1
Tutorial Week 8: Americantype Contingent Claims in CRR
Model
Consider the CRR binomial model with the initial stock price S0 = 9, interest rate r = 0:01 and
the volatility = 0:1.
1. Use the CRRpar
1
Tutorial Week 910: Ito formula and BlackScholes Formula
1. Let Wt denote a Brownian motion. Ise Itos formula to compute the dierentials of the
following stochastic processes:
1
a) Xt = e 2 t cos (
MATH3075/3975
FINANCIAL MATHEMATICS
ChristianOliver Ewald and Marek Rutkowski
School of Mathematics and Statistics
University of Sydney
Semester 2, 2014
Students enrolled in MATH3075 are expected to
Calculation with interest rate (Lecture summary)

EAR (Equivalent Annual Rate).

used to illustrate the full percentage cost of overdrafts and any type of account
that can be in credit and also go o
Types of interest (Lecture Summary)
The mathematics that underlies costing loans and pensions and predicting movements
in the financial market all relies on what is called the time value of money.
Mon
QUICK SUMMARY OF 2M
PART 1: MODELLING
1. Maths behind the modelling
1.1. Linear functions. A straight line has equation
y = kx + p,
where k is the gradient and p is an intersection with yaxis. If we a
Department of Mathematics
Financial Modelling 1: Models from Economics
Natural logarithms (i.e. logarithms to the base e) are denoted log in this course; these logarithms
are often denoted ln, especia
Financial Modelling
Sheet 2: Compound interest, annuities, mortgages and
securities
Compound interest
1. Calculate the accumulated value of 1000 invested for 5 years in an account bearing (i) simple
i
APR and AER (Lecture summary)
Doubling Time.

A savings account pays interest at an annual rate of i%. Show that capital
invested in this account doubles over approximately (0:35+0:70=i) years. Let t
QUICK SUMMARY OF 2M
11
2.9. Market surveys. Information about the demand for a particular
product can be estimated by using market surveys: Would you pay
p1 , p2 , p3 , . . . pN 1 , pN for BrandX? Ass
8
PART 1: MODELLING
2.4. Market equilibrium (Market price). The market balances
where q s (p) = q d (p). If q s is strictly increasing and q d is strictly decreasing as a function of price, then there
Thursday, 17th December, 2009
@ University
w of Glasgow
EXAMINATION FOR THE DEGREES OF
MA. AND B.Sc.
13.00 pm. to 14.30 pm.
Mathematics 2M  Financial Modelling
An electronic calculator may be used pr
Friday, 6th August, 2010 2.30 pm. to 4.00 pm.
5 Universit
QfGlasgowy
Emmi
EXAMINATION FOR THE DEGREES OF
M.A. AND B.Sc.
Mathematics 2M Financial Modelling
An electronic calculator may be used provid
QUICK SUMMARY OF 2M
5
2. Models from Economics and Finance
2.1. Simple Interest.
Simple interest is paid only on the original balance.
P is the principal the original (at time t = 0) deposit.
r is t
1
Tutorial Week 7: CRR Formula
1. We take for granted the CRR call option pricing formula
C0 = S0
T
X
T k
p^ (1
k
p^)T
T
X
T k
K
p~ (1
T
(1 + r)
k
k
p~ =
k
^
k=k
^
k=k
where
p~)T
1+r d
;
u d
p^ =
p~u