CHAPTER 1
18
the positiOn where they face risk associated with the price of an asset. They use
derivatives to reduce or eliminate this risk. Speculators wish to bet on future movements
in the price of an asset. They use derivatives to get extra leverage.
CHAPTER 1
Introduction
Practice Questions
Problem 1.8.
Suppose you own 5,000 shares that are worth $25 each. How can put options be used to provide you
with insurance against a decline in the value of your holding over the next four months?
You should buy
Missing Data & How to Deal: An
overview of missing data
Melissa Humphries
Population Research Center
Goals
Discuss ways to evaluate and understand missing data
Discuss common missing data methods
Know the advantages and disadvantages of common
methods
Rev
Homework 4
Due Tuesday October 13 at 6:00pm. On paper.
Hull 13.5
Hull 13.14
Hull 13.21
1. This problem is about the dierences between E(|Fn ) and E(|Xn ). Let Xn be
a simple symmetric random walk. Let i be independent, identically distributed
random varia
Homework 3
Due Monday October 5 at 6:00pm. On paper.
1. Let 1 , 2 , . be independent identically distributed random variables with discrete
distribution
1
1
P (i = .1) = , P(i = .05) = .
2
2
Let X0 = 1000 and
n
Xn = 1000
(1 + i ).
i=1
Let Fn represent all
Homework 7
Due Monday November 16 at 6:00pm. On paper.
1. At time t, the value of a long forward contract with delivery price K and delivery
date T is
V (t, S(t) = S(t) Ker(T t) .
What is the of a forward contract? Relate this to the work we did with arbi
Homework 10
Due Monday December 7 at 6:00pm. On paper.
Hull 7.1
Hull 7.3
Hull 7.9
Hull 7.22
Hull 7.23
6. Some time ago you purchased a oating rate bond with principal of $100 that pays
coupons of the 6-month LIBOR rate every six months. The bond has a rem
Homework 3
Due Monday November 9 at 6:00pm. On paper.
1. Create your own BSM calculator in Excel or Google Drive. Make columns
1
2
A
S(0)
B
r
C
T
D
K
E
sigma
F
c
G
p
In cell F2, enter the formula for the Black-Scholes model. All functions must start
with
Homework 4
Due Monday October 19 at 6:00pm. On paper.
1. Write the following dierentiable functions in the integral form
t
f (t) = x +
b(s)ds.
0
Example f (t) = cos(t)
If we plug in 0 for t in the integral form, we see that f (0) = x. In this case,
theref
Homework 8 Due Monday November 23 at 6:00pm. On paper.
1. Properties of stochastic integrals. Let i be a sequence of independent identically
distributed N (0, .01) random variables. Let g(x) be any bounded, continuous function. Let X0 = 0 and
n
Xn =
g(Xk1
Practice Midterm October 19, 2015
NOTE: This is way more questions than the real exam will be.
1. The spot price of gold today (October 19) is $1177 per ounce. The risk-free rate of
interest (compounded continuously) is 5% per annum. The futures price for
Midterm Exam October 26, 2015
INSTRUCTIONS:
You may use notes and calculators.
You may not use textbooks, computers, phones, smart watches, or anything that is
connected to the internet.
Write all of your answers in sentences. Explain your reasoning.
Practice Midterm December 7, 2015
NOTE: This is way more questions than the real exam will be.
1. Consider a security on a non-dividend-paying stock that pays $10 if the stock price
is above $50 in three months and it pays $0 if the stock price is below $
The Greek letters and the volatility smile
Mickey Salins
Boston University
November 9, 2015
Mickey Salins (BU)
Hull 19 & 20
November 9, 2015
1 / 32
Hedging a call option
A European call option on a stock with strike price 40, and time to
expiry 1/2 is sel
11 MARCH 2010
FROM MOODYS KMV
CDS-implied EDF Credit Measures
and Fair-value Spreads
Authors
Abstract
Douglas Dwyer
In this paper, we present a framework that links two commonly used risk metrics:
default probabilities and credit spreads. This framework p
A Non-Quantitative
Introduction to EDF~
Terry Tse
Moodys KMV
Last Modified: 5/1/02
3)
A Non-Quantitative Introduction to EDPs
Last Modified: 511/02
1. INTRODUCTION
The purpose of this document is to provide a non-technical introduction to the main theoret
CHAPTER 2
Mechanics of Futures Markets
Practice Questions
Problem 2.8.
The party with a short position in a futures contract sometimes has options as to the precise
asset that will be delivered, where delivery will take place, when delivery will take plac
11
Introduction
Figure 1.3 Net prot per share from (a) purchasing a contract consisting of
100 Google December call options with a strike price of $880 and (b) selling a contract
consisting of 100 Google September put options with a strike price of $840.
CHAPTER 3
Hedging Strategies Using Futures
Practice Questions
Problem 3.8.
In the Chicago Board of Trades corn futures contract, the following delivery months are
available: March, May, July, September, and December. State the contract that should be
used
CHAPTER 5
Determination of Forward and Futures Prices
Practice Questions
Problem 5.8.
Is the futures price of a stock index greater than or less than the expected future value of the
index? Explain your answer.
The futures price of a stock index is always
CHAPTER 10
Properties of Stock Options
Practice Questions
Problem 10.8.
Explain why the arguments leading to putcall parity for European options cannot be used to
give a similar result for American options.
When early exercise is not possible, we can argu
CHAPTER 12
Introduction to Binomial Trees
Practice Questions
Problem 12.8.
Consider the situation in which stock price movements during the life of a European option
are governed by a two-step binomial tree. Explain why it is not possible to set up a posi
1
Probability Spaces
Nobody can exactly predict the future, but we can often quantify the likelihood that a
particular set of events will occur. Probability theory provides a rigorous mathematical
framework for studying these likelihoods. Mathematically,
CHAPTER 11
238
Consider a dividend whose ex-dividend date is during the life of an option. The value of
the option is negatively related to the size of the dividend if the option is a call and
positively related to the size of the dividend if the option i
105
Determination of Forward and Futures Prices
5.2
SHORT SELLING
Some of the arbitrage strategies presented in this chapter involve short selling. This
trade, usually simply referred to as shorting, involves selling an asset that is not
owned. It is some
13
C H A P T E R
Binomial Trees
A useful and very popular technique for pricing an option involves constructing a
binomial tree. This is a diagram representing dierent possible paths that might be
followed by the stock price over the life of an option. Th
3
C H A P T E R
Hedging Strategies
Using Futures
Many of the participants in futures markets are hedgers. Their aim is to use futures
markets to reduce a particular risk that they face. This risk might relate to uctuations
in the price of oil, a foreign e