Formulas:
Common payos:
Long forward: ST F0,T
Long call: Max[0, ST K ]
Long put: Max[0, K ST ]
prot of most derivatives:
prot = payo FV(premium)
Put-Call parity
Call(K, T ) Put(K, T ) = PV(F0,T K )
Price of the prepaid forward
P
F0,T = S0
Forward
Derivatives
Spring, 2014
Chapter 4
A gold-mining rm Golddiggers will be selling gold in 1 year, with a production cost of
$380 per ounce. The eective interest rate is 5%.
Lets compare two hedging strategies:
1. buying a 420-strike put with premium of $8.7
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301CDE DERIVATIVES
FIRST SEMESTER, 2010-2011
Chapter 3 Insurance, Collars, and Other Strategies
Supplementary Notes
(adapted from John C. Hull 2006, Options, Futures, and Other derivatives
Chapter 11
The Black-Scholes Formula
FINA0301 Derivatives
Faculty of Business and Economics
University of Hong Kong
Dr. Tao Lin
1
Chapter Outline
Introduction to the Black-Scholes formula for pricing
2
European options
Applying the formula to other under
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301CDE DERIVATIVES
FIRST SEMESTER, 2010-2011
Tutorial 4 Chapter 4 Introduction to Risk Management
For Question 1-6, assume the following:
Consider the following three firms:
XYZ mines copp
FINA 0301/2322 Derivatives, Spring 2015
Review Questions 1
1. Which of the positions can result in the following prot diagram?
Prot
d
d
d
d
d
d
d
d
d
Stock price
d
d
(a) Buy one low-strike call, sell two high-strike calls.
(b) Buy one high-strike call, se
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301CDE DERIVATIVES
FIRST SEMESTER, 2010-2011
Homework Assignment 1
Due Date: 6th October, 2010 (Wednesday) by 6pm
Please drop your homework into Clives mailbox at 9/F KKL Building directly
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301CDE DERIVATIVES
FIRST SEMESTER, 2010-2011
Tutorial 5 Chapter 5 & 6 Financial Forwards and Futures
Question 1 (Cash and Carry Arbitrage)
The S&R index spot price is 1100 and the continuo
FINA0301/FINA2322 Prof. Zhang
Spring, 2015
Problem Set 1
Name:
Instructions:
Read the questions carefully, write all your steps where necessary.
You dont have to computer-type the solution. However, the hand-written version has to be
reader-friendly.
N
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301CDE DERIVATIVES
FIRST SEMESTER, 2010-2011
Homework Assignment 2
Due Date: 25th October, 2010 (Monday) by 6pm
Please drop your manuscript into Clives mailbox at 9/F KKL Building directly
FINA0301/FINA2322 Prof. Xu
Fall, 2013
Homework Questions 2: Due dateTuesday, Oct 22, 2013
Name:
Instructions:
Read the questions carefully, write all your steps where necessary.
You dont have to computer-type the solution. However, the hand-written vers
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301/2322 DERIVATIVES
SECOND SEMESTER, 2014-2015
Tutorial 3 Chapter 4 Introduction to Risk Management
For Question 1-6, assume the following:
Consider the following three firms:
XYZ mines c
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301/2322 DERIVATIVES
SECOND SEMESTER, 2014-2015
Tutorial 2 Chapter 3 Insurance, Collars and Other Strategies
For the following problems, assume the following:
Effective 6-month interest ra
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301CDE DERIVATIVES
FIRST SEMESTER, 2010-2011
Tutorial 10 Chapter 10 & 11
Chapter 10
Question 1 (Put-call Parity)
Consider a one-period binomial model with h = 1, where S = $100, r = 0.08,
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301/2322 DERIVATIVES
FIRST SEMESTER, 2013-2014
Tutorial 5 Answer to the Eurodollar futures example
Example
(A)
The quoted Eurodollar futures price is: 100-4 X 3-month LIBOR rate in percent
The Wide World of Futures Contracts
Currency contracts
Eurodollar futures
An introduciton to commodity futures
Energy futures
Weather and housing futures
1 / 19
Currency Contracts
Widely used to hedge against changes in exchange rates
WSJ listing
2 / 19
The Black- Scholes Formula
Introduction to the Black-Scholes
formula
Applying the formula to other assets
Option greeks
Delta-hedging
Volatility
1 / 39
Binomial pricing
Vary the number of binomial steps (think about the
multiperiod example), x the expirat
Derivatives
Fall, 2013
Chapter 9
call perspective: give up dollar for euros
1. Suppose that you buy a e1,000,000 call option against dollars with a strike price of
$1.2750/e. Describe this option as the right to sell a specic amount of dollars for
euros a
THE UNIVERSITY OF HONG KONG
FACULTY OF BUSINESS AND ECONOMICS
FINA0301/2322 DERIVATIVES
FIRST SEMESTER, 2013-2014
Tutorial 5 Slides
Chapter 5&6 Financial Forwards and Futures
Topics Today:
-Cross-Hedging
-Currency Forward
-Eurodollar Futures
Cross-Hedgin
Derivatives
Fall, 2013
Chapter 8
1. Suppose the forward curve for oil rises by $2 in years 1 and 2. The year 1 forward
price is $22 and year 2 is $23. The market value of the original swap is no longer
zero. With same interest, new swap price is $22.483 (
!
!
Tutorial 9 Chapter 10 & 11!
!
!
!
Chapter 10!
Question 1 (Put-call Parity)!
Consider a one-period binomial model with h = 1, where S = $100, r = 0.08, = 30%,
and = 0. Compute American put option prices for K = $100, $110, $120, and $130.!
!
(a) At whi
Derivatives
Fall, 2013
Chapter 8
1. Suppose the forward curve for oil rises by $2 in years 1 and 2. The year 1 forward
price is $22 and year 2 is $23. The market value of the original swap is no longer
zero. With same interest, new swap price is $22.483 (
Derivatives
Fall, 2013
Chapter 11
1. S = $41, K = $40, = 0.3, r = 8%, t = 0.25, Div = $3 in one month. What is the BS
European call price?
P
F0,T (S) = S PV (Div)
= 41 3e0.08/12
= 38. 020
P
F0,T (K) = 40e0.08/4 = 39. 208
d1
P
P
ln F0,T (S) /F0,T (K) + 1 2
Section 9 Derivatives Markets (Part 3)
Derivatives Markets (Part 3)
The positions taken in Section 8 are directional, meaning a profit/(loss) occurs
if the spot price at expiration of the underlying asset has either
increased/(decreased) or decreased/(inc
Derivatives
Fall, 2013
Chapter 7
What are the implied forward rate r0 (2, 3) and forward zero-coupon bond price P0 (2, 3)
from year 2 to year 3?
The formula is
[1 + r0 (t1 , t2 )]t2 t1 =
P (0, t1 )
[1 + r0 (0, t2 )]t2
=
t1
[1 + r0 (0, t1 )]
P (0, t2 )
Plu
An Introduction to Forwards and Options
Forward contracts
Call options
Put options
Summary of forward and option
positions
Options are insurance
1 / 32
Introduction
Basic derivatives contracts
Forward contracts
Call options
Put Options
Types of positi
Interest Rate Forwards and Futures
Bond basics
Forward rate agreements, eurodollars,
and hedging
Duration and convexity
Treasury-bond and treasury-note
futures
Repurchase agreements
1 / 25
Bond Basics
U.S. Treasury
Bills (<1 year), no coupons, sell at di
Insurance, Collars, and Other Strategies
Basic Insurance Strategies
Using options to create synthetic
forwards
Spreads and collars
Speculating on volatility
Application: equity-linked CD
1 / 40
Basic Insurance Strategies
Options can be
Used to insure lon