ACTSC 446/846 Winter 2013 Mathematical Models for Finance
Assignment 2 Department of Statistics and Actuarial Science University of Waterloo, Canada
Due: Thursday Feb 26th, 2013 in class. Hard copy please. No electronic version. To earn the full credit of
Problem 1. The process
Zt =
t
0
es dBs
has an integral representation with u = 0 and v(s) = es . The process cfw_Xt can be
obtained from cfw_Zt through the transformation Xt = g(t, Zt ) with
g(t, z) = et [x + z],
for which we have
gt = et [x + z], gz =
STAT/ACTSC 446/846
Assignment #3 (due November 9, 2007)
Note:When handing in your assignment, please use a cover page showing only your UWID number and section (lecture)
number. Please write your name on the rst actual page of your assignment. ACTSC/STAT
STAT/ACTSC 446/846
Assignment #1 (due September 28, 2007) Introduction to derivatives
Note: When handing in your assignment, please use a cover page showing only your UWID number and section (lecture) number. Please write your name on the rst actual page
STAT/ACTSC 446/846
Assignment #4 (due November 23, 2009)
1. Let cfw_Wt be dened by the SDE dWt = dt + dBt , where Bt is a standard Brownian motion. Use Itos formula to write the following processes Yt in the form of a stochastic integral (dYt = u(Yt , t)
ACTSC 446/846 Winter 2013
Mathematical Models for Finance
Assignment 2
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Due: Thursday Feb 26th, 2013 in class. Hard copy please. No electronic version.
To earn the full credit of
Department of Statistics and Actuarial Science
University of Waterloo
ACTSC/STAT 446/846 - Midterm Exam
February 23, 2010
Last name:
First name:
Course: 446 or 846 (circle one)
Section: 1 or 2 (circle one)
(Write your UWID number on the back of this page
Question Set 03 Solution
1.
ACTSC 446/846, Fall 2016
a. Note that the inequality C(K1 ) C(K2 ) K2 K1 is violated, where K1 = 90 and
K2 = 95. Therefore, to undertake an arbitrage, we sell the 90-strike call, buy the 95-strike
call, and invest the net premi
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 6
Single-period Market Model (1)
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Fall 14 L6
Previously on 446
Question Set 04
ACTSC 446/846, Fall 2016
1. Consider a binomial tree model, with four time steps, an effective interest rate per time step r =
0.1, initial stock price S0 = 100, u = 1.25 and d = 1/u = 0.8. Determine the price of an
at-the-money American p
Question Set 02 Solution
ACTSC 446, Winter 2016
1. A bull spread or a bear spread can never have an initial premium of zero because we are buying
the same number of calls (or puts) that we are selling and the two legs of the bull and bear spreads
have dif
Actsc 446/846 (Winter 2016)
Solution to Assignment 1
1. (a) The payoff to a long forward at expiration is equal to:
Payoff to long forward = ST K
Therefore, we can construct the following table:
Price of asset in 6 months
40
45
50
55
60
Agreed forward pri
Question Set 04 Solution
1.
ACTSC 446/846, Fall 2016
Question Set 04 Solution
2. (a)
ACTSC 446/846, Fall 2016
Question Set 04 Solution
2. (b)
ACTSC 446/846, Fall 2016
Question Set 04 Solution
ACTSC 446/846, Fall 2016
3. The risk neutral probability of goi
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 8
Single-period Market Model (3)
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Fall 14 L8
Previously on 446
ACTSC 446/846 Fall 2014
Mathematical Models for Finance
Supplementary Note 2
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Those are exactly the board work in Lecture 8.
Theorem 1 (Complete market and unique state price vec
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 7
Single-period Market Model (2)
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Fall 14 L7
Previously on 446
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: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Fall 14 L2
P
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 5
Properties of Option Prices (2)
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Fall 14 L5
Previously on 44
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 3
Basics of Financial Markets
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Fall 14 L2
Previously on 446
Le
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 1
Review of Financial Markets
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Fall 14 L1
Lecture 1
Financial
ACTSC 446 Fall 2014
Mathematical Models for Finance
Lecture 4
Properties of Option Prices
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Fall 14 L4
Previously on 446
Le
Question Set 01
1.
ACTSC 446, Winter 2016
(a) Suppose you enter into a long 6-month forward position at a forward price of $50. What is
the payoff in 6 months for prices of $40, $45, $50, $55, $60?
(b) Suppose you buy a 6-month call option with strike pri
ACTSC 446/846 Winter 2013
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 risk-free interest ra
ACTSC 446 Winter 2013
Mathematical Models for Finance
Lecture 13
Binomial Trees Models 3
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Winter13 L13
Review of Lecture 1
ACTSC 446 Winter 2013
Mathematical Models for Finance
Lecture 14
Brownian Motion
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Winter13 L14
Review of Lecture 1-13
In t
ACTSC 446 Winter 2013
Mathematical Models for Finance
Lecture 9
Multi-period Model 2
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Winter13 L9
Review of Lecture 8
One-
ACTSC 446 Winter 2013
Mathematical Models for Finance
Lecture 15
Brownian Motion II
Ruodu Wang
Department of Statistics and Actuarial Science
University of Waterloo, Canada
Email: wang@uwaterloo.ca
Ruodu Wang
ACTSC446 Winter13 L15
Review of Lecture 14
Bro
Question Set 02
ACTSC 446, Winter 2016
1. Can a bull spread or bear spread have zero initial premium? Why or why not?
2. A $50 stock pays a $1 dividend every 3 months, with the first dividend coming 3 months from
today. The continuously compounded risk-fr