Mathamatics. Table of Contents. Question 1 2. Question

MATHAMATICS

Table of Contents
Question 1................................................................................................................ 2
Question 2................................................................................................................ 3
1.......................................................................................................................... 3
2.......................................................................................................................... 3
3.......................................................................................................................... 4
4.......................................................................................................................... 4
Question 3................................................................................................................ 4
1.......................................................................................................................... 4
2.......................................................................................................................... 4
3.......................................................................................................................... 5
4.......................................................................................................................... 5
5.......................................................................................................................... 5
6.......................................................................................................................... 5
7.......................................................................................................................... 5
Question 4................................................................................................................ 5
Question 5................................................................................................................ 6
PART A................................................................................................................ 6
Part B.................................................................................................................. 6
Question 6................................................................................................................ 6
Part A.................................................................................................................. 6
Part B.................................................................................................................. 7
Question 7................................................................................................................ 7
PART A................................................................................................................ 7
PART B................................................................................................................ 9
Reference............................................................................................................... 10
Question 1

Consider the non dividing stock force of interest
R=0.045, σ =0.24
T=1/4
S0=$45
, , , , and .
d1=ln ( $ 45
70 ) +¿ ¿= -0.62090
D2=d1-0.24√ 1/4= -0.7409
The risk rate on the interest is,
=0.045 e0.25 X 0.25N (0.62090)-0.24(-0.7409)
st −st −1=0.165
Question 2

1.
The value function of the special option at time−T, i.e., its payoff function (Chow and
Teicher, 2011), is
This means that we can replicate the special option with a long zero-coupon bond redeemable
at time−T for K and a short European time−T, strike−K put option. So, the current delta of
the special option is
2.
C= S0N(d1)-Xe−rtN(d2)
C=S0N(d1)-Xe−rtN(d2)+Xe−rT
= S0N(d1)+ Xe−rt [1- N(d2)]
= S0N(d1)+ Xe−rt [1- N(−d2)]
3.
Ln(40/42)+(r+0.045)(0.25)=0(r+0.045)(0.25)= ln(45/40)(r+0.045)(0.25)in(50/40)
R=4ln(42/40)-0.045=0.1502
4.
The Black–Scholes–Merton formula for a European put option is
so that
or
or