21-270
Intro to Math Finance
Spring 2012
Solutions to Assignment 2
1.13 Observe rst that
V1 (1 ) = $20, V1 (2 ) = 0, V1 (3 ) = $20.
Let us try to replicate V by purchasing shares of S 1 , shares of S 2 , and
investing in the bank at t = 0. The value of ou
21-270
February 22, 2012
INTRO TO MATH FINANCE
Spring 2012
Test 1
Name:
Write your answers clearly in the spaces provided. You may use the back of a page
for additional space; please indicate clearly when you do so. Show all work. No credit
will be given
21-270
April 30, 2012
INTRO TO MATH FINANCE
Spring 2012
Test 3
Name:
Write your answers clearly in the spaces provided. You may use the back of a page
for additional space; please indicate clearly when you do so. Show all work. No credit
will be given for
21-270
Introduction to Mathematical Finance
Homework #1
Spring 2009
Problem 4 is due in class on Wednesday, January 21.
1. Assume the following exchange rates are valid:
1. US Dollar = 0.68 British Pound
1 US Dollar = 1.22 Canadian Dollars
1 US Dollar = 1
21-270
Introduction to Mathematical Finance
Homework #4 Solutions [Partial]
Spring 2009
1. [Exercise 2.8]
mN
4, 000 =
AD(
i=1
mN
1, 100 =
i=1
Since
10
i=1
i
50D( 2 )
1
10
=
i
)=
m
10
i=1
q [m]
i
F
D ( ) + F D (N ) =
m
m
10
i=1
i
500D( 2 )
=
1
4000
10
i
50
21-270
Introduction to Mathematical Finance
Homework #2
Spring 2009
Due in class on Wednesday, January 28. All problems should be turned in.
1. This problem refers to Example 1.22 in the text. In class, we used a replicating portfolio
40
to compute the in
Chapter 5
Arbitrage-Free Pricing in
One-Period Finite Models
The simplest financial models involving random evolution of prices are those in which
there are only two trading times and the prices of the basic securities are modelled
as random variables on
21-270
Introduction to Mathematical Finance
Homework #1
Spring 2016
1. [Exercise 1.1] Let T > 0 be given. Let C denote a call option (on a stock S) with exercise
date T and strike price Kc = $50. Let P denote a European put option on the same stock
with e
21—270 Introduction to Mathematical Finance D. Handron
Exam #2
March 18, 2016 Name: SOLA‘OAS
#:54—
I will pick up my exam in class, accepting the possibility that others may see my score.
I will pick up my exam from the TA during ofﬁce hours.
Cl
1. (25 points)
(a)
Consider a simple ﬁnancial model with several banks, each with interest rates at time
0 that do not depend on the length of the deposit or loan. One bank offers interest
that is compounded quarterly at the nominal rate T[4] = .05 and tr
21-270
Introduction to Mathematical Finance
Homework #6
Spring 2009
Due in class on Wednesday, March 4. All problems should be turned in.
1. In this exercise we have two bonds. Each of these bonds pays a coupon once per year, has
a nominal coupon rate q [
21-270
Intro to Math Finance
Spring 2012
Solutions to Assignment 1
1.1
1. If S1 = 53.47, then
CT = 53.47 50 = 3.47,
PT = 0.
2. If ST = 48.52, then
CT = PT = 0.
3. If ST = 42.71, then
CT = 0,
PT = 47.5 42.71 = 4.79.
1.2 The short sale of the puts generates
21-270
Intro to Math Finance
Spring 2012
Solutions to Assignment 3
2.6
1. Observe that
1
1
= D(T ) =
,
T
(1 + R (T )
1 + T R (T )
from which we conclude that
(1 + R (T )T 1
.
R (T ) =
T
If R (30) = .10, then we have
(1.1)30 1
R (30) =
= .548313.
30
2. Con
21-270
Intro to Math Finance
Spring 2012
Solutions to Assignment 4
2.17
12
rI [12]
1+
12
RI =
.075
1+
12
=
1
12
1 = .077633.
Let
=
=
1
1
=
[12]
(1 + RI )1/12
1 + rI12
1
= .9937888.
1 + .075
12
We then have
180
1 180
1
Ai = A
125, 000 =
i=1
.
It follows t
21-270
Intro to Math Finance
Spring 2012
Solutions to Assignment 5
3.1 To replicate the long position, we invest
1
B
(1 + R (3)3
B
units of B between t = 0 and t = 3 at the eective rate R (3) = 4% and we
borrow
B
FA
A
(1 + R (3)3
A
units of A between t =
21-270
Intro to Math Finance
Spring 2012
Solutions to Assignment 6
3.6 Observe that
D(1) =
1
.
1.1
By put-call parity, we have
P0 C0 = D(1)(K F ).
It follows that
K=F+
P0 C0
.
D(1)
Substituting in the numbers, we obtain
K = 296 + (9.11 6.85)(1.1) = 298.48