Monte Carlo Simulation Regime Switching
Not to be Handed In
We will discuss this in class
Write a VBA function that is callable from an Excel file. The VBA Function should be
able to calculate the value of a call option assuming that the volatility can sw

BUFN 766 Financial Engineering
Not to be handed in.
I suggest doing these problems with a calculator.
Problem 1.
Assume that a stocks prices follow the binomial model as follows:
Assume that the gross risk free return is 1.07 (7% per period), and that the

BUFN 766 Financial Engineering
Not to be handed in.
I suggest doing these problems with a calculator.
Problem 1.
Assume that a stocks prices follow the binomial model as follows:
Assume that the gross risk free return is 1.07 (7% per period), and that the

Financial Engineering Assignment
Not to be handed in
Monte Carlo Simulation Asian Options
Write a VBA function that is callable from an Excel file. The VBA Function should be
able to calculate the value of an Asian call.
Use the Lognormal model to find as

Monte Carlo Simulations
Using The Lognormal Model
Mark Taranto
Monte Carlo Simulations
With a Monte Carlo simulation, we take a
sample of a random variable, and determine
the value of a process if that number comes
up.
Then we repeat the process, finding

Market Microstructure
and Algorithmic Trading
Financial Engineering
Mark Taranto
Auctions
We will discuss two types of financial
auctions that illustrate a problem associated
with trading large blocks of an asset.
Rational Expectations Model
Implicit auct

Final Review
Financial Engineering
Final Exam
Two Hour Exam
May 13, 10:30-12:30 in our usual classroom
120 points (12 10 point questions)
Most questions will require a short answer
Some will require calculations
You will need a calculator
Closed Book/Clos

Survivorship Bias
Financial Engineering
Mark Taranto
WW II Airplanes
In WW II, the US conducted bombing raids over
Germany originating in England.
When the planes returned, men were sent to inspect the
planes for bullet holes.
Information was gathered, an

MCS-Example
Step 1: Generate normal random numbers
Step 2: For each random number, generate
future prices using the lognormal model
2
St S0e
rf
z t
t
2
max 0, S t K
Step 3: Generate the payoff for that value
Step 4: Using the risk free rate, find the

Excel & Math Tools for Portfolio
Models and Default Models
Financial Engineering
Mark Taranto
Matrix Algebra
We can think of a matrix as a table where a matrix of dimension mn
has m rows and n columns.
For example, a 32 matrix looks like:
while a 23 matri

Default Models
Markov Processes
Financial Engineering
Mark Taranto
Markov Processes
We can consider any process through time where
there are a finite number of possible states.
For example:
At any time, there are two states, economic expansion
or recessio

VBA Programming
Mark Taranto
BUFN 766
Schedule
VBA
Getting Started
Conditional Statements
Looping
Arrays
We will talk about these when we cover Binomial Trees
Examples (using financial applications)
VBA
We have all used built-in Excel functions
VBA (Visua

Chooser Options
Financial Engineering
Mark Taranto
Chooser Options
A Chooser Option allows the buyer to
decide if she wants a Put or a Call at some
future date.
For a simple chooser option, the Put and
Call are European options that have the
same expirati

Brownian Motion
Mark Taranto
Random Walk
A random walk is one where each new value is
equal to the old value plus a random piece
Consider a random walk where a new step is taken
after equal time steps of length t. At each step, you
add the random piece x

The Black Scholes Formula
Mark Taranto
Bonds
Let B(t) be the price of a bond at time t
Then r is constant, so:
dB t
dB t
dt
r
dt or
r
B t
B t
The general solution to the differential equation is :
B t Ae r T T0
If we know the current price and th

Convertible Bonds
Mark Taranto
Convertible Bonds
A Typical Convertible Bond:
A long-maturity bond issue (face value $1000)
Issued at or near Par, with semiannual coupons
Bondholders have the right to convert the bond for shares
at a fixed price (e.g., 50

Option Greeks and Delta Hedging
Mark Taranto
Financial Engineering
Replicating Options
We saw with Binomial Option Pricing that we can
replicate the payoff of an option with:
A portfolio of the underlying asset and a bond
A rule for rebalancing the portfo

Lognormal Model of
Stock Prices
Mark Taranto
Todays Plan
Review of Discrete Probability
Distributions
Normal Distribution
Lognormal Distribution
Lognormal Model of Stock Prices
Discrete Probabilities
Distributions
Suppose x is a random variable with finit

Binomial Trees
Mark Taranto
BUFN 766
Binomial Trees
We have talked a little about Binomial Trees.
We showed that we can price options in a simple tree with
one time period
We talked about how this idea can be extended
European Options can be priced using

Introduction to Option Pricing
Mark Taranto
Financial Engineering
Bet on a Coin Flip
How much would you pay for a security
that pays $1000 in one month if a coin flip
comes up heads?
Assume Price of One Year Treasury Bill is
99.98% of face value
Bet on a

Financial Engineering
Mark Taranto
BUFN 766
RH Smith School
Part 1
Introduction
About You
About Me
Syllabus
Questions for Study
Introduction to Option Pricing
Introduction to VBA
Financial Engineering
What will we be doing this term?
Are there any topics