The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS5030
Quantitative Modeling of Derivatives Securities
Test One Fall 2012
Time allowed: 75 minutes
Course instructor: Prof. Y.K. Kwok
[points]
1. Consider an asset with price ST at time T . Show that an investor who puts down
a cash amount Gt,T that equ
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS5030 Quantitative Modeling of Derivative Securities
Course objective
This course is directed to those students who would like to acquire an introduction to the
pricing theory of financial derivatives. The course starts with the exposition of basic
der
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman/teaching/DerivSec10/resources.html
Week 9
1
Bond rating model
We gave a simple model of
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman/teaching/DerivSec10/resources.html
Week 4
1
Mathematical preliminaries
If X and Y are r
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman
Week 1
1
Introduction
These notes are supplements to the textbook (Hull, seventh editio
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman/teaching/DerivSec10/resources.html
Week 5
1
The Greeks
Derivatives of option prices wit
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman/teaching/DerivSec10/resources.html
Week 8
1
Credit risk
Counterparty risk is the risk t
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman
Week 2
1
Introduction
This class begins the discussion of option pricing. We use an abs
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman/teaching/DerivSec10/resources.html
Week 10
1
More on the Gaussian copula model
There is
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman/teaching/DerivSec10/resources.html
Week 6
1
The Ito integral
The Black Scholes reasonin
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman
Week 3
(note: formula (10) corrected Sept. 27)
1
Dynamic replication
The dynamic replic
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
Derivative Securities, Fall 2010
Mathematics in Finance Program
Courant Institute of Mathematical Sciences, NYU
Jonathan Goodman
http:/www.math.nyu.edu/faculty/goodman/teaching/DerivSec10/resources.html
Week 7
1
The backward equation
The last big piece of
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
(FINA3204)[2012](f)midterm~jguoah^_42571.pdf downloaded by maaqil from http:/petergao.net/ustpastpaper/down.php?course=FINA3204&id=0 at 20161004 07:13:28. Academic use within HKUST only.
Midterm Exam Papers Solution
Course: Fina3204 Fall 2012
Derivative
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030 Quantitative Modeling of Derivative Securities
Topic 2 Discrete securities models
2.1 Singleperiod models: Dominant trading strategies and linear
pricing measure
2.2 Noarbitrage theory and risk neutral probability measure: Fundamental Theorem
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030
Quantitative Modeling of Derivative Securities
Homework Three
Course Instructor: Prof. Y.K. Kwok
1. Consider the Brownian motion with drift dened by
X(t) = t + Z(t),
X(0) = 0, Z(t) is the standard Brownian motion,
nd E[X(t)X(t0 )], var(X(t)X(t
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030  Quantitative Modeling of Derivative Securities
Solution to Homework Three
1. (a) It is easily seen that
)
[ (
( s )]
t+s
Z 2
X1 (t + s) X1 (s) = k Z
k2
k
(
)
is normally distributed with mean zero and variance k 2 t+s ks2 = t. Also
k2
the incr
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030
Quantitative Modeling of Derivative Securities
Homework Four
Course Instructor: Prof. Y.K. Kwok
1. Suppose the dividends and interest incomes are taxed at the rate R but capital gains
taxes are zero. Find the price formulas for the European put
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030
Quantitative Modeling of Derivative Securities
Solution to Homework Two
Course Instructor: Prof. Y.K. Kwok
1. part: The trading strategy H with V0 < 0 and V1 () 0, , dominates the zeroholding trading strategy H = (0 0 0)T . The zeroholding stra
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030  Quantitative Modeling of Derivative Securities
Solution to Homework Four
1. When the dividends are taxed at the rate R, the dierential of the portfolio value
= c + S is given by
[
]
(
)
c 2 2 2 c
c
d =
+ S
+ (1 R)qS dt +
dS.
t
2
S 2
S
Note
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS5030
Quantitative Modeling of Derivatives Securities
Test  Fall 2013
Time allowed: 80 minutes
Course instructor: Prof. Y.K. Kwok
1. (a) Explain how the forward price on a tradeable commodity can be enforced using an
appropriate replication procedure.
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS5030
Quantitative Modeling of Derivative Securities
Final examination Fall 2012
Time allowed: 2 hours
Course instructor: Prof. Y.K. Kwok
[points]
1. (a) Let F be an algebra. Explain why E[XF] can be interpreted as a random
variable that is measurable
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030
Quantitative Modeling of Derivatives Securities
Final Examination Fall 2013
Time allowed: 120 minutes
Course Instructor: Prof. Y. K. Kwok
[points]
1. Consider the discrete multiperiod version of the Fundamental Theorem of Asset Pricing.
Recall
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030
Quantitative Modeling of Derivative Securities
Homework One
Course Instructor: Prof. Y.K. Kwok
1. Consider a oneyear forward contract whose underlying asset is a coupon paying bond
with maturity date beyond the expiration date of the forward co
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030
Quantitative Modeling of Derivative Securities
Solution to Homework One
Course Instructor: Prof. Y.K. Kwok
1. There will be two coupons before delivery: one in 6 months and one just prior to
delivery. Using the present value formula:
$94.6 =
F +
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030  Quantitative Modeling of Derivative Securities
Topic 3 BlackScholesMerton framework and Martingale
Pricing Theory
3.1 Review of stochastic processes and Ito calculus
3.2 Change of measure Girsanovs Theorem
3.3 Riskless hedging principle and
The Hong Kong University of Science and Technology
Quantitative Modeling of Derivative Securities
MAFS 5030

Fall 2014
MAFS 5030
Quantitative Modeling of Derivative Securities
Homework Two
Course Instructor: Prof. Y.K. Kwok
1. Show that a dominant trading strategy exists if and only if there exists a trading strategy satisfying V0 < 0
and V1 () 0 for all .
Hint: Consider