ACTSC 446/846 Fall 2014
Mathematical Models for Finance
Assignment 1
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Due: Thursday Oct 10th, 2014 in class. Hard copy please. No electronic version.
To earn the full credit of t
Actsc 446/846: Midterm  Winter 2014
Department of Statistics and Actuarial Science, University of Waterloo
March 4, 2014
Last name:
First name:
I.D.#:
Time Period:
8:30 am  9:50 am
Notes:
Show all work.
Aid: Calculator (Financial or Scientic)
Unless
ACTSC/STAT 446/846 Assignment 1 Solutions
(Note that I accidentally listed the two rst problems as suggested problems in the rst problem set
and therefore gave away the solution: so they are not listed here. Each of 2.7 and 3.3 were marked out
of 1 mark.)
ACTSC/STAT 446/846 Assignment 2 Due on November 3 at 1:00pm
Note: A dropbox on UWACE will be created where you can hand in your assignment.
(Option a: electroniconly submission): Hand in one main document with all your answers as well
as any les used i
ACTSC/STAT 446/846 Assignment 3 Due on December 5 at 11:30am
Problem 1: Itos Lemma
[7pts] Let Xt be dened by the SDE
dXt = dt + dWt ,
where > 0, > 0 and cfw_Wt , t 0 is a standard Brownian motion.
(1) Use Itos formula to write the following processes Yt i
ACTSC/STAT 446/846 Assignment 3 Solutions
Problem 1: Itos Lemma
[7pts] Let Xt be dened by the SDE
dXt = dt + dWt ,
where > 0, > 0 and cfw_Wt , t 0 is a standard Brownian motion.
(1) Use Itos formula to write the following processes Yt in the form of a sto
ACTSC/STAT 446/846 Midterm 1 Fall 2011 Solutions
1. [12 points] Consider an equitylinked contract as seen in class, in which an investor receives
$1000 max 1, 1 + 0.6
S (T )
1
S (0)
()
at T = 2 years, where S (t) is the value of the index at time t. The
ACTSC/STAT 446/846 Midterm 2 Fall 2011 Solutions
1. [14 points] A stock with current price S (0) = 100 is modeled by a binomial model with two
timesteps of length h = 0.5 year each, using u = e(r)h+ h and d = e(r)h h . The stock
pays a continuous dividen
ACTSC 446/846 Mathematical Models in Finance, Fall 2014  Week 12
Problem Set 5.
For all questions, assume B = cfw_Bt , t 0 is a standard Brownian motion under risk neutral
probability measure Q, cfw_Ft , t 0 is the ltration generated by B. Suppose the ri
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Assignment 1, ACTSC 446/846 Winter 2015
Instructor: Bin Li
Due date: February 23, 2015 (Monday, in class)
NOTE: You need to justify your solution!
1. Consider a threeperiod binomial model on a stock price with T = 1, u=d = 4=3, qu = 1=3, S(0) = 80
and r
ACTSC/STAT 446/846 Assignment 2 Solutions
1. Binomial Model [10pts]
Using a binomial tree with n = 8 time steps, S (0) = 100, expiration of 1 year (and therefore h = 1/8),
r = 5%, = 0.3 and = 3.5%. (a) Compute European and American put option prices for K
Assignment 1, ACTSC 446/846 Winter 2015
Instructor: Bin Li
Due date: January 28, 2015 (Wednesday, in class)
NOTE: You need to justify your solution!
1. Consider that the 6month eective (simple) interest rate is 2%, the S&R 6month forward price is
1020 a
Assignment 1, ACTSC 446/846 Winter 2015
Instructor: Bin Li
Due date: January 28, 2015 (Wednesday, in class)
NOTE: You need to justify your solution!
1. Consider that the 6month eective (simple) interest rate is 2%, the S&R 6month forward price is
1020 a
Assignment 3, ACTSC 446/846 Winter 2015
Instructor: Bin Li
Due date: April 6, 2015 (Monday, in class)
NOTE: You need to justify your solution!
We denote by fW (t)gt
0
a standard Brownian motion.
The formulas of Greeks can be found in lecture note 11 as we
ACTSC/STAT 446/846 Assignment 1 Due on Oct. 6 at 1:00pm
Note: A dropbox on D2L will be created where you can hand in your assignment. Otherwise, hand
in your assignment in class on the due date.
1 Problems from McDonald: [24 points] 2.7, 3.3, 3.11, 3.13
ACTSC/STAT 446/846 Midterm 1 Fall 2010
Department of Statistics and Actuarial Science, University of Waterloo
Oct. 22, 2010
Last Name:
First Name:
446 or 846 ?
(Please write your UWID number on the back of this page only.)
Version A
Duration: 50 minutes
T
ACTSC/STAT 446/846 Midterm 1 Solutions (A)
1. [11 points] Consider a straddle, made up of a long position in a call and a long position in a
put, each with a strike price of $20 and an expiration time in T = 2 months. The price of the
underlying asset is
ACTSC/STAT 446/846 Midterm 2 Fall 2010
Department of Statistics and Actuarial Science, University of Waterloo
Nov. 19th, 2010
Last Name:
First Name:
446 or 846 ?
(Please write your UWID number on the back of this page only.)
Version A
Duration: 50 minutes
ACTSC/STAT 446/846 Midterm 2 Solutions (A Blue)
Problem 1
(a) The tree of stock prices and payos (in boldface) is shown on the gure below. Note that because
of the nonproportional dividend, the tree is not recombining.
21
0
211
=20
0
19
1
20
191
=18
18.9
Also write your name here:
ACTSC 446/846 Fall 2014
Mathematical Models for Finance
Assignment 3
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Due: Tuesday November 25th, 2014 in class. Hard copy please. No electronic versio
Also write your name here:
ACTSC 446/846 Fall 2014
Mathematical Models for Finance
Assignment 3
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Due: Tuesday November 25th, 2014 in class. Hard copy please. No electronic versio
ACTSC 446/846 Fall 2014
Mathematical Models for Finance
Practice Problem set for Midterm
Department of Statistics and Actuarial Science
University of Waterloo, Canada
1. The S&R index spot price is $1,000, the continuously compound riskfree interest rate
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 20
General continuoustime market models 2
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: [email protected]
Ruodu Wang
ACTSC446 Fall 14 L20
Previo
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 22
Interest Rate Models
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: [email protected]
Ruodu Wang
ACTSC446 Fall 14 L22
Previous on 446
Lecture 2
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 10
Multiperiod Market Model (2)
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: [email protected]
Ruodu Wang
ACTSC446 Fall 14 L10
Previously on 44
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 11
Binomial Trees
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: [email protected]
Ruodu Wang
ACTSC446 Fall 14 L11
Previously on 446
Lecture 10
Ma
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 2
Assumptions on Financial Markets and Arbitrage
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: [email protected]
Ruodu Wang
ACTSC446 Fall 14 L2
P
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 12
Binomial Trees (2)
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: [email protected]
Ruodu Wang
ACTSC446 Fall 14 L12
Previously on 446
Lecture 1
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 8
Singleperiod Market Model (3)
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: [email protected]
Ruodu Wang
ACTSC446 Fall 14 L8
Previously on 446
Tutorial 1  Short Solutions
1. r = 9.9%.
ACTSC 446/846, Fall 2071
2. r = 6%.
3. The payoff is ST for both (a) and (b). The cost is 1020 for both (a) and (b).
4. Payoff of (a) is
100
(ST 1050)+ (ST 950)+ = 950 ST
0
Payoff of (b) is
0
(1050 ST )+ (950 ST )