STAT 2820
Chapter 5 Risk Management - Hedging
by K.C. Cheung
5.1 Basic risk management: example from producers perspective
5.1.1 Assume that a gold miner plans to mine and sell 400000 ounces of gold next year. The
price of gold today is known: $400 per ou
STAT 2820
Chapter 6 Futures/Forward Price
by K.C. Cheung
6.1 No-Arbitrage Principle
An arbitrage opportunity allows one to get something from nothing, i.e. to make a sure
prot with no risk and no money down free lunch! A fundamental idea in modern nancial
STAT 2820
Chapter 3 Introduction to Options
by K.C. Cheung
3.1 Types of Options
3.1.1 A call option gives the holder the right to buy a certain asset by a certain date at
a certain price. A put option gives the holder the right to sell a certain asset by
STAT 2820
Chapter 4 Option Strategies
by K.C. Cheung
4.1 Insuring a Long Position: Floors
4.1.1 Suppose that we invest in a certain asset at time 0, for instance, n shares of stock ABC,
and plan to sell these stocks in T years. If the stock price drops af
STAT 2820
Chapter 8 Interest Rate Swaps
by K.C. Cheung
8.1 Interest rate swap
8.1.1 Suppose that ABC has an n-year $A oating-rate debt, so that at the end of the i-th
year (i = 1, 2, . . . , n), the interest payment of ABC is $A r(i 1, i). The rate r(i 1,
STAT 2820
Chapter 7 Interest Rate Forwards
by K.C. Cheung
7.1 Zero-coupon bonds
7.1.1 A zero-coupon bond is a bond that makes only a single payment at its maturity. The
price of a zero-coupon bond quoted at time t, with the bond to be purchased at time t1
STAT2820 Introduction to Financial Derivatives
Tutorial 1
Exercise 1
A trader buys a call option on a stock at a strike price $40 with premium $3, sells 2 put options at
strike price $35 with premium $2, and longs a forward with forward price $38. The cur
STAT2820 Introduction to Financial Derivatives
Tutorial 5
Exercise 1
Given the current stock price and 6-month forward price is $20 and $20.5 respectively. The risk-free
continuously compounded interest rate is 8%. The company is going to distribute a div
STAT2820 Introduction to Financial Derivatives
Tutorial 2
Exercise 1 (Reference: lecture notes Ch.3 p.9 about equity-linked CDs.)
The investor pays $10,000 at time 0 in return of the payoff after 5 years
= 10,000 538.46
13 . Given that the risk-free effec
STAT2820 Introduction to Financial Derivatives
Tutorial 3
Exercise 1
Given that the current stock price is $500 and the 3-month forward price is $490. A 3-month
EUROPEAN call option with strike price $480 is sold at $60. You are also given that a 3-month
STAT2820 Introduction to Financial Derivatives
Tutorial 4
Exercise 1
Construct a synthetic riskless discount bond which pays K after 3-months by using 3-month call and
put option with strike price K, and underlying asset.
Solution
By put-call-parity, c p
STAT2820 Introduction to Financial Derivatives
Tutorial 6
Exercise 1
Suppose the gold spot price is $300/oz., the 1-year forward price is 310.686, and the continuously
compounded risk-free rate is 5%. Determine the lease rate and interpret its meaning. He
STAT2820 Introduction to Financial Derivatives
Tutorial 8
Exercise 1
Show by constructing relevant cash tables that under no-arbitrage conditions C P S0 Ke-rT,
where C is the American call premium with strike price K, P is the American put premium with
st
STAT2820 Introduction to Financial Derivatives
Tutorial 9
Exercise 1
To finance your purchase of a house, you borrow money at a floating rate from a bank. Given that
your rate of borrowing in year i is r(i 1, i) + c, where r(i 1, i) is the floating rate a
STAT2820 Introduction to Financial Derivatives
Tutorial 7
Exercise 1
Given the continuously compounded risk-free interest rate is r and the underlying asset pays a
discrete dividend D at time t2. For two standard financial forward contracts which the one
STAT 2820
Chapter 1 Introduction to Derivatives
1.1 Derivatives
A derivative is a nancial instrument whose value depends on (or derived from) the values of
other more basic underlying variables.
Financial instrument or nancial asset is a contract/agreeme
STAT 2820
Chapter 2 Forward Contracts
2.1 Futures Contracts
2.1.1 A forward contract is an agreement between two parties to buy or sell an asset (underlying asset) at a certain time in future (delivery date/maturity) for a certain price
(forward price/del
Example on margin account operation
Hang Seng Index Futures
Initial Margin
84300
Maintennance Margin
67450
Margin formula
Long:
Short:
Day
1
2
K (Futures price)
20000
19800
3
19500
4
20200
5
(Daily change in margin account balance)=50*(Daily change in K)
Academic Year 2007 2008
STAT2808
Numerical Solution
1.
2. a)
3. a)
b)
c)
d)
4. a)
b)
c)
5. c)
13.25
0.015
48.01
28.76
48.33
28.76
3.266
21.2367
3.266
$11, $1
I
THE UNrVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT2820 INTRODUCTION TO FINANCIAL DERIVATWES
December 9, 2010
Time: 9:30 a.m. - 11:30 a.m.
Only approved calculators as announced by the Examinations Secretary can be used
in th
STAT 2820: Introduction to nancial derivatives
Assignment 1
Due: Oct 9, 2009
Problem 1 ABC stock has a bid price of $40.95 and an ask price of $41.05. Assume there is
a $20 brokerage commission.
(a) What amount will you pay to buy 100 shares?
(b) What amo