MATH 2281 3.00MW (Winter 2011)
Financial Economics
Course Outline
Prerequisites:
Interest rates (MATH 2280 or equivalent)
Probability and mathematical statistics (MATH 2131)
Linear algebra (MATH 1021 or MATH 2221)
Lectures:
MWF 1:30-2:20 in CB115 (Chem
Binomialpricing:Europeancall(nodividends)
T
S0
r
sigma
K
periods
dt
u
d
R
p
s
del
v
d1
d2
BSMprice
(att=0)
1
10
4%
15%
9.5
6
0.1666666667
1.06315111
0.940600062
1.0066889384
0.539276305
Weuseu=e^(sigmasqrt(dt),d=1/u
s
del
v
s
del
v
s
del
v
0.684
0.534
1.1
BINOMIAL OPTION PRICING IN EXCEL
This note explains how to create a binomial tree and use it to price a call option via an Excel
spreadsheet.
(1) Open Excel and have a look at a spreadsheet. A typical le includes three worksheets
(labelled Sheet1, Sheet2,
ICE Futures Canada
Jan 26, 2011
Canola Futures
Contract Specifications
Description
The canola futures contract is the world benchmark for canola trading. The
contract prices physical delivery of canola seed free-on-board value in the
par delivery region.
Amer call
Binomial Tree
Stock model: CRR calibration
Option: American call
Q-prob
138.62 I del
233.62 S v
H B
Calibration
r (int rate)
q (div rate)
sigma (vol)
initial S
Strike
T
n
delta t
Node values
I:
H:
v:
B:
del:
S:
93.97 I del
188.97 S v
93.73 H B
(
MATH 2281 3.00MW (Winter 2012)
Financial Economics
Course Outline
Prerequisites:
Interest rates (MATH 2280 or equivalent)
Probability (MATH 2030)
Linear algebra (MATH 1021 or MATH 2221)
Note that MATH 2131 is no longer a prerequisite.
Course Webpage
www.m
York University
MATH 2281 3.00MW Financial Economics
Instructors: A. Kuznetsov, T. Salisbury
Assignment 4
Due March , 2012
(1) Do problem 14.28(a) of Hull, assuming S0 = 2, T is 1 year, r = 3%, and
= 25%.
(2) Price the following derivatives expiring in 1
York University
Faculty of Science and Engineering
MATH 2281 3.00MW Financial Economics
Instructor: T. Salisbury
Second Midterm Examination Solutions
March 18, 2011
NAME:
SIGNATURE:
STUDENT NUMBER:
Instructions:
(1) You have 50 minutes to complete this ex
York University
Faculty of Science and Engineering
MATH 2281 3.00MW Financial Economics
Instructors: A. Kuznetsov, T. Salisbury
Second Midterm Examination Solutions
March 23, 2012
NAME:
SIGNATURE:
STUDENT NUMBER:
Instructions:
(1) You have 50 minutes to c
NAME
STUDENT #
York University
MATH 2281 3.00MW Financial Economics
Midterm Examination I Solutions (Salisbury)
February 11, 2011
You have 50 minutes to complete this examination. There are 4 pages to the
examination, consisting of 4 questions, for a
York University
MATH 2281 3.0MW (Financial Economics)
Practice problems II Solutions
April 2011 Salisbury
I was asked for some additional practice problems on topics like what came up on
the midterms. Here are some you might think about.
(1) Recall that i
York University
MATH 2281 3.0MW (Financial Economics)
Assignment 3 Solutions
February 2011 Salisbury
Problem 5.12
(a) An S&P contract is for $250 times the index. The notional value is
V0 = 10 $250 950 = $2, 375, 000; With an initial margin of 10% of
noti
York University
MATH 2281 3.0MW (Financial Economics)
Assignment 1 Solutions
January 2011 Salisbury
Problem 1.3
(a) It will cost 100 $41.05 + $20 = $4, 125 to buy 100 shares.
(b) You will receive 100 $40.95 $20 = $4, 075 from selling 100 shares.
(c) The r
York University
MATH 2281 3.0MW (Financial Economics)
Assignment 2 Solutions
January 2011 Salisbury
Problem 5.5
(a) 9 months is 0.75 years, so S0 erT = 1100 e0.050.75 = 1142.03
(b) You will have a long futures position. To hedge a long forward position
yo
York University
MATH 2281 3.0MW (Financial Economics)
Practice problems Solutions
April 2011 Salisbury
Problem 13.2
The put option parameters are K = 40, r = 0.08, = 0, and = 0.30;
91
The portfolio is initiated with T = 91 days = 365 = 0.249315 and S = 40
York University
MATH 2281 3.0MW (Financial Economics)
Assignment 5 Solutions
March 2011 Salisbury
1. European Put
We are using a model with no dividends. The argument given in class works for all
payo functions, giving a price
v0 = erT EQ [f (Se(r
2
)T +
York University
MATH 2281 3.0MW (Financial Economics)
Assignment 4 Solutions
March 2011 Salisbury
Problem 9.1
By put-call parity,
P = C SeT + KerT = 2.27 32e0.060.5 + 35e0.040.5 = 5.52
Problem 9.9
There are several arbitrage possibilities (though you only
York University
MATH 2281 3.0MW (Financial Economics)
Assignment 6 Solutions
April 2011 Salisbury
(1) I started with the spreadsheet of assignment 4. I modied it to incorporating
the formula for delta and B that includes dividends. See the accompanying
sp
York University
Faculty of Science and Engineering
MATH 2281 3.00MW Financial Economics
Instructors: A. Kuznetsov, T. Salisbury
First Midterm Examination Solutions
February 10, 2012
NAME:
SIGNATURE:
STUDENT NUMBER:
Instructions:
(1) You have 50 minutes to
NAME
STUDENT #
York University
MATH 2281 3.00MW Financial Economics
Midterm Examination I
February 11, 2011
You have 50 minutes to complete this examination. There are 4 pages to the
examination, consisting of 4 questions, for a total score of 60 mark