The First Midterm: A
(60) In a two step binomial tree model as given in Figure 1, assume that r = 0.25 and p = 0.9, q = 0.1.
Answer the following questions.
16
8
4
4
2
1
Figure 1: Binomial tree.
Usi
W4635 (Spring 2015)
Lecture 1
Hongzhong Zhang
Department of Statistics
Columbia University
January 20, 2015
1 / 11
Introduction
Purpose for mathematical/stochastic nance: pricing
nancial contracts. Th
Homework # 1 for STAT W4635
Professor Protter
January 24, 2016
Due: This homework is due on Tuesday, February 2, in class.
Please do the following exercises, showing all of your work. For these exerci
Homework # 3 for STAT W4635
Professor Protter
February 10, 2016
Due: This homework is due on Tuesday, February 16, in class.
Please do the following exercises, showing all of your work. For these exer
Homework # 2 for STAT W4635
Professor Protter
January 30, 2016
Due: This homework is due on Tuesday, February 9, in class.
Please do the following exercises, showing all of your work. For these exerci
Homework # 5 (Review Problems) for STAT
W4635
Professor Protter
February 28, 2016
Due: This homework consists of Review Problems for the Midterm, which is on Thursday,
March 10, in class. It is not to
Homework # 4 for STAT W4635
Professor Protter
February 26, 2016
Due: This homework is due on Tuesday, March 1, in class.
Please do the following exercises, showing all of your work. For these exercise
Homework #9 for STAT W4635
Professor Protter
April 15, 2016
Special Note: This is the last homework for the semester. Since it is being assigned only on
Thursday, the due date will be in class on Tues
Homework # 7 for STAT W4635
Professor Protter
March 27, 2016
Due: This homework is due on Tuesday, April 4, in class.
1.) Suppose a zero coupon bond with maturity 10 is issued by a risky firm at time
W4635 (Spring 2015)
Lecture 5
Hongzhong Zhang
Department of Statistics
Columbia University
February 10, 2015
1 / 15
Pricing derivatives with risk-neutral measure
In the binomial tree model with no arb
W4635 (Spring 2015)
Lecture 4
Hongzhong Zhang
Department of Statistics
Columbia University
February 4, 2015
1 / 15
Formalization: Information&Filtration
A discrete-time stochastic process cfw_Sn n0 is
W4635 (Spring 2015)
Lecture 3
Hongzhong Zhang
Department of Statistics
Columbia University
February 1, 2015
1 / 16
Pricing an option using replicating
Theorem
ln a N step binomial tree model, any opti
W4635 (Spring 2015)
Lecture 11
Hongzhong Zhang
Department of Statistics
Columbia University
March 23, 2015
1 / 16
Delta hedge in a binomial tree
In a binomial tree, we select a strategy cfw_n 1nN to
r
W4635 (Spring 2015)
Lecture 12
Hongzhong Zhang
Department of Statistics
Columbia University
March 25, 2015
1 / 15
It integral of a Brownian motion
o
Recall that
t
1
1
Bs dBs = (Bt )2 t
2
2
0
Sanity ch
W4635 (Spring 2015)
Lecture 8
Hongzhong Zhang
Department of Statistics
Columbia University
February 23, 2015
1 / 15
Hedging an American call option r = 5%,
= 15%
A possible trajectory of a winner stoc
W4635 (Spring 2015)
Lecture 13
Hongzhong Zhang
Department of Statistics
Columbia University
March 29, 2015
1 / 15
Its lemma in terms of a product table
o
Its lemma is essentially Taylors expansion. We
W4635 (Spring 2015)
Review for the Midterm
Hongzhong Zhang
Department of Statistics
Columbia University
March 4, 2015
1 / 14
Basic concepts in no-abitrage pricing
What is the risk-neutral measure? Is
W4635 (Spring 2015)
Lecture 10
Hongzhong Zhang
Department of Statistics
Columbia University
March 23, 2015
1 / 12
Reection principle I
For the Bachelier model, we have
m S0
Q(m T ) = Q(ST m) = 2Q(ST m
W4635 (Spring 2015)
Lecture 7
Hongzhong Zhang
Department of Statistics
Columbia University
February 16, 2015
1 / 14
Review of stopping times
Are the following random variables stopping times?
(HH) =
W4635 (Spring 2012)
Lecture 6
Hongzhong Zhang
Department of Statistics
Columbia University
February 11, 2015
1 / 12
Exercising strategies
For an American option, we know that the optimal
exercise time
Homework #8 for STAT W4635
Professor Protter
April 2, 2016
Due: This homework is due on Tuesday, April 12, in class.
1. Recall the framework from Exercise 2 of Homework 7: Suppose the default time com