IEOR 4700: Derman: Homework 1: January 27 2014
Page 1 of 2
Homework 1: January 27 2014
Due Monday Feb 3 2014.
Problem 1.
Total 100 points
[20 points]
Slowistan is a small island country whose currency is the US dollar. On Jan 1 2014 the price of a
stock S
IEOR 4700: Derman: Homework 5: February 24, 2014
Page 1 of 3
Homework 5: February 24, 2014
Due Monday Mar 3, 2014. More Problems may be added Wednesday
Total 100 points
Problem 1.
[20 points]
Suppose that y is the continuously compounded yield on a perpet
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
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 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 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
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
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, 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 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 4700: Derman: Homework 8: Wed April 9, 2014 Due Mon April 21, 2014.
Total 100 points
Homework 8: Wed April 9, 2014
Due Mon April 21, 2014.
Total 100 points
Problem 1. Delta
[10 points]
For a call C that satisfies the Black-Scholes formula with a divi
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
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
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 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 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
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
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
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(1)
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
Suggested Solutions to Assignment 8: Q1Q4
1. (a) The implied volatility is
T
t
(u)2 du
.
T t
(b) We have
1
0
2
0
(u)2 du
= 0.25,
10
(u)2 du
= 0.2,
20
from which we nd
2
2
2
1
2
(u)2
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
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 th
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, Fall 2013
Suggested Solutions to Final Examination
1. (a) r = 3%, = 25%, K = 48, S0 = 50, D = 5, t0 = 1.5/12. The adjusted
stock price is
S0 = S0 Dert0 = 45.0187.
As a result,
d1 =
ln(S0 /K) + (
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
Suggested Solutions to Assignment 5
1. [L] Chapter 12: Exercise 1
The payo of the long position of a call with strike price K1 is max(0, S(T )
K1 ), and the payo of the short positi
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
Suggested Solutions to Final Examination
1. Suppose the hedging strategy is to buy H(t) British pounds at time t [0, T ).
Consider the portfolio consisting of 1 shares of the option
IEOR E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
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 E4700 Introduction to Financial Engineering
Xuedong He, Spring 2013
Suggested Solution to Assignment 10
Assignment
1. Let S(t) and P (t, S(t) be the exchange rate and the value of the delta-neutralized
portfolio. Applying It lemma and recalling that