AMS-514 Computational Finance
Assignment 1
(1). Use Wekipedia to nd the following topics:
Euroupean Options, Put and Call
Single Step Random Walk
Brownian Motion
Central Limit Theorem
Wieners Process
Itos Lemma
Black-Scholes Equation
Write a readin
AMS-514 Computational Finance
Final Project 1
Presentation Guideline
(1). In cover page, show project title and names of the team members.
(2). Abstract of the project, no more than 75 words.
(3). Outline of the presentation.
(4). Mathematical analysis.
(
AMS-514 Computational Finance
Final Project 1
Presentation Guideline
(1). In cover page, show project title and names of the team members.
(2). Abstract of the project, no more than 75 words.
(3). Outline of the presentation.
(4). Mathematical analysis.
(
AMS-514 Computational Finance
Final Project 3
Presentation Guideline
(1). In cover page, show project title and names of the team members.
(2). Abstract of the project, no more than 75 words.
(3). Outline of the presentation.
(4). Mathematical analysis.
(
AMS-514 Computational Finance
Final Project 2
Presentation Guideline
(1). In cover page, show project title and names of the team members.
(2). Abstract of the project, no more than 75 words.
(3). Outline of the presentation.
(4). Mathematical analysis.
(
AMS-514 Computational Finance
Final Project 2
Presentation Guideline
(1). In cover page, show project title and names of the team members.
(2). Abstract of the project, no more than 75 words.
(3). Outline of the presentation.
(4). Mathematical analysis.
(
AMS-514 Computational Finance
Final Project 1
Presentation Guideline
(1). In cover page, show project title and names of the team members.
(2). Abstract of the project, no more than 75 words.
(3). Outline of the presentation.
(4). Mathematical analysis.
(
AMS-514 Computational Finance
Final Project 1
Presentation Guideline
(1). In cover page, show project title and names of the team members.
(2). Abstract of the project, no more than 75 words.
(3). Outline of the presentation.
(4). Mathematical analysis.
(
0.1. DERIVATION OF BLACK-SCHOLES EQUATION
0.1
0.1.1
3
Derivation of Black-Scholes Equation
The Diusion Equation
For the parabolic diusion equation
Figure 1: Solution of diusion equation with initial condition as the delta
function Eq. (7). The diusion coe
To run FronTier on galaxy.ams.sunysb.edu:
cp ~linli/FronTier.gas.09_15_11.tar.gz .
tar xvfz FronTier.gas.09_15_11.tar.gz
cd FronTier
build.sh -d -n
make
cp ~linli/func.tar .
cd functions
make
./func -i in-gauss -o out-gauss
./func -i in-step -o out-step
AMS-514 Computational Finance
Assignment 3
The standard random number generator in C language has the following probability
functions
0 x<0
x
P ( X x) = F ( x) =
f (u)du = x 0 x 1
1 x>1
and probability density function
0 x<0
f (x) = 1 0 x 1 .
0 x>1
With
AMS-514 Computational Finance
Assignment 2
(1). Using van Neumann analysis, nd the stability conditions of schemes for the wave
equation
ut + aux = 0
(a). The backward scheme
un un1
un+1 un
j
j
j
+a j
=0
t
x
(b). The MacCormack scheme
un+1 = un R + un ,
j
AMS-514 Computational Finance
Assignment 2
(1). Using van Neumann analysis, nd the stability conditions of schemes for the wave
equation
ut + aux = 0
(a). The upwind scheme
un+1 un
un un1
j
j
j
+a j
=0
t
x
(b). The MacCormack scheme
un+1 = un R + un ,
j
j
AMS-514 Computational Finance
Assignment 1
(1). For the initial value problem of the heat transfer equation
ut = uxx ,
u(x, 0) = u0 (x),
x (, ),
using fourier transform, we have found the general solution in the following form
1
u(x, t) =
2
u(k, t)eikx d
Introduction
Stable Distribution
Algorithms and Numerical Results
Brief Introduction to Advanced Topics
Stable Distribution: Theory and Application
Author: Yiyang Yang
Advisor: Pr. Xiaolin Li, Pr. Zari Rachev
Department of Applied Mathematics and Statisti