Introduction to arbitragefree pricing of financial derivatives
STAT 473

Spring 2014
STAT 473!
HW 1 Solution
!
1.!
!
Recall C ( K , T ) P ( K , T ) = S0 K e rT !
Since both options are atthe money, K = S0 .!
!
(
)
We have C ( K , T ) P ( K , T ) = S0 S0 e rT = S0 1 e rT !
!
!
T > 0,
r T < 0
!
!
e rT < 1
RHS = S0 (1 e rT ) > 0
!
!
!
There
Introduction to arbitragefree pricing of financial derivatives
STAT 473

Spring 2014
STAT 473 Quiz 1
You are given
(i) The stock price is 40 per share.
(ii) The stock pays continuous dividends propositional to its price at a rate oi 2%
(iii) A 182day European put option on the stock with strike K costs 0.80
(iv) A 182day European cal
STAT 473.
Practice Problems for Final
Spring 2014
FigueroaLpez
o
Description:
(A) The problems below are only intended to serve as preparation or practice for your actual
nal exam. The solution key of the exam is provided at the end of the document.
(B)
STAT 473. Practice Problems for Exam 2
Spring 2014
Description:
(A) Exam 2 will cover Chapter 10 (Binomial Model), Sections 12.112.5 (BlackScholes framework and Greeks), DeltaGammaTheta Approximation, Section 13.B (Greeks using Binomial Trees), and Se
Introduction to arbitragefree pricing of financial derivatives
STAT 473

Spring 2014
mean
st. dev
nozzle
X
Z
P(Z<2.2)
1050
150
760 ml/min
1425
2.5
0.9861
950
0.67
P(Z>0.667)
P(0.67<Z<2.2)
0.2514
0.7486
phi(2.2)phi(0.67)
smallest 2%
Z(.02)
742.5
P(Z>1380)
0.0139
P(Y>=1) 1P(Y=0)
0.067595
0.7347
2.05
mean
st. dev
X
Z
P(Z>=0.667)
Z
P(
Introduction to arbitragefree pricing of financial derivatives
STAT 473

Spring 2014
A particular telephone number is used to receive both voice calls and fax messages.
Suppose that20%of the incoming calls involve fax messages, and consider a sample of20incoming calls. (R
80% voice calls
(a) What is the probability that at most7of the cal
Introduction to arbitragefree pricing of financial derivatives
STAT 473

Spring 2014
Signal 1
Signal 2
0.45
a.)
Signal 1 or 2
0.5
Signal 1&2
0.4
b.)
Signal 1 but not 2
0.05
c.)
Exactly 1
0.15
0.55
Ai
i
1
P(A1)
P(A2)
0.13
2
P(A3)
0.1
3
P(A1UA2) P(A1UA3) P(A2UA3) P(A1&A2&A3)
0.06
0.16
0.16
0.13
a.)
What is the probability that thesystem doe
Introduction to arbitragefree pricing of financial derivatives
STAT 473

Spring 2014
y
p(y)
45
0.06
46
0.1
47
0.13
48
0.14
49
0.24
50
0.16
51
0.06
a.) Probability that all ticketed passengers will be accommodated
0.83
b.) What is the probability that not all ticketed passengers wil be accommadated?
0.17
c.) If you are the first person on
Introduction to arbitragefree pricing of financial derivatives
STAT 473

Spring 2014
STAT 473
1.!
!
rd = 4% , re = 6% !
!
By Call Put Parity,!
!
0.1 0.082 = x e6%1 0.9 e4%1
x = 0.93729
HW 2 Solution
!
!
!
!
C ( x, T ) P ( x, T ) = x (T ) e reT K e rdT
!
Page 1 of 6
STAT 473
HW 2 Solution
2.!
!
x0 = 0.95 $ , rd = 4% , re = 6% !
!
By Call
Introduction to arbitragefree pricing of financial derivatives
STAT 473

Spring 2014
STAT 473. Practice Problems for Exam 1
FigueroaLpez
o
Description:
(A) Exam 1 will cover Chapter 9 from McDonalds textbook.
(B) The problems below are intended to serve as preparation or practice for your exam.
(C) You should not expect that your actual
STAT 473. Practice Problems for Exam 2. Solutions.
Spring 2014.
Problem 1.
a)
b)
Problem 2.
Problem 3.
Problem 4.
Binomial Tree for the future price
80
96
72
115