, 1,000, 1,000, 1,000, 1,000 while
for B it is 1,900, 900, 900, 900, 900, 900. At any interest rate P VA < P VB because the
initial dierence is less tha
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
Homework Set 3
Due Feb. 14
Reading
[L] Ch6: Section 1-7.
Assignment
1. [L] Chapter 6: Exercise 2
(Dice product) Two dice are rolled and the two resulting values are multiplied
togeth
IEOR 4700: Homework 9
Chap 12
Problem 3 . (Parity formula)
Therefore,
Q = max[ 0, S K ] max[ 0, K S ] + K
= ( S K ) 0 + K = S if S K
= 0 ( K S ) + K = S if S K
Q = S.
Problem 4 . (Call strikes)
(a) Assume K 2 > K1 , and suppose to the contrary that C ( K
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
Suggested Solutions to Assignment 11
1. Plugging all the numbers in the formula in Slides 11 of the lecture notes:
F (t, T1 , T2 ) =
T2 t
T1 t
y0 (t, T2 )
y0 (t, T1 ),
T2 T1
T2 T1
w
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2012
Suggested Solutions to Assignment 9
1. One possible Matlab code for simulating the monthly log return for then years
is shown as follows:
% True annual expected growth rate and volat
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
Homework Set 11
Due May 2
Reading
Lecture notes;
[H] Ch4: Sections 1,3,6,7,10 and Chapter 7: Sections 1,4,7
Assignment
1. Suppose that spot interest rates with continuous compounding
IEOR4700 Introduction to Financial Engineering
David D. Yao
Practice Midterm Examination
(150 minutes)
All problems are equally weighted.
1. Recall the relationship between the change in bond price (P ) and the change in yield ()
can be approximated as: P
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2012
Midterm Examination: Part II
(75 minutes)
Return this problem sheet with your solutions. The number in the round bracket
at the end of each problem is the points assigned to this pro
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Fall 2013
Midterm Examination: Part I
(75 minutes)
Return this problem sheet with your solutions. Please explain the reasoning behind
your responses: answers will not be considered sucient if th
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Fall 2014
Homework Set 3
Due Sep. 25
Reading
[L] Ch6: Section 1-7.
Assignment
1. [L] Chapter 6: Exercise 2
(Dice product) Two dice are rolled and the two resulting values are multiplied
together
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2012
Suggested Solutions to Assignment 6
1. By It formula,
o
1
S (1) = S (0)e( 2
2 )+W (1)
= e0.12+0.4W (1) ,
where W (1) follows the standard normal distribution. Thus, we have
E ln S (
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2012
Suggested Solutions to Assignment 7
1. Let T T be the maturity of the futures contact and let F (t) be the future
price. Then F (t) = S (t)er(T t) . Suppose the number of shares of t
Lecture 12:
Derivatives: Forwards & Options
IEOR 4700: Introduction to Financial Engineering
Lecture 12: Forwards, Futures, Options
page 1/29
Schedule from here on out
1. Begin modeling futures, forwards and options (2 classes)
MIDTERM EXAM
Next longer ho
Lecture 15:
Options:
No Arbitrage Constraints
Black-Scholes PDE
Black-Scholes Solution
IEOR 4700: Introduction to Financial Engineering
Lecture 15: Options: No Arbitrage, BS PDE
page 1/36
Schedule from here on out
Makeup class on Fri March 28th, 501 NW, 9