August 16, 2012
A Brief History of Bond Market Disasters
Those who cannot remember the past are condemned to repeat it. George Santayana
The History of Bonds
The Eisenhower Recession Multiple-Year Bond Losses
Bond-like financial instruments have a long hi
Guidelines to Project Proposal and Report Marking
A single score out of 10 under each heading is selected. As a guide to calibration: 3 = "failing", 5 =
"satisfactory", 7 = "good", 9 = "excellent". The phrases at the ends of the scales are prompts only, n
Evaluation Form for an Oral Presentation
Title:_
Members:_
1. Determine the confidence of the speaker. The speaker should be comfortable and easily connect
with the audience. If a speaker acts uncomfortable or nervous, the presentation is not going well.
MATH 6911
Numerical Methods in Finance
Hongmei Zhu
Department of Mathematics & Statistics
York University
hmzhu@yorku.ca
Math6911 , HM Zhu
Motivations on Financial Mathematics
Quants: The Alchemists of Wall Street
Clips: from 2 to 8:30 minutes
The Ascent
Question
How to generate samples according to standard
normal distribution N(0,1) from U(0, 1) ?
Math6911,
, HM ZHU
Generate a general distribution
F(x) from U(0, 1):
Inversion Method
Given the distribution function F x PX x, we can generate
random varia
3. Monte Carlo Simulations
Math6911 , HM Zhu
References
1. Chapters 4 and 8, Numerical Methods in Finance
2. Chapters 17.6-17.7, Options, Futures and Other
Derivatives
3. George S. Fishman, Monte Carlo: concepts,
algorithms, and applications, Springer, Ne
2. Lattice Methods
(Hull, Chap. 11)
(Brandimarte, Chapter 7)
2.1 A Simple Binomial Option Pricing Model
Math6911 , HM Zhu
General One-Step Binomial Tree
(No-arbitrage evaluation)
A derivative lasts for time T and is dependent on a stock
S0
v=?
S0 u
vu
S0d
7. Greek Letters, Value-at-Risk
7.1 Greek Letters
(Ref. Hull)
Math6911, W14, HM Zhu
Outline
Delta, Delta hedging
Theta
Gamma
Relationship between delta, Theta and Gamma
Vega
2
Math6911, W14, HM ZHU
=
S
Delta
Delta () is the rate of change of the value
o
Math 6911 W2015: Suggested Project List
In the course projects, you are expected to learn about the methods, implement them and
then test its computational accuracy and efficiency and comments on its advantages and
limitations, on some set of financial pr