Spring 2013
Math 194
Homework 1
Instructions: Answer each question in a clear and concise manner. Your answers should be
written out in complete sentences. Always explain what you are doing when you make a calculation
so there is some context for the read
Math 194, Winter 2010 Homework 1 Solutions 1. A forward contract is an agreement to buy or sell an asset at a certain future time for a certain price (called the forward price ). At the time a forward contract is entered into, no money changes hands. The
Spring 2013
Math 194
Homework 6
Instructions: Answer each question in a clear and concise manner.
Recall the following denitions: If Y is a random variable on (, P ) and A , then the
conditional expectation of Y given A is dened to be
E[Y |A] =
Y () P (cf
Spring 2013
Math 194
Midterm Exam vA
University of California, San Diego
Department of Mathematics
1. Write your Name, PID, Section, and Exam Version on the front of your Blue Book.
2. You may use a calculator, but no other electronic devices are allowed
Spring 2013
Math 194
Homework 7
Instructions: Answer each question in a clear and concise manner.
1. Consider a viable T -period Binomial Model with parameters d, r, u, and p = 1 . (Note that u,
2
r, and d are xed but arbitrary real numbers.) Let cfw_St :
Spring 2013
Math 194
Homework 3
Instructions: Answer each question in a clear and concise manner. Your answers should be
written out in complete sentences. Always explain what you are doing when you make a calculation
so there is some context for the read
Spring 2013
Math 194
Homework 5
Instructions: Answer each question in a clear and concise manner.
The following questions refer to a 3-period Binomial Model with B0 = 1, S0 = 4, d = 1/2, u = 3/2,
r = 1/6, and p = 1/2.
1. Draw a tree diagram illustrating t
Spring 2013
Math 194
Homework 4
Instructions: Answer each question in a clear and concise manner. Your answers should be
written out in complete sentences. Always explain what you are doing when you make a calculation
so there is some context for the read
Spring 2013
1.
2.
3.
4.
Math 194
Final Exam vA
Write your Name, PID, Section, and Exam Version on the front of your Blue Book.
You may use a calculator, but no other electronic devices are allowed during this exam.
You may use one page of notes, but no bo
Math 194 Homework 4
1. Textbook Vol I, Chapter 4, Exercise 4.1.
2. Textbook Vol I, Chapter 4, Exercise 4.2.
3. Consider the sample space = cfw_HH, HT, T H, T T in the 2-period binomial model. A stopping
time is a random variable mapping to cfw_0, 1, 2,
Math 194 Homework 2
1. Textbook Vol I, Chapter 2, Exercise 2.2.
2. Toss a fair coin repeatedly. Let i = 1 if you get head on i-th toss and i = 1 otherwise. The
symmetric random walk is the sequence of random variables, X0 , X1 , . . . , Xn , . . . where X
Spring 2013
Math 194
Homework 8
Instructions: The following exercises explore the existence of equivalent martingale measures
(EMMs) in the Finite Market Model. Recall that Q is an EMM on if Q(cfw_) > 0 for all
,k
,k
and if E Q [St |Ft1 ] = St1 for all t
Spring 2013
Math 194
Homework 9
Instructions: Answer each question in a clear and concise manner. (This assignment is not to be
turned it. It is worth zero points and has no due date. Solutions will be posted before the nal
Figure 1: Tree for Problem 1.
e
Spring 2013
Math 194
Homework 4
Instructions: Answer each question in a clear and concise manner. Your answers should be
written out in complete sentences. Always explain what you are doing when you make a calculation
so there is some context for the read
Spring 2013
Math 194
Homework 2
Instructions: Answer each question in a clear and concise manner. Your answers should be
written out in complete sentences. Always explain what you are doing when you make a calculation
so there is some context for the read
Spring 2013
Math 194
Homework 5
Instructions: Answer each question in a clear and concise manner.
The following questions refer to a 3-period Binomial Model with B0 = 1, S0 = 4, d = 1/2, u = 3/2,
r = 1/6, and p = 1/2.
1. Draw a tree diagram illustrating t
Spring 2013
Math 194
Homework 3
Instructions: Answer each question in a clear and concise manner. Your answers should be
written out in complete sentences. Always explain what you are doing when you make a calculation
so there is some context for the read
Spring 2013
Math 194
Homework 6
Instructions: Answer each question in a clear and concise manner.
Recall the following denitions: If Y is a random variable on (, P ) and A , then the
conditional expectation of Y given A is dened to be
E[Y |A] =
Y () P (cf
Spring 2013
Math 194
Homework 1 (Solutions)
Instructions: Answer each question in a clear and concise manner. Your answers should be
written out in complete sentences. Always explain what you are doing when you make a calculation
so there is some context
Spring 2013
Math 194
Homework 8
Instructions: The following exercises explore the existence of equivalent martingale measures
(EMMs) in the Finite Market Model. Recall that Q is an EMM on if Q(cfw_) > 0 for all
,k
,k
and if E Q [St |Ft1 ] = St1 for all t
Spring 2013
Math 194
Homework 7
Instructions: Answer each question in a clear and concise manner.
1. Consider a viable T -period Binomial Model with parameters d, r, u, and p = 1 . (Note that u,
2
r, and d are xed but arbitrary real numbers.) Let cfw_St :
Spring 2013
Math 194
Homework 9
Instructions: Answer each question in a clear and concise manner. (This assignment is not to be
turned it. It is worth zero points and has no due date. Solutions will be posted before the nal
exam.)
1. Chapter 3, Exercise 2
Spring 2013
Math 194
Homework 2
Instructions: Answer each question in a clear and concise manner. Your answers should be
written out in complete sentences. Always explain what you are doing when you make a calculation
so there is some context for the read