SHS Web of Conferences 12, 010 8 4 (2014)
DOI: 10.1051/shsconf/ 201412010 8 4
C Owned by the authors, published by EDP Sciences, 2014
Corporate Diversification and Firm Performance: Evidence
from Asian Hotel Industry
Chai-Aun Ooi1 , Chee-Wooi Hooy2, Ahmad
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 the
original argument used by Black and Scholes. Let Xt b
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 = rXt dt + X Xt dwtX ,
dYt = rYt dt + Y Yt dwtY ,
where wt
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
European calls and puts, we defined d+ and d by
ln(Xt /K
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-financing
strategies given in lecture slides. For this, co
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
= 69,069 and = 1. Assuming the initial seed of X0 = 1,
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-Scholes
model to the following market observed implied v
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 and/or Skills: This unit requires students to have bas
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
simulation, and concerned about the potentially high simul
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 = 0.74%.
(a) Compute the 25-delta call volatility
call,
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%, and
the asset volatility is 20%. Compute the price of a 1
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
so that
1
p
(i (Xi | Xi1 ),
gi (Xi | Xi1 ) =
Xi ti1
wh
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 measure
in the Hull-White model.
Solution. From lectures, re
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 coupon bonds
Caplets and floorlets
definition
caplet
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
the equation
dxt = xt + 2 (t)(t, ) dt + (t)dwt .
By follo
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 independent, dwt
Integrals of Wiener processes:
T
t
ps q dws
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 (). Then the dynamics of c(t, Xt ) is given by
1 2
c
c
c
2c
Quantitative Finance
FINC6000
Lecture 6: Monte Carlo I
Oh Kang Kwon Discipline of Finance The University of Sydney
Table of Contents
Overview
Uniform random number generators
pseudo random generators
low discrepancy sequences - Sobol
Converting from
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 WASHINGTON, SEATTLE, WA 98195
Firm Internationalization
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 concerned about the potentially high simulation error.
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 argument used by Black and Scholes. Let Xt be the price
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) Compute the 25-delta call volatility
call,0.25 .
(b) C
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
zero coupon bonds, and forward and short rates
Hull-W
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 theorem and Wiener processes
numeraires
change of numeraire
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
antithetic variates
Simulation of correlated assets
two asse
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 expectation
estimation of simulation error
European opt
Quantitative Finance
FINC6000
Lecture 4: Black-Scholes Model - Probabilistic Approach
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Overview
Probabilistic approach to pricing
review of the Black-Scholes model
European call o
Quantitative Finance
FINC6000
Lecture 10: Monte Carlo III
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Monte Carlo sensitivities
background
finite difference approximation
pathwise derivative estimate
likelihood ratio method
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 dynamics under the risk-neutral measure
Black-Scholes P
Quantitative Finance
FINC6000
Lecture 5: Volatility Smile
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Overview
Implied volatility
Expiry dependent volatility
Volatility smile
Gatherals SVI parameterization
SABR paramet
Quantitative Finance
FINC6000
Lecture 8: Foreign Exchange Market
Quan Gan
Discipline of Finance The University of Sydney
Table of Contents
Overview
Market conventions
exchange rate quotation
volatility quotation
FX modelling
vanilla options
option d