No-arbitrage for the one-period binomial model
Parsiad Azimzadeh
January 13, 2015
1
One-period binomial model
Consider a coin ip with outcomes
=
H, with probability p
T,
.
with probability 1 p
Assume that a stock S starts at price S0 at time zero and beco
CS335
Matlab Tutorial
CS335 - Computational Methods in Business and Finance
Fall 2016
1 / 51
CS335
Outline
Matlab Overview
Useful Commands
Matrix Construction and Flow Control
Script/Function Files
Basic Graphics
2 / 51
CS335
Getting to Matlab
Everyo
Marking Sheet Assignment 4
CS335 Fall 2016
Name:
ID:
1.
(a) Part a
(4)
(b) Part b
(3)
(c) Part c
(3)
/10
2.
(a)
(10)
/10
3.
(a) Part a
(5)
(b) Part b
(5)
/10
4.
/10
3.
(a) Explanation
(3)
(b) Graph and comment
(2)
(c) Simulation and table
(4)
(d) Compute
CS 335: Assignment 3 Solutions
November 24, 2013
1
We sometimes omit the dependence on t in writing X (t) and Z (t) (i.e. X and Z) for brevity.
a
X (t) Z (t)
f (x, t) (x + t) ext/2
1
df (X (t) , t) = ft dt + fx |X dX + fxx |X dX 2
2
1
1
= eXt/2 (t + X 2)
CS 335: Assignment 4 Solutions
November 26, 2013
1
See Algorithm 1, Table 1 and Figure 1. Note that the mean tends to 1, while the variance tends to 0. This
suggests that I (t), as t 0, is 1. Recall that
n1
2
lim I (t) = lim
n0
t0
In particular, this agre
CS 335: Assignment 2 Solutions
October 28, 2013
1
First, note that
|g (x) g (y)| = |min (f (x) , b) min (f (y) , b)|
max (|f (x) f (y)| , b b)
= |f (x) f (y)| .
Note that since f is continuous and bounded, g must be too1 . We can use the mean value theor
CS335: Numerical methods for business and finance
Spring 2013
Lecture 5 and 6: Monte Carlo simulation
Duy Minh Dang
1 / 31
1
Monte-Carlo simulation
2
Error estimation
3
Multi-asset MC
2 / 31
Risk-neutral world
Under GBM, the no-arb. value of an option can
CS 335: Computational methods in business and finance
Assignment 3
Fall 2013
Instructor: Dr. Duy Minh Dang
Office: DC3327
e-mail: dm2dang@uwaterloo.ca
Due Nov. 13, in class
IMPORTANT: In this and in future assignments, most of the marks for programming qu
CS 335: Computational methods in business and finance
Assignment 4
Fall 2013
Instructor: Dr. Duy Minh Dang
Office: DC3327
e-mail: dm2dang@uwaterloo.ca
Due Nov. 27, in class
IMPORTANT: In this and in future assignments, most of the marks for programming qu
CS335: Numerical methods for business and finance
Fall 2013
Lecture 3: No-arbitrage and binomial trees
Duy-Minh Dang
1 / 35
1
Options
2
No-arbitrage pricing
3
One-period binomial model
4
Pricing options on binomial trees
2 / 35
Outline
1
Options
2
No-arbi
CS335: Numerical methods for business and finance
Fall 2013
Lecture 4: Brownian motion, Itos lemma, and binomial trees
Duy-Minh Dang
1 / 21
1
Brownian motion
2
It
os lemma
3
Binomial model for asset price
2 / 21
Outline
1
Brownian motion
2
It
os lemma
3
B
CS335: Numerical methods for business and finance
Fall 2013
Week 2 summary
Duy-Minh Dang
dm2dang@uwaterloo.ca
1
Computer arithmetic (cont.)
1.1
Cancelation error
Consider the situation in the following example:
Subtraction between two p-digit numbers hav
Marking Sheet Assignment 2
CS350 Fall 2016
Name:
ID:
1.
(a) part a
(5)
(b) part b
(5)
/10
2.
/5
3.
(a) part a
(5)
(b) part b
(5)
(c) part c
(5)
(d) part d
(5)
/20
4.
/10
Total:
/45
Numerical Methods for Option Pricing
Mark Richardson
March 2009
Contents
1 Introduction
2
2 A brief introduction to derivatives and options
2
3 The
3.1
3.2
3.3
3.4
Black-Scholes Model
Asset prices and Itos Lemma . . . .
Derivation of the Black-Scholes PDE
Estimating the drift and volatility of an asset from a time series
Parsiad Azimzadeh
January 27, 2015
1
Geometric Brownian motion
Make the assumption that your asset follows geometric Brownian motion with constant drift and volatility:
dS
= dt + dZ.
S
The
CS 335: Computational methods in business and nance
Assignment 3
Fall 2013
Instructor: Dr. Duy Minh Dang
Oce: DC3327
e-mail: dm2dang@uwaterloo.ca
Due Nov. 13, in class
IMPORTANT: In this and in future assignments, most of the marks for programming questio
CS 335: Computational methods in business and nance
Assignment 4
Fall 2013
Instructor: Dr. Duy Minh Dang
Oce: DC3327
e-mail: dm2dang@uwaterloo.ca
Due Nov. 27, in class
IMPORTANT: In this and in future assignments, most of the marks for programming questio
CS 335: Computational methods in business and nance
Assignment 2
Fall 2013
Instructor: Dr. Duy Minh Dang
Oce: DC3327
e-mail: dm2dang@uwaterloo.ca
Due Oct. 23, in class
IMPORTANT: In this and in future assignments, most of the marks for programming questio
CS335: Numerical methods for business and nance
Fall 2013
Week 1 summary
Duy Minh Dang
dm2dang@uwaterloo.ca
1
Introduction to scientic computing
1.1
Sources of error in scientic computing
There are several sources of error in solving real-world scientic c
CS335: Numerical methods for business and nance
Fall 2013
Week 2 summary
Duy-Minh Dang
dm2dang@uwaterloo.ca
1
Computer arithmetic (cont.)
1.1
Cancelation error
Consider the situation in the following example:
Subtraction between two p-digit numbers havin
Midterm oct 20 in class
Material allowed: course note (printed and handwritten), my own assignment
The midterm does not contain Matlab programming, but pseudo code may be asked.
Marking
Assignment: 32% (4 assignment, 8% on each assignment)
Midterm: 24%
Fi