Put-Call Parity Formulas
c + Ke rT = p + S0
Stock, no dividend
Stock, discrete dividend
Stock, continuous dividend
c + Ke rT = p + S0 PV0,T (Div)
c + Ke rT = p + S0e qT
c + Ke rT = p + x0e f
c + Ke rT = p + B0
Futures and Forwards
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
Binomial Trees and
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
Introduction to Derivatives
What Is A Derivative?
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
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
There is a payoff from the option of
for the highest final node (which
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
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withdrawn if the futures price falls by 30
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
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
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.
FIN 403 / IE 412
Derivative Securities / Financial Engineering
Sample Midterm Exam
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
Lectures 2 & 3
Options Markets and
Properties of Stock Options
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