University of Waterloo
Term and Year of Offering: Fall 2013
MATBUS 470 Derivatives: LEC: 10:00-11:20 TTh E2 1303
Instructor: R. Keith Freeland, M3 2016, rkfreeland@uwaterloo.ca, extension 33356
Office hours: 10:00-11:00 Mondays and Wednesdays
Course Descr

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MATBUS 470 Winter 2015
MATBUS 470 Fall 2015 assignment 1.
Due: October 16th before 11:30 am in M3-2001
You are giving the following information:
The current price of copper is $230 per 100 lbs.
The risk-free rate of interest is 4% p.a. fo

MATBUS 470 Fall 2013
Assignment 3
Due: Noon November 25th in M3 2001.
1. Consider a stock where the price remains constant until the price jumps and when
the price jumps it always jumps up by 2%. The time between jumps is exponentially
distributed with a

MATBUS 470
Assignment 2
Due: November 13th at the beginning of class
1) A stock price is currently $40. It is known that at the end of one month it will be either $42 or
$38. The risk-free interest rate is 8% per annum with continuous compounding. Conside

MATBUS 470
Assignment 3
Due: April 3rd at the beginning of class
1) Derive a formula for the delta of a European call option under the Black-Scholes-Merton pricing
formula. That is, take the partial derivative with respect to S0 of the function given in e

University of Waterloo
Term and Year of Offering: Winter 2013
MATBUS 470 Derivatives: LEC: 10:30-11:30 MWF PHY 313
Instructor: R. Keith Freeland, M3 2016, rkfreeland@uwaterloo.ca, extension 33356
Office hours: 2:00-3:00 Wednesdays and Thursdays
Course Des

MATBUS 470
Assignment 2
Due: November 13th at the beginning of class
1) A stock price is currently $40. It is known that at the end of one month it will be either $42 or
$38. The risk-free interest rate is 8% per annum with continuous compounding. Conside

MATBUS 470
Assignment 3
Due: Dec 3rd before 10:00 am in M3 2001
1) A stock index currently stands at 300 and has a volatility of 20%. The risk-free interest rate is 8%
and the dividend yield on the index is 3%. Use a three-step binomial tree to value a si

MATBUS 470 Winter 2014
Assignment 2
Due: Noon March 13th in M3 2001.
1. A stock price is currently $30. During each two-month period for the next four months it
is expected to increase by 8% or reduce by 10%. The risk-free interest rate is 5%. Use a
two-s

MATBUS 470
Assignment 2
Due: March 11th at the beginning of class
1) A stock price is currently $50. It is known that at the end of six months it will be either $60 or
$42. The risk-free rate of interest with continuous compounding is 12% per annum. Calcu

MATBUS 470
Assignment 1
Due: February 6th at the beginning of class
1) A portfolio manager has maintained an actively managed portfolio with a beta of 0.2.
During the last year the risk-free rate was 5% and equities performed very badly
providing a return

MATBUS 470 Assignment 2 Solutions
1) A stock price is currently 550. It is known that at the end of six months it will be either 560 or
$42. The risk-free rate of interest with continuous compounding is 12% per annum. Calculate the
value of a six-month E

MATBUS 470
Assignment 1 Solutions
1) A portfolio manager has maintained an actively managed portfolio with a beta of 0.2.
During the last year the risk-free rate was 5% and equities performed very badly
providing a return of 30%. The portfolio manage prod

Bond
A
B
settlement
Maturity
YTM
Coupon
31-Jan-13
31-Oct-15
1.45%
4%
31-Jan-13
1-Jun-21
2.21%
6%
last
next
Total
Days to next
31-Oct-12
30-Apr-13
181
89
1-Dec-12
1-Jun-13
182
121
shif
0.01%
0.01%
price
AI
FP
106.8271211223
1.0165745856
107.8436957079
128.

MATBUS 470 Winter 2013 Test 2 a)
1. [ijonsider a two-step binomial tree. The current stock price is 100. At each step the stock price is
either multiplied by 2 or 1/2. The per period interest rate is r = 0.25 ($1 grows to $1.25 after one
period, i.e. erA

MATBUS 470 Fall 2013 assignment 1.
Due: November 5th at the beginning of class
1. Problem 12.16.
A stock price is currently $50. It is known that at the end of six months it will be either $60 or
$42. The risk-free rate of interest with continuous compoun

Tree Display
At each node:
Upper value = Underlying Asset Price
Lower value = Option Price
Values in red are a result of early exercise.
Strike price = 40
Discount factor per step = 0.9900
Time step, dt = 0.2500 years, 91.25 days
Growth factor per step, a

Tree Display
At each node:
Upper value = Underlying Asset Price
Lower value = Option Price
Values in red are a result of early exercise.
Strike price = 40
Discount factor per step = 0.9960
Time step, dt = 0.1000 years, 36.50 days
Growth factor per step, a

The midterm has 6 questions.
Q 1. forward contracts (focus on 5.1-5.10)
Q 2. Properties of Stock Options (Ch. 10) requires no arbitrage arguments
Q 3. Continuous time stock model (13.3, 13.7 and 14.1)
Q 4. Ito's lemma (univariate case only)
Q 5. binomial