Lectures 2 & 3
Options Markets and
Properties of Stock Options
Review
2
Last week, we learned that an option gives the holder of
the option the right to do something, but the holder
does not have to exercise this right.
By contrast, in a forward or futu
Lecture 4
Futures and Forwards
Example
2
On March 5, a trader in New York may call a broker with
instructions to buy 5,000 bushels of corn for delivery in July.
The broker would issue instructions to a trader to buy (take a
long position in) one July cor
Lecture 4
Binomial Trees and
Black-Scholes-Merton Model
Binomial Trees
2
A useful and very popular technique for pricing an option
involves constructing a binomial tree.
This is a diagram representing different possible paths
that might be followed by t
Lecture 1
Introduction to Derivatives
What Is A Derivative?
2
A derivative is a financial instrument whose value
depends on, or is derived from, the values of other, more
basic underlying variables.
Usually, the variables underlying derivatives are the
Payoff from a long position in a call option: max(ST K, 0)
Payoff from a long position in a put option: max(K ST, 0)
Payoff from a short position in a call option: max(ST K, 0) = min(K ST, 0)
Payoff from a short position in a put option: max(K ST, 0) = mi
HOMEWORK 3
This homework is due on March 6 th. It should be handwritten and handed in at the beginning of our
lecture. You can also scan your handwritten assignments and email them to me. No late homeworks
will be accepted. Please show all your work to re
HOMEWORK 3 SOLUTIONS
1) A tree describing the behavior of the stock price is shown below. The risk-neutral probability of
an up move, , is given by
p
p
e005312 095
05689
106 095
There is a payoff from the option of
for the highest final node (which
5618
HOMEWORK 1 SOLUTIONS
1) a) The upfront cost for the stock alternative is 871.37 10 = $87,137.
The upfront cost for the option alternative is 41.60 100 = $4,160.
b) The gain from the stock alternative is 950 10 87,137 = $7,863.
The total gain from the opti
HOMEWORK 2 SOLUTIONS
1) a) The lower bound is
28 25e 00803333 $366
b) The lower bound is
15e 006008333 12 $293
2) Put-call parity for dividend-paying stocks gives
c Ke rT D p S 0
or
p c Ke rT D S 0
In this case
p 2 30e 016 12 (05e 012 12 05e 01512 ) 29 25
HOMEWORK 4 SOLUTIONS
1) There is a margin call if $1000 is lost on the contract. This will happen if the price of wheat
futures rises by 20 cents (=1000/5000) from 750 cents to 770 cents per bushel. $1500 can be
withdrawn if the futures price falls by 30
HOMEWORK 4
This homework is due on March 13 th. It should be handwritten and handed in at the beginning of
our lecture. You can also scan your handwritten assignments and email them to me. No late
homeworks will be accepted. Please show all your work to r
FIN403/IE412
2015-2016
Solutions for Exercises
1) A butterfly spread is created by buying the $55 put, buying the $65 put and selling two of the $60
puts. This costs 3 8 2 5 $1 initially. The following table shows the profit/loss from the
strategy. The bu
FIN403/IE412
2015-2016
Some Exercises for Practice
1) Three put options on a stock have the same expiration date and strike prices of $55, $60, and $65.
The market prices are $3, $5, and $8, respectively. Explain how a butterfly spread can be created.
Con
FIN 403 / IE 412
Derivative Securities / Financial Engineering
Sample Midterm Exam
Calculators allowed
Documents NOT allowed
Textbook NOT allowed
Computers NOT allowed
You have 2.5 (two and a half) hours to solve the 6 (six) problems below. You should use
Put-Call Parity Formulas
Underlying Asset
Put-Call Parity
c + Ke rT = p + S0
Stock, no dividend
Stock, discrete dividend
Stock, continuous dividend
Currency
c + Ke rT = p + S0 PV0,T (Div)
c + Ke rT = p + S0e qT
r T
c + Ke rT = p + x0e f
c + Ke rT = p + B0
Formula Sheet 1
Fin301 Financial Management
Prof. Aysun Alp
Time Value of Money
P V (single cash f low) =
CT
(1 + r)T
F V (single cash f low) = C0 (1 + r)T
P V (perpetuity) =
C
r
P V (growing perpetuity) =
P V (annuity) =
C
rg
C
1
(1
)
r
(1 + r)T
P V (g
Lecture 6
Valuing Stocks
Fundamental Analysis
How to identify stocks that are mispriced relative to
some measure of true value.
True value can only be estimated, therefore analysts
use models to estimate the fundamental value of a
stock from observable
Aysun Alp
FIN301 Financial Management
Assignment 2
1. White Wedding Corporation will pay a $3.05 per share dividend next year. The
company pledges to increase its dividend by 5.25% per year, indefinitely. If you require
an 11 percent return on your invest
Solutions to Assignment 1
1. Stock account: FVA=800[(1+(.12/12)]^480-1/(.12/12)]=9,441,818.008
Bond account: FVA=400[1+(.08/12)]^480-1/(.08/12)]=1,396,403.133
So the total amount saved at retirement is:
9,441,818.008+1,396,403.133=10,781,221.14
Solving fo
Aysun Alp
FIN301 Financial Management
Assignment 1
1. You are planning to save for retirement over the next 40 years. To do this, you
will invest $800 a month in a stock account and $400 a month in a bond account.
The return of the stock account is expect
Aysun Alp
FIN301 Financial Management
Solutions to Assignment 3
1. Answer the following questions comparing the IRR rule with the NPV rule:
a. What conditions must be satisfied for the IRR rule to result in the same decision as the NPV
rule for independen
In-Class Exercise 1
On September 1 2007 Susan bought a motorcycle of $25000. She paid $1000 down and
financed the balance with 8.4% APR, compounded monthly with a five year loan. She
started the monthly payments exactly one month after the purchase (Octob
Solution to In-Class Exercise 1
On September 1 2007 Susan bought a motorcycle of $25000. She paid $1000 down and
financed the balance with 8.4% APR, compounded monthly with a five year loan. She
started the monthly payments exactly one month after the pur
Aysun Alp
FIN301 Financial Management
Assignment 3
1. Answer the following questions comparing the IRR rule with the NPV rule:
a. What conditions must be satisfied for the IRR rule to result in the same decision as the NPV
rule for independent projects?
b
In-Class Exercise 3
Lean Dining Restaurant is considering the purchase of a $16,000 waffle maker. The waffle
maker has an economic life of four years and will be fully depreciated by the straight-line
method. The machine will produce 2,000 waffles per yea
In-Class Exercise 4
Let x and y be two stocks with E(R)=12% for x and E(R)=20% for y, x=50%, y= 70%, xy =
0.1, where denotes volatility and denotes correlation. You invest 30% of your wealth in
stock x and 70% in stock y.
a) What is the expected return of
In-Class Exercise 5
Find the WACC of William Tell Computers. The total book value of the firm's equity is
$10M. Book value per share is $20. The stock sells for a price of $30 per share. The cost
of equity is 15%. The firm's bonds have a face value of $5M
In-Class Exercise 3
Lean Dining Restaurant is considering the purchase of a $16,000 waffle maker. The waffle
maker has an economic life of four years and will be fully depreciated by the straight-line
method. The machine will produce 2,000 waffles per yea
In-Class Exercise 4
Let x and y be two stocks with E(R)=12% for x and E(R)=20% for y, x=50%, y= 70%, xy =
0.1, where denotes volatility and denotes correlation. You invest 30% of your wealth in
stock x and 70% in stock y.
a) What is the expected return of