Problem Set Arbitrage Bounds, Put Call Parity,
and Early Exercise
1. Put Call Parity
(a) The continuously-compounded risk free rate per annum is 20% per year. European call options
on the stock of XYZ CORP with an exercise price of $35 and a maturity date

Problem Set Forwards and Futures
1. Suppose that you enter into a six-month forward contract on a non-dividend-paying stock when the
stock price is $30 and the risk-free interest rate (with continuous compounding) is 12% per annum.
What is the forward pri

Solution for Review & Introductory Material
Problem Set
1. First, a plot of natural log and ex
The natural logarithm ln(x) is the logarithm having base e,
where e=2.718281828.
3
2
1
ln(x)
0
-1
0
2
4
6
8
10
-2
-3
-4
-5
x
8
7
6
5
ex
4
3
2
1
0
-2
-1
0
x
1
2

Solution for Arbitrage Bounds, Put Call Parity, and
Early Exercise Problem Set
1.
(a) Put Call Parity for European options on a non-dividend paying stock:
S = c(K) + KerT p(K).
The payoff from the stock is equivalent to the payoff from a strategy of buyin

Solution for Payoff Diagram Problem Set
1. Positions
What is the difference between a long forward position and a short forward position?
With a long forward position, you are obligated to buy in the future at a pre-determined price.
With a short forward