Quantitative Finance
FINC6000
Lecture 2: Black-Scholes Model - PDE Approach
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Overview
Black-Scholes model
assumptions
asset
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 8
1. Suppose that the EUR/USD volatility quotes are
atm = 21.6215%, RR0.25 = 0.5%, and
BF0.25 =
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 9
1. You have been asked to value a discrete arithmetic Asian call option, p, by Monte Carlo
sim
UTS:
UNIVERSITY OF TECHNOLOGY, SYDNEY
PROCUREMENT & CONTRACT
MANAGEMENT (SN 16423)
WEEK 10
6 October 2015
Variations/Progress Payment Claims
UTS:
UNIVERSITY OF TECHNOLOGY, SYDNEY
Overview Week 10
1.
2
BUSINESS SCHOOL
Unit of Study Outline
Unit Code FINC6000
Unit Title Quantitative Finance
Semester 2, 2016
Pre-requisite Units: FINC5001
Co-requisite Units:
Prohibited Units: FINC5002
Assumed Knowledge
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 5
1. Assuming a piecewise constant asset volatility as a function of time, calibrate the Black-S
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 6
1. Suppose that the coefficients for a pseudo-random number generator with period n = 231 are
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 1
1. The purpose of this question is to provide some intuition behind the definition of self-fin
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 4
1. Let Xt be the stock price at time t with constant volatility . Recall that in considering
E
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 7
1. The current price of a non-income paying asset is X0 = 10.0, the risk free rate is 4.0%, an
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 10
1. Let gi (Xi | Xi1 ) be the lognormal density of Xi+1 given Xi under the Black-Scholes model
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 11
1. Show that the ratio, P (t, )/P (t, T ), where T is a martingale under the T -forward measu
BUSINESS SCHOOL
Unit of Study Outline
Unit Code FINC6000
Unit Title Quantitative Finance and Derivatives
Semester 1, 2017
Pre-requisite Units: FINC5001
Co-requisite Units:
Prohibited Units: FINC5002
A
Steven R. Dunbar
Department of Mathematics
203 Avery Hall
University of Nebraska-Lincoln
Lincoln, NE 68588-0130
http:/www.math.unl.edu
Voice: 402-472-3731
Fax: 402-472-8466
Stochastic Processes and
Ad
Relationship between Probabilities, Wiener Processes, and
Numeraires
FINC6000 - Quantitative Finance and Derivatives
Oh Kang Kwon
The purpose of this short note is to make explicit the interrelated co
Quantitative Finance
FINC6000
Lecture 2: Black-Scholes Model - PDE Approach
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Overview
Black-Scholes model
assumptions
asset
Useful Formulae
Unless explicitly stated otherwise, Xt in the formulae below will refer to a process satisfying the equation
dXt = (t, Xt )dt + (t, Xt )dwtX .
()
It
os lemma: Let Xt be given by ().
Quantitative Finance
FINC6000
Review and Information on Final Exam
Quan Gan
Discipline of Finance The University of Sydney
Review
Mathematical Concepts
Wiener process wt : increments dwt are indepen
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 12
1. The dynamics of the process, xt , in the G1+ model under the -forward measure satisfies
th
Quantitative Finance
FINC6000
Lecture 12: Interest Rate Derivatives
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Quick review of the G1+ model
European options on zero
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 3
asset prices Xt and Yt satisfy sdes
1. Suppose that under the risk-neutral measure P,
dXt = r
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Solution to Tutorial Set 2
1. This question provides an alternative derivation of the Black-Scholes equation following th
Quantitative Finance
FINC6000
Lecture 7: Monte Carlo I
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Overview
Basic facts on Monte Carlo
numerical integration of the ex
Quantitative Finance
FINC6000
Lecture 9: Monte Carlo II
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Variance reduction techniques
background
control variates
antithe
Quantitative Finance
FINC6000
Lecture 3: Preliminaries II
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Mathematical results
change of probability measures
Girsanov theor
Quantitative Finance
FINC6000
Lecture 11: Interest Rate Market and the Hull-White Model
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Interest rate modelling
background
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Tutorial Set 8
1. Suppose that the EUR/USD volatility quotes are
atm = 21.6215%, RR0.25 = 0.5%, and
BF0.25 = 0.74%.
(a)
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Tutorial Set 2
1. This question provides an alternative derivation of the Black-Scholes equation following the
original a
The University of Sydney
Discipline of Finance
FINC6000 - Quantitative Finance
Tutorial Set 9
1. You have been asked to value a discrete arithmetic Asian call option, p, by Monte Carlo
simulation, and
7/31/2001codedJFQA #36:3 Reeb, Mansi, and AlleePage 395
JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS
VOL. 36, NO. 3, SEPTEMBER 2001
COPYRIGHT 2001, SCHOOL OF BUSINESS ADMINISTRATION, UNIVERSITY OF W