B. Maddah ENMG 602 Introduction Financial Engg 09/28/11
Brief Review of the Theory of Interest
Interest concept: Review
Recall that interest is the manifestation of time value of
money.
Under a compound interest rule, an investment earns interest
on inte

Dr. Maddah
ENMG 624 Financial Engg I
03/15/06
Chapter 6 (Supplement)
Probability Primer1
Sample space and Events
Suppose that an experiment with an uncertain outcome is
performed (e.g., rolling a die).
While the outcome of the experiment is not known i

B. Maddah
ENMG 625 Financial Engg II
07/07/09
Chapter 12 Basic Option Theory (2)
Early Exercise (Ross 2003)
Proposition One should never exercise an American style call
option before its expiration time T.
Proof. Suppose that the stock price at time t <

Dr. Maddah
ENMG 625 Financial Engg I
09/29/11
Chapter 11 Models of Asset Dynamics
Overview
Stock price evolution over time is commonly modeled with
one of two processes: The binomial lattice and geometric
Brownian motion.
Both of these are stochastic pro

Dr. Maddah
ENMG 625 Financial Engg II
01/21/08
Chapter 10 Forwards, Futures, and Swaps (1)
Forward Contracts
A forward contract on a commodity is a contract to purchase
or sell a specific amount of an underlying commodity at a
specific price and at a spe

Dr. Maddah
ENMG 625 Financial Engg II
11/09/06
Chapter 10 Forwards, Futures, and Swaps (2)
Swaps
A swap is an agreement to exchange one cash flow stream for
another.
In a plain vanilla swap, one party swaps a series of fixedlevel payments for a series of

Dr. Maddah
ENMG 624 Financial Engg I
04/05/06
Chapter 7 The Capital Asset Pricing Model
The capital asset pricing model (CAPM) gives the price of a
risky asset within the framework of the mean-variance setting.
Market equilibrium
Assume that
o All inves

Dr. Maddah
ENMG 624 Financial Engg I
03/22/06
Chapter 6 Mean-Variance Portfolio Theory
Single Period Investments
Typically, in an investment the initial outlay of capital is
known but the return is uncertain.
A single-period investment is as follows: M

Dr. Maddah
ENMG 624 Financial Engg I
05/24/06
Chapter 9 General Principles (Continuous)
Log-optimal pricing
The portfolio optimality conditions may be seen as pricing
n
*
equations. Given the optimal portfolio x* = d j j , the price
j =1
of security i is

Dr. Maddah
ENMG 624 Financial Engg I
04/26/06
Chapter 8 Models and Data
The mean-variance theory mainly applies to stocks. However, it
is not easy to estimate the required parameters (means,
variances, and covariances) in the case of stocks.
Factor mode

Dr. Maddah
ENMG 624 Financial Engg I
05/17/06
Chapter 9 General Principles
St. Petersburg Paradox
How do you decide about uncertain payoffs?
Based on expected value perhaps?
How much would you pay to play the following game?
o Flip a coin until the first

Dr. Maddah
624 Financial Engg I
12/12/07
Chapter 6 Mean-Variance Portfolio Theory (continuous)
The Markowitz Model
The Markowitz model determines the portfolio in the
minimum-variance set corresponding to a mean return r .
1 n n
min wi w j ij
w1 , wn 2

B. Maddah
ENMG 625 Financial Engg II
07/07/09
Chapter 12 Basic Option Theory (1)
Option basics
An option is the right, but not the obligation, to sell or buy an
asset at specific terms.
E.g., the option of purchasing a home in exactly one year for
$200 K