21-270
Introduction to Mathematical Finance
Homework #1
Spring 2011
Problem 4 is due in class on Wednesday, January 19.
1. Assume the following exchange rates are valid:
1 US Dollar = 0.68
1 US Dollar = 1.22
1 US Dollar = 1.50
1 British Pound = 1.09
Briti
21-270
Introduction to Mathematical Finance
Homework #5 Solutions
1. [Exercise 2.18] Let =
Spring 2011
1
1+
rI [12]
12
. Then from the formula for the sum of monthly payments
we get 200, 000 = 1, 310.52 1 (1 360 ). From which we have 1, 310.52361 201.3105
21-270
Introduction to Mathematical Finance
Week #8 Solutions
Spring 2011
1. [Exercise 3.5] Let F0 = 285 be the forward price that has been agreed before and let
F1 = 275 be the todays forward price for delivery in 1 year. Susan already agreed to sell
100
Course Notes for Introduction to Mathematical
Finance (21-270)
William J. Hrusa & Dmitry Kramkov
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
January 25, 2015
2
Part I
Introduction to Financial Markets,
Replication a
Chapter 2
Fixed-Income Securities and
Interest Rates
We now begin a systematic study of xed-income securities and interest rates. The
literal denition of a xed-income security is a nancial instrument that promises xed
(or denite) payments at prescribed fu
21-270
Introduction to Mathematical Finance
Week #11 Solutions
Spring 2011
1. [Exercise 3.13] (a) By put-call parity P0.5 =$ 2.9595. Therefore the amount of extra cash
is 10, 000 (C0.5 P0.5 ) = $75, 304.92
(b) The value of the clients portfolio at time 1
21-270
Introduction to Mathematical Finance
Week #13 Solutions
Spring 2011
1. [Exercise 5.1]
1. The payos from the call are $50 and $0. Risk-nuteral probabilities are
u1r
1
. Thus, C0 = 1+r (50 1+rd + 0 u1r ) = 19.84
ud
ud
ud
1
2. Similarly, P0 = 1+r (0 1
21-270
Introduction to Mathematical Finance
Week #12 Solutions
Spring 2011
1. [Exercise 4.5]
(1) the event of the occurrence A and B simultaneously contains the following sequences=cfw_HHT ,
HHT with probability 1/4+1/12 = 5/12. On the other hand P (A)P
21-270
Introduction to Mathematical Finance
Week #10 Solutions
Spring 2011
1. [Exercise 3.6] Using Put-Call Parity we have:
P0 C0 = D(T )(K F )
and we deduce from it
K = (9.11 6.85) 1.1 + 296 = 298.49
2. [Exercise 3.12] a) Note that from Put-Call Parity w
196
Part 2 Interest Rates and Valuing Cash Flows
Chapter 6 APPENDIX B
The Yield Curve and the Law of One Price
Thus far, we have focused on the relationship between the price of an individual bond
and its yield to maturity. In this section, we explore the