Exercises on Differentiation Rules
Please write down the 1st order derivative for give functions.
In functions, x is a random variable and a, b, c, r are constants.
Function
c
1st order derivative
Function
1
x2
x
1st order derivative
Function
ax
ln x
ax+b

Exercises on Integration Rules
0dx =
1dx =
1
dx =
x
e dx =
x
xdx =
2
x dx =
ln xdx =
a dx =
x
x dx =
n
1
x dx =
1
x 2 dx =
1
x
n
xdx =
3
dx =
xdx =
log
a
xdx =
Suppose normal random variable X has mean and variance
2 , i.e., X ~ N ( , 2 ) . Pl

MFIN7003: Mathematical Techniques in Finance _Dr. Rujing Meng
Homework 3
This homework is due on Sept 21
1. Brownian motion and martingale. Let Bt be a standard Brownian motion under a
measure P. Please find out whether the following processes are marting

MFIN7003: Mathematical Techniques in Finance _Dr. Rujing Meng
Homework 4
This homework is due on Sept 30
1. Given the standard normal cumulative distribution function
2
x
x
1 y2
e dy ,
2
and formulas
ln
d1
St
1
r 2 T t
2
K
T t
ln
d2
(1). Please

Homework 1
This homework is due on Sept 2
1. Pricing a forward contract.
Definition of a forward contract: A contract that obligates the holder to buy or sell an
asset for a predetermined delivery price at a predetermined future time.
Definition of forwar

Homework 2
This homework is due on Sept 9
1. Linear property of normal random variables.
Suppose the price of stock A, St , is lognomally distributed with parameters 4 and 0.1.
That is, the log-price, ln St , is normally distributed with mean 4 and standa

MFIN7003: Mathematical Techniques in Finance _Dr. Rujing Meng
In Class Exercise 3
Please fill in the blanks. The price of a European call is given by the BlackScholes formula
ct = St _ Ke _ ( _ )
the price of a corresponding European put is given by
pt =

In Class Exercise 2
1. What is a discrete process? What is a continuous process?
2. Please write down the Maclaurin series for e x (that is, Taylor expansion of e x about
the point of x = 0 ).
3. Bernoulli random variable (or binary random variable) is a

MFIN7003: Mathematical Techniques in Finance _Dr. Rujing Meng
In Class Exercise 1
Framework:
There are one risky stock S , one riskless cash bond D and one derivative F in
the economy.
The stock price starts at s0 ( S0 = s0 ). A short tick later ( t ),