Economics 765 Assignment 1
1.3 In the one-period binomial model (as considered in the rst class), suppose we want
to determine the price at time zero of the derivative security with payo V1 = S1 . Thi
June 2011
Final Examination
Models for Financial Economics
Economics 765
Take-home exam due on or before Friday June 21st 2013.
This exam comprises 6 pages, including the cover page
Economics 765
Page
Economics 765 Assignment 5
6.1
Consider the stochastic dierential equation
dX (u) = (a(u) + b(u)X (u) du + ( (u) + (u)X (u) dW (u),
(6.2.4)
where W (u) is a Brownian motion relative to a ltration F (u
Economics 765 Final Exam
1. Use the probabilistic argument in Shreve section 5.2.5 to obtain an explicit
expression for the function p(t, x), which gives the value of a European put option
at time t w
Economics 765 Assignment 4
4.19
Let W (t) be a Brownian motion, and dene
t
sign(W (s) dW (s),
B (t) =
0
where
sign(x) =
1
1
if x 0,
if x < 0.
(i) Show that B (t) is a Brownian motion.
The dierential o
Economics 765 Assignment 3
3.2 Let W (t), t 0, be a Brownian motion, and let F (t), t 0, be a ltration for this
Brownian motion. Show that W 2 (t) t is a martingale.
The easiest way to show this is to
Economics 765 Assignment 2
2.5
Let (X, Y ) be a pair of random variables with joint density function
fX,Y (x, y ) =
2|x|+y
2
exp
(2|x|+y )2
2
if y |x|,
if y < |x|.
0
Show that X and Y are standard no