HW: 6
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 3
University of Texas at Austin
HW Assignment 6
Provide a complete solution to the following problem(s):
Problem 6.1. Let Z be a standard Brownian motion. Dene the process Y = cfw_Y (t),
Exam MFE/3F Spring 2009
Answer Key
Question #
Answer
1
E
2
B
3
B
4
D
5
E
6
D
7
D
8
B
9
E
10
C
11
C
12
E
13
A
14
E
15
C
16
A
17
A
18
A
19
D
20
C
1
1. Answer: E
We have S0 = 10, = 0.05, = 0.3, r = 0.05, and h = 1. By (10.10),
u = exp[(r )h + h ] = exp[(0.05
May 2007 Exam MFE Solutions
1.
Answer = (B)
Let D = the quarterly dividend.
Using formula (9.2), put-call parity adjusted for deterministic dividends, we have
4.50 = 2.45 + 52.00 D e 0.01 D e 0.025 50 e 0.03
= 54.45 D ( 0.99005 + 0.97531) 50 0.970446 .
R
Quiz: 4
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 2
University of Texas at Austin
Quiz # 4
Prerequisite material. Binomial interest-rate trees.
Please, provide a complete solution to the following problem(s):
Problem 4.1. (5 points) Tw
SAMPLE MFE PROBLEM saw
39. A discrete-time model is used to model both the price of a nondividend-paying
stock and the short-term (risk-free) interest rate. Each period is one year.
At time 0, the stock price is SO 2 100 and the effective annual interest
K 6.
PM M N
Su N Sq =Su
5(0) 5103 = 3(0) N
H: 8d F 3d =Sd
Aswme: (pf; (W are ue"/8u39jed1va Probabs>
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N V
51500] =fysu +(4~'(S)Sc\ =15<su~sd3 +35
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M339W/389W Financial Mathematics for Actuarial Applications
University of Texas at Austin
Sample Midterm Exam
Instructor: Milica Cudina
Notes: This is a closed book and closed notes exam.
Time: 75 minutes
MULTIPLE CHOICE
1 (5)
TRUE/FALSE
a
b
c
d
e
1 (2)
T
In-Class: 2
Course: M339D/M389D - Intro to Financial Math
Page: 1 of 5
University of Texas at Austin
Quiz #2
Annuities immediate. Continuous annuities. Expected value. Graphing functions.
Problem 2.1. By scenario A there is an oer to pay at the rate of $1
M339W/389W Financial Mathematics for Actuarial Applications
University of Texas at Austin
Snow-Day Mock Exam - Solutions
Instructor: Milica Cudina
Notes: This is a closed book and closed notes exam.
Time: 75 minutes
MULTIPLE CHOICE
1 (5)
TRUE/FALSE
a
b
c
HW: 1
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 4
University of Texas at Austin
HW Assignment 1
Black-Derman-Toy
Provide a complete solution to the following problem(s):
Problem 1.1. (16 points) Source: Problems 24.12 and 24.13 from th
HW: 2
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 4
University of Texas at Austin
HW Assignment 2
Normal distribution. Log-normal distribution. Log-normal stock prices.
Provide a complete solution to the following problem(s):
Problem 2.1
Lecture: 1
Course: M339W/M389W - Fin Math for Actuaries
Page: 1 of 8
University of Texas at Austin
Lecture 1
Caps. Binomial Interest Rate Trees.
1.1. Caps. Building up on the reasoning for the introduction of swaps on interest rates, we
introduce another
Lecture: 3
Course: M339W/M389W - Fin Math for Actuaries
Page: 1 of 1
University of Texas at Austin
Lecture 3
The Uniform distribution.
3.1. The uniform distribution. Let a < b be two real numbers. We say that a random
variable X is uniformly distributed o
Lecture: 2
Course: M339W/M389W - Fin Math for Actuaries
Page: 1 of 4
University of Texas at Austin
Lecture 2
Black-Derman-Toy.
2.1. The Black-Derman-Toy (BDT) Tree. The basic idea of the BDT model is to compute a binomial tree of short-term interest rates
Lecture: 4
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 3
University of Texas at Austin
Lecture 4
A True Probability Measure.
4.1. Pricing by Replication. So far we have used pricing by replication to gure out
the price of derivatives und
Name:
M339W/389W Financial Mathematics for Actuarial Applications
University of Texas at Austin
Midterm Exam
Instructor: Milica Cudina
Notes: This is a closed book and closed notes exam. The maximum nuber of points on this
exam is 100.
Time: 75 minutes
TR
HW: 3
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 1
University of Texas at Austin
Quiz 3
Binomial interest-rate trees.
Problem 3.1. MFE Exam, Spring 2007: Problem #9.
You use a binomial interest rate model to evaluate a 7.5%-interest-rat
M329F/M389F
(Sections 1.3 - 1.9) Accumulation Functions
8/30/16
Goals
Learn what an amount function and accumulation function is.
Learn examples of accumulation functions, including
simple interest accumulation function (Section 1.4)
compound interest
HW: 5
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 2
University of Texas at Austin
HW Assignment 5
Provide a complete solution to the following problem(s):
Problem 5.1. Suppose that ABC is a non-dividend-paying stock whose price is modele
HW: 4
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 2
University of Texas at Austin
HW Assignment 4
Provide a complete solution to the following problem(s):
Problem 4.1. (10 points) Source: Problem 18.10 in McDonald.
Let the stock price at
HW: 3
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 3
University of Texas at Austin
HW Assignment 3
Provide a complete solution to the following problem(s):
Problem 3.1. (9 points) Assume that Y1 = eX where X is a standard normal random va
HW: 2
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 2
University of Texas at Austin
HW Assignment 2
Provide a complete solution to the following problem(s):
Problem 2.1. (8 points) Source: Problems 24.12 and 24.13 from the textbook.
Here i
HW: 1
Course: M339W/M389W - Financial Math for Actuaries
Page: 1 of 3
University of Texas at Austin
HW Assignment 1
Provide a complete solution to the following two problems:
Problem 1.1. (3 pts) A biased coin (probability of heads is 0.7) is tossed 1000
NAME:
M339W/389W Financial Mathematics for Actuarial Applications
Spring 2013
University of Texas at Austin
In-Term Exam II
Instructor: Milica Cudina
Notes: This is a closed book and closed notes exam. The maximum number of points on this
exam is 100.
Tim
Tuesday, February 26th
M339W/389W Financial Mathematics for Actuarial Applications
Spring 2013, University of Texas at Austin
In-Term Exam I
Instructor: Milica Cudina
Notes: This is a closed book and closed notes exam.
Time: 75 minutes
TRUE/FALSE
1 (2)
TR
M329F/M389F
(Section 1.3) Amount of Interest, Effective Interest Rate
(Section 1.6) Amount of Discount, Effective Discount Rate
8/25/16
Goals
Learn the definitions of amount of interest, amount of discount, effective interest rate,
and effective discount
M329F/M389F
(Section 1.12) Force of Interest Function
(Section 1.14) Inflation Rate
9/8/16
Notes for Section 1.12: The Force of Interest Function
1. (Big picture and vocabulary/notation) In Section 1.11, we assumed that the account was
governed by compoun
M329F/M389F
(Sections 1.7, 1.9) Discount Function, Discount Factor, PV, and NPV
9/1/16
Goals
Learn what the discount function v(t) is and how to use it to pull back.
Learn how to answer questions such as Given the value at time t1 , find the value of sa
M329F/M389F
(Sections 1.10) Nominal Interest, Nominal Discount
(Section 1.11) Constant Force of Interest
9/6/16
Using the TI BAII Plus or BAII Plus Professional
You should start bring one of these to class. If you have already been using it, make sure it