Institute for Applied and Numerical Mathematics
Prof. Dr. Tobias Jahnke Dr. Tudor Udrescu Marcel Mikl
Numerical methods in
Minimizing with respect to both p and q, gives us
Problem sheet 5
The Distribution of S&P 500 Index Returns
William J. Egan, Ph.D.
January 6, 2007
This paper examines the fit of three different statistical distributions to the returns of the S&P 500 Index from
1950-2005. The normal distribution
Jump-diusion models: a practitioners guide
Universit Paris 7
Universit Toulouse 1
[email protected][email protected]
The goal of this paper is to show that the ju
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Brownian Motion and Geometric Brownian Motion
academic year 201011
Standard Brownian Motion
Denition. A Wiener process W (t) (standard Brownian Motion) is a stochastic process
with the following properties:
Homework Assignment 6
1. While searching for the minimum of
f(x) = [x12 + (x2+ 1)2][x12 + (x2 - 1)2]
the algorithm terminates at the following points:
x(1) = [0,0]T
x(2) = [0,1]T
x(3) = [0,
C&O 367: Optimality Conditions and
Duality, Assignment 5
Due on Friday, April 4, 2008.
2 Problems on Definitions of (CP)
3 Rockafellar-Pshenichnyi Optimality Conditions for (CP)
4 Generalized Farkas Lemma
Assignment 3, C&O 367, W08
This assignment has 7 problems and 3 pages.
Due Wed.Feb. 27, 2008
MATLAB (Roundoff Error)
1. Pretend you have a computer with base 10 and precision 4 that truncates after each
arithmetic operation; for example, the sum of 24
EECS 598: Statistical Learning Theory, Winter 2014
Lecturer: Clayton Scott
Scribe: Andrew Zimmer
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications.
They may be distributed
Problem Set 1
Due on Wednesday Oct 5 at 4pm.
Note: The time step t used in all the problems is one year and r is a continuously
compounded annual interest rate unless otherwise specified .
1. (Binomial Tree Model and Call-Put Parity) Consider a 3-period r
ACT460/STA2502 Assignment 2
Due at 4pm, Wednesday Oct 19, 2016
Question 1 You are to build a three-period binomial model for stock price St , S0 = 100,
with the time step equal to 6 months (t = 0.5) such that the random return for each period
having d = 1
The price St of a stock is assumed to follow the process
St = 100e0.05 t+0.2 Wt .
Time is counted in years, today is t = 0, and the annual interest rate compounded continuously is 3%. Find the probability that six months from now,
Problem Set 4 Part One
Due on Wednesday Nov 30 at 4pm
A European option written on a stock St , S0 = 45 has the following payoff at time T = 1
(ST ) =
if ST 60
2ST 120 if ST 60.
Assuming the Black-Scholes model with the risk-free i
U.U.D.M. Project Report 2003:18
Examensarbete i matematik, 20 pong
Handledare: Ola Hammarlid , Swedbank Markets
Examinator: Johan Tysk
Department of Mathematics
In the orig