Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
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RMSC4001 Final Exam Questions 2015
Name: _~_
Student I.D.: _ _:._ _ _
This examination paper consists of THREE parts with full marks of 100.
Students should answer all questions and put your written answers in the
anSwer book provide
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 4 Solution: BlackScholes Model and Itos integral
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
BlackScholes Model
2
Itos integral
Exercise 2.1.
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC4001 Final
Questions 2014
examination
consists of
parts with
marks of 100.
put your written answers in the
Students should answer all questions
answer book provided. You should save all of your programming code into
the floppy disk provided.
Time: 3 H
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Assignment 1
Due: February 2, 2016
1. A oneyearlong forward contract on a nondividendpaying stock is entered into
when the stock price is $40 and the riskfree rate of interest is 5% per annum with
continuous compounding.
(a) What are the fo
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
Options
Options were first traded on an organized
exchange in 1973. Since then there has
been a dramatic growth in option markets.
There are two basic types of options: Call
option and Put Option.
A call (put) option gives the holder the
right to buy (
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 8: Value at Risk and its simulations
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Value at Risk(VaR)
Exercise 1.1. (2010 final)
Suppose the 3mon
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
1
An Introduction to Excel VBA
1.1
1.1.1
HOW TO START EXCEL VBA
Introduction
VBA stands for Visual Basic for Application. It is a programming language that can assist your work
in Excel. It enables you to instruct Excel to perform tasks automatically for
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
S
K
r
sigma
T
N
Call or Put
European or American
u
d
q
exp(rt)
Option Price
50
50
0.1
0.4
1
12
p
a
1.122401
0.890947
0.507319
0.991701
5.909054
79.35276
0.364193
70.69912
1.016882
62.98919
2.138242
56.12005
3.773733
50
5.909054
62.98919
1.706235
56.12005
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 1: Options and Futures
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Forward and Futures
In this section we examine how forward prices and futures
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Class practice
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Exercises
Exercise 1.1. (Warm up)
(a) Let W (t) denote the Wiener Process. Evaluate
Rt
(i) t01
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 6: Random number generation II
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Acceptancerejection method
Suppose we want to generate X F with dens
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 8: Value at Risk and its simulations
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Value at Risk(VaR)
Value at Risk (VaR) summarizes the worst los
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 3 Solution: Wiener process and Itos rule
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Wiener Process
Exercise 1.1. Actually Wiener process can be
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 3: Wiener process and Itos rule
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Wiener Process
Definition 1.1. A stochastic process W is called a Wi
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
. ...
The Chinese University of Hong Kong
Course Examination 2nd Term, 20102011
RMSC4001 Simulation Methods for Risk Management Science and Finance
This examination paper consists of THREE parts with full marks of 100.
Students should answer all questi
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
Assignment 2
RMSC 4001
Due: February 29, 2016
1. A fourmonth European call option on a dividendpaying stock is currently selling for
$5. The stock price is $64, the strike price is $60, and a dividend of $0.8 is expected
in onemonth. The riskfree inte
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
Introduction
Derivatives: Forward
and Futures
A financial derivative is a security whose
value depends on the values of other
more elementary securities, like equity,
bond and commodity. Forward contracts
and futures contracts are two typical
derivatives
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001 Simulation Methods for Risk Management and Finance
1a)
Assignment 2 Suggested Solutions
It is possible to establish a perfectly hedge portfolio by short selling the call
option as well as holding certain amount, say , of the XYZ shares. i.e.
S.
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC4001 Midterm (8/3) Seating plan
(Rlab LSB G25)
_
Whiteboard_
AU Ka Ki
CHAN Hin
Yue
CHAN Ho
Sing
CHAN Ka
Chun
CHAN Kin
Cheung
CHAN Lok
Tung
CHAN
Sing
Hang
CHAN
Wing Ho
CHENG Hei
Ming
CHEUNG
Hang Kin
CHOI Ka
Fong
CHUNG
Kwai Fong
HE Zixuan
HUNG
Siu
Chun
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 9: Variance reduction method I
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Antithetic variables
Idea
Suppose we want to estimate = E[H(X)], wher
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 2: Binomial Tree models and its VBA simulation
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Binomial Tree Models
Binomial Tree Model is a simplif
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 11: Final revision
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
RMSC4001 Final revision
Exercise 1.1. Consider evaluating the price of a European
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 5: Random number generation
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Monte Carlo simulation
Exercise 1.1. Suppose the stock follows the dynam
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 9 Solution: Variation reduction method I
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Antithetic variables
R1 3
Exercise 1.1. Consider = 0 ex dx
Simulation Techniques in Financial Risk Management
RMSC 4001

Fall 2016
RMSC 4001
Simulation Methods for Risk Management Science
and Finance
Tutorial 10: Variation reduction method II
KWOK Kai Yin
Department of Statistics, The Chinese University of Hong Kong
1
Stratified sampling
Stratification is the process of dividing memb