The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Monte Carlo Method
Monte Carlo simulation is the most simple and powerful method for pricing European options. It
consists of calculating the expectation based on the Strong Law of Large Numbers.
Strong Law of Large Numbers. Let Xk be i.i.d. (independent
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Investment Models
Yves GUO
Fall 2015
APT Arbitrage Pricing Theory
Based on market equilibrium, CAPM assumes that the market portfolio is the
only source of priced risk.
Arbitrage Pricing Theory (Stephen Ross 1976) extended CAPM by allowing
multiple risk s
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Investment Models
Yves GUO
Fall 2015
Efficient Frontier with a RiskFree Asset
Lets consider a portfolio composed of
a riskfree asset ( : riskfree return)
a portfolio of risky assets (with weights )
James Tobin (1958) was the first who analyzed this p
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Investment Models
Yves GUO
Fall 2015
CAPMCapital Asset Pricing Model
The MeanVariance portfolio analysis leads to the Capital Asset Pricing
Model (CAPM) which was derived by Jack Treynor, William Sharpe,
John Lintner, Jan Mossin at about the same time.
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Investment Models
Yves GUO
Fall 2015
MeanVariance Analysis
The MeanVariance analysis, pioneered by Markowitz (1952), considers
the tradeoff between the expected return and variance of a portfolio
of assets.
Under this framework, the risk is represented
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
AMA2701/2701A  Advanced Calculus and Linear Algebra
Assignment 1
Due: 5:00 pm, 22 October 2014
NOTE: To save space some vectors are written in rows. Keep in mind that when you do matrix
multiplication, your vectors must be written in columns.
1. Let B =
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Investment Models
Yves GUO
Feb 2015 May 2015
1
Dynamic Asset Allocation
Dynamic asset allocation is the mechanism for controlling the timing and
quantity of the investments across the assets. It can be used for achieving one
or more of the following targe
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Investment Models
Yves GUO
Feb 2015 May 2015
Feb 2015 May 2015, Yves GUO
1
Mutual Funds
A mutual fund is collective investment scheme that pools money from many
investors to purchase securities. It has the following features:

Highly Regulated
in Europe,
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Foreign Exchange Modeling
Composite/Quanto Options
1/8
Domestic RiskNeutral Probability for a Foreign Asset
Let S t be a foreign asset process and Xt be the exchange rate process (units of domestic
currency per unit foreign currency).
Assume the followi
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Non constant volatility
Volatility is the most important parameter for the valuation of an option. From the price of a
market traded Vanilla option (i.e. call or put), we can reverse calculate the volatility from
BSM formula. This volatility is called imp
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Option Derivatives In Real World
Yves GUO
Presentation Plan
Organization of financial market activities
Review of option derivatives
Option models in practice
Numerical methods
Pricing with Monte Carlo method
System framework
Examples of Option Pri
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Annex B
Derivation of the Main Results
(through illustration rather than rigorous mathematics)
March 2015, Yves GUO
1
Annex B  Stock and Portfolio under
Under RiskNeutral Probability :
Discounted stock price is a martingale
This is because = ( )
Dis
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
An Approximation Formula for AtTheMoney Forward Call/Put Options
The strike of an option is said to be AtTheMoney Forward (ATMF) if the strike level is
K = erT S0 . In this case, the European call and put options have the same price.
For an ATMF call
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Presentation at Macau University
A Primer on
Stock Option Pricing
Yves GUO
November 2014
1
Presentation Plan
Derivative Contracts
Pricing / Hedging
Long History of Derivatives
BlackScholes Formula
Replication of a Derivative Contract
Partial Different
The Hong Kong University of Science and Technology
MAFS 5210

Fall 2015
Investment Models
Yves GUO
Fall 2015
Stocks
Key Characteristics of a Common Stock

Equity: an ownership position in a corporation

Voting Rights

Dividends: Cash dividend or Stock dividends

Priority to companys assets after Debt and Preferred Shares