Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Practice Problems Homework 10
Steve Dunbar
Monday, December 7, 2009
Initialization of Necessary Packages
(1.1)
_R
(1.2)
(1.2)
Problem 1
Find the mode (the value of the independent variabl
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 10
Steve Dunbar
Due Wednesday, December 8, 2010
Problem 1
S imulate the solution of the stochastic differential equation dX(t) = X(t)dt + 2*X(t)*
dW on the interval [0, 1] with
i
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 9
Steve Dunbar
Due Mon, November 22, 2010
1. Let W1 (t) be a Brownian motion and W2 (t) be another independent
Brownian motion, and is a constant between 1 and 1. Then consider
th
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework
Steve Dunbar
Due Wed, November 10, 2010
1. If you buy a lottery ticket in 50 independent lotteries, and in each
lottery your chance of winning a prize is 1/100, write down and ev
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 7
Steve Dunbar
Due Wed, October 20, 2010
1. Suppose X is a continuous random variable with mean and variance
both equal to 20. What can be said about P [0 X 40]?
Solution: P [0 X
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 6
Steve Dunbar
Due Monday, October 13, 2010
Problem 1
(1.1)
(1.1)
Part a
For $ T_0 = 10 $ and $ a = 20 $ , draw a graph of theduration as a function of
t he probability $ q $ .
1
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 5
Steve Dunbar
Due Wed, October 6, 2010
1. Use a fair coin, say a penny, to play a simple coinipping game, as
described throughout the chapter. Use the chart in the section to re
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 4
Steve Dunbar
Due Sept 27, 2010
1. Consider a stock whose price today is $50. Suppose that over the next
year, the stock price can either go up by 6%, or down by 3%, so the stoc
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 3
Steve Dunbar
Due Sept 22, 2010
1. The current exchange rate between the U.S. Dollar (USD) and the
Great Britain Pound (GBP) is 1.5641, that is, it costs $1.5641 to buy
one Poun
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 2 Solutions
Steve Dunbar
Monday, September 13, 2010
1. Consider the hypothetical country of Elbonia, where the government
has declared a currency band policy, in which the exchang
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 1
Steve Dunbar
Due Friday, September 3, 2010
Problem 1
part a
Find and write the definition of a `future', also called a
futures contract. Graph the intrinsic value of a futures
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
M onte Carlo Methods for Integration
A Project for Math 489/889
Steven R. Dunbar
November 2010
Suppose we wish to numerically evaluate
r eliably to some specified
e rror. We will evaluate this integral with basic calculus. We will also pretend that this
i
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Final Exam Solutions
Steve Dunbar
Thursday, December 17, 2009
Initializations
(1.1)
(1.1)
(1.2)
_R
(1.3)
Problem 1
A stock has a constant volatility of 18% and the riskfree
interest rate
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
M ath 489/889
Stochastic Processes and
Advanced Mathematical Finance
Final Exam Solutions
Steve Dunbar
Tuesday, December 14, 2010
1
` `Short Answer', use a single sentence or`True or False' and if false, give a
r eason why it is false in a single sentence
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Monday, October 26, 2009
Problem 1 2 3 4
Possible 15 20 20 20
Points
Exam 1
Name:
Total
75
1. (15 points) According to the article Bullion bulls on page 81 in the October 8, 2009 issue
of The Economist, gold has risen from about $510 per ounc
Stochastic Processes and Advanced Mathematical Finance
MATH 889

Fall 2010
Math 489/889
Friday, October 29, 2010
Problem 1 2 3 4
Possible 20 20 20 20
Points
Exam 1
Name:
Total
80
1. (20 points) You can enter into futures contract to buy a Treasury bond that in 6 months time
will be worth $950. The current price of the Treasury b