SEMESTER 2 EXAMINATION 2012/2013
MST 30030
Financial Mathematics
Dr. P. Murphy
Dr. H. Render
Time Allowed: 2 hours
Instructions for Candidates
Full marks will be awarded for complete answers to all 8
SOLUTIONS TO SEMESTER 1 EXAMINATION 2013/14
MST 30030 Financial Mathematics
1. a) What are European and American call options?
A European call option is an agreement between two parties giving the hol
Financial Mathematics, MST 30030
Lecturer: Masha Vlasenko
Introduction: nancial markets, derivatives and traders
Interest rates
Properties of stock options
Some probability theory
Binomial model for o
Lecture 3: Interest Rates
Reading: J.C.Hull, Chapter 4
Example (interest compounded annually)
Suppose we have a principal of 50 Euro and an interest rate of
10% compounded annually. Then after one yea
SOLUTIONS TO SEMESTER 2 EXAMINATION 2012/13
MST 30030 Financial Mathematics
1. Solution: a) A European call option is an agreement between two parties
giving the holder of the option the right to buy
Lecture 2. Traders
We will consider the following types of traders depending on the
way they use nancial derivatives:
hedgers to reduce the risk they face from potential future
movements in a market v
Lecture 5: Put - Call Parity
Reading: J.C.Hull, Chapter 9
Reminder: basic assumptions
1. There are no arbitrage opportunities, i.e. no party can get a
riskless prot.
2. Borrowing and lending are possi
Lecture 4: Properties of stock options
Reading: J.C.Hull, Chapter 9
An European call option is an agreement between two parties
giving the holder the right to buy a certain asset (e.g. one stock
unit)
Lecture 16: Delta Hedging
We are now going to look at the construction of binomial trees as
a rst technique for pricing options in an approximative way.
These techniques were rst proposed in:
J.C. Cox
Chapter 9: Two-step binomial trees
Example
Suppose we have a 6 month European call option with K = A 21.
C
Suppose S0 = A 20 and in two time steps of 3 months the stock
C
can go up or down by 10% (u =
SEMESTER 1 EXAMINATION 2013/2014
MST 30030
Financial Mathematics
Dr. P. Murphy
Dr. M. Vlasenko
Time Allowed: 2 hours
Instructions for Candidates
Full marks will be awarded for complete answers to seve
Lectures 6-10: Axioms of Probability Theory
Let X be a set.
We denote by 2X the set of all subsets of X .
Denition
A collection of subsets F 2X is called an algebra if
, X F
A F Ac F
A, B F A B F
1 /