Math 623, W 2007: Homework 4.
For full credit, your solutions must be clearly presented and all code included.
Time is counted in years and the interest rate is r = 2%, continuously compounded.
(1) In this problem you are asked to value an out-of-the-mone
Lectures in Functional Analysis
Roman Vershynin
Department of Mathematics, University of Michigan, 530 Church
St., Ann Arbor, MI 48109, U.S.A.
E-mail address : romanv@umich.edu
Preface
These notes are for a one-semester graduate course in Functional Analy
Math 623 (IOE 623), Fall 2011: Final exam
Name:
Student ID:
This is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam. You may also
use a calculator but not its memory function.
Please write all your solutions in this exa
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Math 623 (IOE 623), Fall 2011: Final exam
Name:
Student ID:
This is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam. You may also
use a calculator but not its memory function.
Please write all your solutions in this exa
Math 623 (IOE 623), Fall 2008: Final exam
Name:
Student ID:
This is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam. You may also
use a calculator but not its memory function.
Please write all your solutions in this exa
Math 623 (IOE 623), Fall 2007: Final exam
Name:
Student ID:
This is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam. You may also
use a calculator but not its memory function.
Please write all your solutions in this exa
Term-Structure Models: a Review
Riccardo Rebonato
QUARC (QUAntitativeResearch Centre) - Royal Bank of Scotland
Oxford University - OCIAM
February 25, 2003
1
1.1
Introduction
Justication for Another Review of Interest-Rate Models
The topic of term-structur
MATH 572
hw#1
Numerical Methods for Scientic Computing II
Winter 2005
due: Tuesday, January 25
0. Write a brief description of your scientic interests and/or reasons for taking this course.
If you work in a lab or research group, please give your supervis
Math 623, F 2011: Homework 6.
For full credit, your solutions must be clearly presented and all code included.
(1) This problem is concerned with calculations on the Hull-White tree constructed in
problem 3 of homework V. You should use spline interpolati
Math 623, F 2011: Homework 5.
For full credit, your solutions must be clearly presented and all code included.
(1) This problem deals with the pricing of a strangle option using a binomial tree.
The underlying stock price St follows geometric Brownian mot
Math 623
HW#4 Solution
Semester :F03
Bear Spread option = Put (K1) Put (K2) ,where K1=60 and K2=50
R=0.02, T=1, =0.2, S0=100, no dividend
( r
2
)T +
2
T )
1a)
S (T ) = S0 e
1f)
As outlined in class, we need to know such that
2
( r
)T + T ( )
Q
2
E S0 e
Math 623 (IOE 623), Fall 2012: Final exam
Name:
Student ID:
This is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam. You may also
use a calculator but not its memory function.
Please write all your solutions in this exa
Math 623 (IOE 623), Fall 2012: Final exam
Name:
Student ID:
This is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam. You may also
use a calculator but not its memory function.
Please write all your solutions in this exa
Math 623 (IOE 623), Fall 2011: Final exam
Name:
Student ID:
This is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam. You may also
use a calculator but not its memory function.
Please write all your solutions in this exa
Math 623, Fall 2013: Homework 1.
For full credit, your solutions must be clearly presented and all code included.
(1) Consider the following initial value problem for the function u = u(x) dened for 0 x 1.
uxx + (1 + x2 )ux (1 + x)u = 0
and u(0) = 1, ux (
Math 623, F 2013: Homework 2
For full credit, your solutions must be clearly presented and all code included.
(1) Consider the situation described in problem (2) of homework I. In this problem we shall use the
Euler method from there (modied appropriately
Math 623, F 2013: Homework 5.
For full credit, your solutions must be clearly presented and all code included.
(1) This problem deals with the pricing of a strangle option using a binomial tree.
The underlying stock price St follows geometric Brownian mot
Math 623, F 2013: Homework 4.
For full credit, your solutions must be clearly presented and all code included.
(1) In this problem we will be interested in valuing an out-of-the-money bear spread option on a
stock St which evolves by geometric Brownian mo
Math 623, F 2013: Homework 3.
For full credit, your solutions must be clearly presented and all code included.
(1) In the Black-Scholes method for pricing of options it is assumed that the stock price evolves
according to geometric Brownian motion:
dSt
=
Math 623 (IOE 623), Winter 2009: Final exam
Name:
Student ID:
This is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam. You may also
use a calculator but not its memory function.
Please write all your solutions in this e
MATH 623
HW#6 Solution
Semester: F03
1a) Bond Pricing Formula (Zero-Coupon Bond)
P(0, T ) = (1 + y )T
And use linear interpolation to yield and calculate bond price for 0<T<20.
See code below.
2b) The Swap rate R(T) at time 0 with maturity Tn is given by
Math 623, F 2011: Homework 4.
For full credit, your solutions must be clearly presented and all code included.
(1) In this problem we will be interested in valuing an out-of-the-money bear spread option on a
stock St which evolves by geometric Brownian mo
Math 623, F 2011: Homework 3.
For full credit, your solutions must be clearly presented and all code included.
(1) In the Black-Scholes method for pricing of options it is assumed that the stock price evolves
according to geometric Brownian motion:
dSt
=
Math 623, F 2011: Homework 2
For full credit, your solutions must be clearly presented and all code included.
(1) Consider the situation described in problem (2) of homework I. In this problem we shall use the
Euler method from there (modied appropriately
MATH 572
Assignment #4
Numerical Methods for Scientic Computing II
Winter 2005
due : Thursday , March 10
1. Consider the 2-step BDF scheme,
un +
1
2
2
un = hf (un ).
a) Find the characteristic roots 1 (h), 2 (h) for the test equation and plot them using
M