STAT/ACTSC 446/846 Assignment #2 (due February 6th, 2009, 2pm)
Note: Recall that, when handing in your assignment, you are requested to use a cover page showing only your
UWID number and your section (846 students: also write 846 on the cover page) and to
ACTSC/STAT 446/846
Tutorial #3
April 1st, 2009
Let W = cfw_Wt , t 0 be a P-Brownian motion. 1. Find a measure P under which t + Wt is a (possibly non-standard) Brownian motion. 2. Assume that S = cfw_St , t 0 follows Black-Scholes model. Compute the premi
ACTSC/STAT 446/846
Assignment #1
Due date: January 23, 2009 Note: Recall that, when handing in your assignment, you are requested to use a cover page showing only your UWID
number and your section (846 students: also write 846 on the cover page) and to wr
ACTSC 446/846 - Problem Set 2
1. Assume a one-period model securities market model with two assets S1 and S2 . The prices
at time 0 and at time 1 are respectively given by:
1.25 10
~
S(0)
= [ 1 , 5 ], S(1, ) = 1.25 6 .
1.25
3
(a) What is the risk-free rat
ACTSC 446/846 - Assignment 1
Due on February 6th, 2014 by the end of class
1. For each of the following strategies, draw a graph of the payoff:
(a) A bull spread: Buy a call with a strike of 9 and sell a call with a strike of 11
(b) A straddle: Buy a call
ACTSC 446/846 - Assignment 2
Due on February 27th, 2014 by the end of class
1. Consider an asset with a current price of $50 and a volatility of 10% each year. Suppose the
assets price is modelled using a binomial tree with monthly time steps. The continu
ACTSC 446/846 - Assignment 3
Due on April 4th, 2014 in M3 3112 by 4pm in M3 3112
(If I am not in my office, slip it under my door)
1. Suppose W = cfw_Wt , t 0 is a standard BM process. Find the dynamics of the following
processes.
(a) Zt =
Rt
0
g(u)dWu ,
STAT/ACTSC 446/846 Assignment #3 (due March 13th, 2009) Over 50 marks
Note: Recall that, when handing in your assignment, you are requested to use a cover page showing only your UWID number and your section (846 students: also write 846 on the cover page)
ACTSC/STAT 446/846
Assignment #4
Due date: April 3rd, 2009 Note: Recall that, when handing in your assignment, you are requested to use a cover page showing only your UWID
number and your section (846 students: also write 846 on the cover page) and to wri
Results on the normal distribution: Let Z be a normal random variable N (m, 2 ) with mean m and variance 2 (under P). Then, we have that E eZ Icfw_eZ <a E eZ Icfw_eZ >a = = 2 2 2 exp m + 2 exp m + N N ln(a) m 2 , m + 2 ln a ,
where N (z ) = Pcfw_N (0, 1)
ACTSC/STAT 446/846 Midterm #1 Winter 2008
(Version A - Section 3)
Department of Statistics and Actuarial Science, University of Waterloo
February, 2008
Section: Name: (Please write your UWID number on the back of this page only.)
Duration: 50 minutes
Ther
STAT/ACTSC 446/846
Assignment #1 (due 25 January, 2008)
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
ACTSC/STAT 446/846
Tutorial #1
January 21, 2009 Let W = cfw_Wt , t 0 be a standard Brownian motion. 1. Let Z1 , Z2 , . . . be positive iid random variables with mean 1. Dene X0 = x and Xn = n=1 Zj j for all n 1. Show that X = cfw_Xn , n 0 is a martingale
ACTSC/STAT 446/846 Midterm #2 Winter 2008
(Section 3 - Version A)
Department of Statistics and Actuarial Science, University of Waterloo
March 18, 2008
Name: Section: (Please write your UWID number on the back of this page only.)
Duration: 50 minutes
Ther
ACTSC 446/846 - Assignment 3 Solution
1. Suppose W = cfw_Wt , t 0 is a standard BM process. Find the dynamics of the following
processes.
Rt
(a) Zt = 0 g(u)dWu , where g is an adapted stochastic process.
Solution:
This is simply an It process in integral