VOLATILITY MODELLING
Dr Antoine Jacquier
www3.imperial.ac.uk/people/a.jacquier
Department of Mathematics
Imperial College London
Summer Term 20132014
MSc in Mathematics and Finance
This version: June 13, 2014
1
Contents
1 Volatility modelling
1.1
5
Exist
Drop all tables if they exist
DROP TABLE f_shift_assignments;
DROP TABLE f_shifts;
DROP TABLE f_order_lines;
DROP TABLE f_orders;
DROP TABLE f_staffs;
DROP TABLE f_food_items;
DROP TABLE f_regular_menus;
DROP TABLE f_promotional_menus;
DROP TABLE f_custo
QUEUEING FORMULAS
= average number of arrivals entering the system per unit time
= the average service rate
The traffic intensity of the queuing system = = / .
20.4 The M/M/1/GD/ Queuing System
L = (1 )
=
=
2
(1 )
1
2
Lq = L Ls =
=
1
1
L = W,
Lq =
UNIVERSITY OF PORT HARCOURT
Emerald Energy Institute
for Petroleum, Energy Economics, Policy and Strategic Studies
PEM 803/903: Applied Mathematics, Linear Programming &
Optimisation Methods.
Spring, 2017
HOMEWORK
ANSWER ALL QUESTIONS.
DUE DATE:
clear all
clc
%Q1. a)
r = 0.031;
K = 80;
T = 20;
V0 = 100;
N = 240;
M = 250000;
dt = 1/12;
t = dt:dt:T;
rng(13)
dW = randn (M,N);
V = NaN (M,N);
V(:,1) = V0;
sigma1 = 0.15;
sigma2 = 0.25;
for i = 1:M
temp = V0;
for j = 2:N
if j>N/2
sigma = sigma2;
else
si
Options Markets
Lost in Translation
This contract is sold in Antwerpen by Alexander Everaerts,
living at the MinderBroedersRuij in S. Ignatius.
Vise 12 April 1730
Registered f 6 (?)
Philip Jacob de Coninck
I undersigned Pierre Cle promise and obligate m
Historical Equity Markets
Imperial College Business School
Imperial means Intelligent Business
1
Key Concepts and Skills
Know how to calculate the return on an
investment
Understand the historical returns and risks to
various types of investments
Under
Risk free VS Default
Imperial College Business School
Lecture 3: EQUITY
Imperial means Intelligent Business
1
Lecture Outline
Part I
Part II
Stock valuation
Overview Of Equity Markets
Note: our focus is very much on listed companies (i.e.
large companies
Introduction to Project Valuation
Lecture 4
Prof. Emiliano Pagnotta
[email protected]
September 2016
The Investment Decision: Hurdle Rates
First Principles
Works as well as the next best alternative in most cases.
Uses variance of actual returns around
Futures Contracts
Topics
Basic Concepts
Understand how futures contracts are
specified
Know who trades futures and why
Understand the main instruments on
which futures contracts a set
Spot and Futures Markets
A Futures contract is an agreement to buy
Bonds and the Money Market
Imperial College Business School
Imperial means Intelligent Business
1
Bonds
Key Concepts and Skills
The structure of bonds
How bonds are priced and the relationship
between price and yield
The Yield curve
Corporate Bonds an
Market and Securities
Imperial College Business School
Imperial means Intelligent Business
1
Topics
Why Finance?
Over 20% of the UK workforce are in finance
and finance related industries
The Flow of Funds (1):
Where does the money come from, where
does
Lecture 4 Questions: History of Markets
Imperial College Business School
Q1: Dividend yield
The common stock of Abaco Ltd. is expected to pay 1.60
in dividends next year. Currently, the stock is selling for
38.90 a share.
What is the dividend yield?
Imp
Lecture 3 Questions: Equity
Imperial College Business School
Q1: Zero growth stock
Rainbow Rentals pays a constant annual dividend of
1.00 per share on their common stock.
How much are you willing to pay for one share of this
stock if you want to earn a
Algebraic Topology M3P21 2015
solutions 3
AC
Imperial College London
[email protected]
11thth March 2015
A small disclaimer
This document is a bit sketchy and it leaves some to be desired in
several other respects too. I thought it is more useful to
Algebraic Topology Comments on Problem Sheet 2
Andrea Petracci
[email protected]
March 2015
Exercise 1. To maintain mental sanity, I will denote points of I (resp.
S 1 , D2 ) by the letters t, s (resp. z, w) and I will use the letters H, G, F fo
Algebraic Topology M3P21 2015
solutions 2
AC
Imperial College London
[email protected]
23rd February 2015
A small disclaimer
This document is a bit sketchy and it leaves some to be desired in
several other respects too. I thought it is more useful to
Algebraic Topology M3P21 2015
solutions 1
AC
Imperial College London
[email protected]
9th February 2015
(1)
(a) Quotient maps are continuous, so preimages of closed sets are closed
(preimages of open sets are open, and f 1 (Y \ A) = X \ f 1 (A) for
M3/4/5P21  Algebraic Topology
Imperial College London
Lecturer: Professor Alessio Corti
Notes typeset by Edoardo Fenati and Tim Westwood
Spring Term 2014
These lecture notes are written to accompany the lecture course of Algebraic Topology in the
Spring
Algebraic Topology Comments on Problem Sheet 1
Andrea Petracci
[email protected]
February 2015
Exercise 2. Let me show a nice trick that I have learned from the
solution of some of you. The following diagram sums up the situation.
`
i
/X Y
X
q
p
Algebraic Topology M3P21 2015
Homework 2
AC
Imperial College London
[email protected]
2nd February 2015
N.B.
Turn in 5 questions by Monday, 16 February, at 12:00 either in
class or in my pigeonhole in the mailroom on the 6th floor.
(1) Show that fo
Algebraic Topology M3P21 2015
Homework 1
AC
Imperial College London
[email protected]
18th January 2015
N.B.
Turn in 5 questions by Monday, 2 February, at 12:00 either in class
or in my pigeonhole on the 6th floor.
(1) Suppose that f : X Y be a quot
Algebraic Topology M3P21 2015
Homework 3
AC
Imperial College London
[email protected]
16th February 2015
N.B.
Turn in 5 questions by Monday, 9th March, at 12:00 either in
class or in my pigeonhole in the mailroom on the 6th floor.
0
1
n1
2
n
(1) Le
MPC notes
Write short notes on Kinetic
Energy of Diatomic molecules
1)
3 parts translational, rotational and vibrational
2) Kinetic Energy of each atom: ki=mivi2
3) Translational:
kCM=mvCM2
VCM=
4) kCM only changed by external forces
5) Rotational: Kro
CMSC 420
Data Structures
Lecture 1: Introduction
Digital Data
Music
Photos
Movies
Protein
Shapes
DNA
gatcttttta
gataagtgat
ccggtgatcg
cagaatcaag
acacattcgt
tttaaacgat
tattcacatg
tattgcgtat
gttgttatgt
tcgcgcgatc
ctctttatta
gcagatcata
aagctgggat
ggatatctac
Tries & Sufx Trees
Storing Collections of Strings
All our dictionary data structures can be used to
store strings, of course.
But strings have several properties that might make
you want a different data structure:

Comparing strings can be slow (not con
q dXe g h d d h Xbtb p qX b d
r %!Sx S 4sgedSl0wyq% Sa%Sa2erSgHS
r aSyXfe
hh d
F ` gh d rXe d hh d
5 !y g 'g cH2#4S kr aSyXfe g )#UcHU%yhq Su )S H% n ! SX Hch
` gh d g r ` b " h e d
hghh de bg q X` r F gh d qg f d X ` r gb X d cfw_ n`eg b p ` b g rg
CMSC 420: Data Structures
Spring 2008
Instructor: Carl Kingsford, Oce: AVW 3223. Email: carlkcs.umd.edu. Oce hours:
Tues 3:154:15. If you cannot attend oce hours, email me about scheduling a dierent
time.
Teaching assistants:
Radu Dondera, [email protected]