CFIN 595: Derivatives and Risk Management Tools
Vadim di Pietro
Assignment 1: Solutions
Note: Unless specified otherwise, all rates are annual rates with annual compounding
Topic: Forward Prices
1) You are given the following information at t = 0
IBM is

Lecture 9 Outline
Black-Scholes Formula
The Greeks
Implied volatility
Implied volatility smiles/smirks/surfaces
The VIX
Geometric Brownian Motion
Recall:
the basic assumption underlying the
Black-Scholes formula is that the stock price
follows Geometric

Lecture 10 Outline
Returns: stylized facts
Autocorrelation
Fat tails
Skewness
Vol dominates mean
Vol clustering
Vol/return correlation
Time varying correlation
Returns: Stylized Facts
We will consider a set of so-called stylized
facts which apply to mos

Lecture 4
Forwards continued
Commodities
Foreign Exchange
Futures contracts
Difference with forwards
Eurodollar futures
Forwards on commodities
We previously used replication arguments to show that
the forward price on a non-dividend paying stock i

Lecture 7 Outline
Liquidity
Market vs. limit orders
Asymmetric information
Informed and
uninformed traders
- Glosten-Milgrom model
of bid-ask spreads
- Inventory Risk
- Estimating Liquidity
Liquidity and liquidity risk
A liquid market is one in which

Lecture 2: Outline
Forward Rates
Bond forwards
Bond duration
and convexity
Forward rates
A forward interest rate is a rate at which parties agree on today to
borrow or lend some amount of money at some point in the future for a
predetermined length of

Lecture 7 Outline
Liquidity
Market vs. limit orders
Asymmetric information
Informed and
uninformed traders
- Glosten-Milgrom model
of bid-ask spreads
- Inventory Risk
- Estimating Liquidity
Liquidity and liquidity risk
A liquid market is one in which

CFIN 595
Derivatives and Risk
Management Tools
Vadim di Pietro
McGill School of Continuing Studies
Career and Professional Development
Syllabus key points
Contact information: vadim.dipietro@mcgill.ca
Please include CFIN 595 in email subject line
Offic

Lecture 3
Forwards continued
Dividend paying stocks
Continuous compounding
Forwards: dividend paying
stocks
We previously used replication arguments to show that
the forward price on a non-dividend paying stock is
F = FV(S0)
The replication argument

CFIN 595
Derivatives and Risk
Management Tools
Vadim di Pietro
McGill School of Continuing Studies
Career and Professional Development
1
Syllabus key points
Contact information: vadim.dipietro@mcgill.ca
Please include CFIN 595 in email subject line
Off

Lecture 5
Options
Introduction
Payout diagrams
Put-call parity
Option strategies
Binomial option pricing: quick intro example
Options: Introduction
Options give the owner the option, but not the
obligation to do something
They can be used for hedging o

Lecture 8 Outline
Stochastic Processes
Geometric Brownian Motion
The lognormal distribution
Arithmetic vs. geometric averages
Stochastic Processes
A stochastic process characterizes the
random evolution of a variable over
time
stochastic means random
E

Lecture 8 Outline
Stochastic Processes
Geometric Brownian Motion
The lognormal distribution
Arithmetic vs. geometric averages
Stochastic Processes
A stochastic process characterizes the
random evolution of a variable over
time
stochastic means random
E

Lecture 6
Binomial Option Pricing
Single step trees
Delta hedging
Risk-neutral pricing
Multi step trees
Dynamic replication
American options and
early exercise
Binomial Pricing: Call Example
Suppose stock ABC is trading at a price of 44 at t = 0

Lecture 9 Outline
Black-Scholes Formula
The Greeks
Implied volatility smiles/smirks/surfaces
The VIX
Geometric Brownian Motion
Recall:
the basic assumption underlying the
Black-Scholes formula is that the stock price
follows Geometric Brownian Motion
(GB

CFIN 595: Derivatives and Risk Management Tools
Vadim di Pietro
Assignment 1
Note: Unless specified otherwise, all rates are annual rates with annual compounding
Topic: Forward Prices
1) You are given the following information at t = 0
IBM is trading at

Q1
a)
b)
t0
t1
t2
-101
1.05 S2
1
-1.05
100
100(1.1)^2
0
0 S2 - 100(1.1)^2
F = 100(1.1)^2 = 121
or:
F = FV(S0 PV(Divs) = (101 1.05/1.05)(1.1)2 = 121
i) Short the forward
ii) Buy the stock at t = 0 for $101
iii) Borrow $1 for 1 year (you will pay this loan

Suu =
Puu =
uu =
Su =
Pu =
u =
S0 = 1500
Sud =
P0 =
Pud =
0 =
ud =
Sd =
Pd =
d =
Sdd =
Pdd =
dd =
Suuu =
Puuu =
Suud =
Puud =
Sudd =
Pudd =
Sddd =
Pddd =
at t = 2 if uu
Buy or Sell:
Borrow or Lend:
at t = 0
Buy or Sell:
Borrow or Lend:
at t = 1 if u
Buy o

CFIN 595: Derivatives and Risk Management Tools
Vadim di Pietro
Assignment 2
Students:
Alexandre Savard
Iman Dorostian, ID: 260595122
Diaa khalifeh, ID: 260620948
Number 1
a)
December 2017 3-Month USD LIBOR fixing expires on December 18th. In order to spe

CFIN 595: Derivatives and Risk Management Tools
Vadim di Pietro
Assignment 3
Topic: Market Microstructure
1) Indicate True or False and give a brief explanation.
a) If you think the price of a stock will likely decrease significantly in the next 5 minutes

CFIN 595: Derivatives and Risk Management Tools
Vadim di Pietro
Assignment 2
Topic: Eurodollars Futures
1) On the day you do this assignment, go to http:/www.cmegroup.com/trading/interestrates/stir/eurodollar.html. Here you will find Eurodollar futures pr

CFIN 595: Derivatives and Risk Management Tools
Vadim di Pietro
Assignment 2: Solutions
Topic: Eurodollars Futures
1) On the day you do this assignment, go to http:/www.cmegroup.com/trading/interestrates/stir/eurodollar.html. Here you will find Eurodollar

Lecture 4
Forwards continued
Commodities
Foreign Exchange
Futures contracts
Difference with forwards
Eurodollar futures
Forwards on commodities
We previously used replication arguments to show that
the forward price on a non-dividend paying stock i

Lecture 3
Forwards continued
Dividend paying stocks
Continuous compounding
Forwards: dividend paying
stocks
We previously used replication arguments to show that
the forward price on a non-dividend paying stock is
F = FV(S0)
The replication argument

Lecture 11 Outline
Non-normality
QQ plots
Student-t distribution
Value at Risk (VaR)
Parametric Models
Historical Simulation
Monte Carlo Simulation
Capital requirements
The generic model
We considered the following generic model of
portfolio retu

Lecture 10 Outline
Returns: stylized facts
Autocorrelation
Fat tails
Skewness
Vol dominates mean
Vol clustering
Vol/return correlation
Time varying correlation
Returns: Stylized Facts
We will consider a set of so-called stylized
facts which apply to mos

Lecture 2: Outline
Forward Rates
Bond forwards
Bond duration
and convexity
1
Forward rates
A forward interest rate is a rate at which parties agree on today to
borrow or lend some amount of money at some point in the future for a
predetermined length