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
Chapter 3 Insurance, Collars, and Other Strategies
Supplementary Notes
(adapted from John C. Hull 2006, Options, Futures, and Other derivatives
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 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
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
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
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 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
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
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 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
Binomial Option Pricing
A one-period binomial tree
Two or more binomial periods
Put options
American options
Options on other assets
1 / 52
Introduction to Binomial Option Pricing
Binomial option pricing enables us to determine the price
of an option, giv
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 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
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
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
Swaps
An example of a commodity swap
Interest rate swaps
Currency swaps
1 / 36
Introduction to Swaps
A swap is a contract calling for an exchange of payments,
on one or more dates, determined by the dierence in two
prices
A swap provides a means to hed