Case study 6:
Financial Derivatives
An application of
stochastic differential equations
Learn very hard
Savings
Stocks
Options
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2
Options
Options
Tsinghua University
3
Black-Scholes
1997
The asset price follow the SDE
U
Chapter 2: Term Structure of Interest Rate
1. Song: page 31, #1
Answer:
(1) If we assume that the coupon is paid annually,
100
Pn
n , so:
For T-Bills: We have
1+
r
12
1-month:
100
99.653
1 , r = 4.178%;
1 r
12
3-month:
100
98.866
3 , r = 4.588%
1 r
12
Assignment 4 (for Chapter 5)
Due by Dec 12, Monday
1. (Song, page 83)
The following two-step binomial tree shows the possible paths of price movement for stock S:
S(t)
t=0
t=1
115
100
t=2
132.25
103.5
90
81
If the risk-free rate is rf =5% , please determi
Chapter 3 & Chapter 4
1. Song: page 47
Answer:
n
(1). Expected return rate of stock A
r
Ai
E (rA ) i 1
n
27.1%
;
n
Expected return rate of market portfolio M
n
(r
2
A
Ai
rAi ) 2
i
1
n1
0.00248
r
Mi
E (rM ) i 1
n
20%
;
, M 2 0.001 , cov(rA , rM ) 0.0015
Assignment #2 (for Chapter 2)
Due by Oct 31, Monday
There are FOUR exercises in this assignment. The first and second exercises are from Songs
book. For students who cannot read Chinese, please use this translated version.
1. (Song: page 31, #1) Quotation
Assignment #3 (for Chapter 3&4)
Due by Nov 21, Monday
1.
(Song: page 47) There is one risk-free security and N risky stocks in the security market.
Assume that there is no market friction. The return rates of stock A and the stock market
portfolio M from
8
What Are These Numbers Trying to Tell?
72
2x3
11=1
10002 =100100100
7/8
Tsinghua University
2
Types of Statistics
Statistical
Methods
Descriptive
Statistics
Inferential
Statistics
Tsinghua University
3
Descriptive Statistics
1. Involves
Collecting d
Case study 5:
Population models
From continuous to discrete
Contents
(population)
Malthus model (ODE)
Logistic model (ODE)
Leslie model (Matrix)
Lotka model (integral equation)
Tsinghua University
2
Population of the World
Tsinghua University
3
Popul
1
2
Case Study
Note: Week 4 Case changed to
Portfolio Optimization
and asset allocation
Deutsche Bank: Discussing the
Equity Risk Premium
Professor Yingzi Zhu
3
Learning Objectives
4
Risky and Risk-free Investments
p =0.6
Risky Inv.
1. Understand the conc
Security Types
Asset Class and Financial Instruments
Prof Yingzi Zhu
Classifying Securities
Our goal in this chapter is to introduce the
different types of securities routinely bought
and sold in financial markets in the United
States as well as worldwide
Investment, Risk and Return
Prof. Yingzi Zhu
Subject of the Course
Essential nature of investment
Reduced current consumption
Planned later consumption
Real Assets
Assets used to produce goods and services: land,
building, machine, knowledge, .
Corpo
Investing in Mutual Funds
Professor Yingzi Zhu
Tsinghua University
Learning Objective
In this lecture we attempt to understand
What are different types of mutual
funds?
BKM Chapter 4 : Page 112-115
How
to evaluate the performance of
mutual funds?
BKM Ch
CAPM (Capital Asset Pricing
Model)
Professor Yingzi Zhu
Tsinghua University
Learning Objectives
1. How is the expected return of a stock
determined? (Theory: CAPM)
2. Given the historical data (past return and
volatility) of a stock, how could you
predict
Basics of Investing
Mechanism
Buying and Selling Securities
This lecture covers the basics of the investing
mechanism
Describe the process of buying and selling
securities.
Analyze the practice of buying on margin and
short selling.
Professor Yingzi Zhu
T
Market Efficiency and Financial
Market Anomalies
Professor Yingzi Zhu
Tsinghua University
Learning Objectives
Foundations and Forms of Financial Market
Efficiency
Efficient Market Hypothesis
Financial Market Anomalies
Key question:
Do you believe in