3}CXJCS Qr CDSH'QMS Q;
S STOCS; QQS .
"I: "Hue [AF/A9
" PiShC-lr JAa/vx
{Web/yo lwxfsivmg
£
¥o\l u
Mok euéevg -/ wt am a + F
\ thm\~§ug (T561403 DkQJSIW53.
weak I | QM
thkloéfC-F" 3 V\D\
WED-J Tm a; Cm\Cu\Ms Mg by; M mag M
*9 W 5? a 00 mghw
Ultimate life table
Annuity factor
Principle
Annuity price
9.7386
10,000.00
97,386.08
Single decrement
Mortality probability version (from Appendix 2A of Bowers et al, 2nd edition)
I've deleted the first 50 mortality values, as they aren't needed for this
York University
MATH 5370 3.00MW Financial Mathematics for Teachers
Assignment 3 part 2 Solutions
Problems 1 and 2 are due April 2. Problem 3 is now due April 9. You should
write your solutions down and submit them to me on paper or by e-mail, but I
also
York University
MATH 5370 3.00MW Financial Mathematics for Teachers
Assignment 4 Solutions
Due April 9. For the last problem, send me your simulation by e-mail.
t
1. Find Xt = 0 Bt dBt , where Bt is a Brownian motion.
2
[Hint: by denition, dXt = Bt dBt .
MATH 5370 3.0MW (Winter 2015)
Financial Mathematics for Teachers - Course
outline
Description:
The world of finance is increasingly mathematical. This potentially affects a broad
spectrum of secondary students, from those actually enrolled in business cou
York University
MATH 5370 3.00MW Financial Mathematics for Teachers
Assignment 3 complete
Problems 1 and 2 are due April 2. Problem 3 is now due April 9. You should
write your solutions down and submit them to me on paper or by e-mail, but I
also want you
York University
MATH 5370 3.00MW Financial Mathematics for Teachers
Assignment 1
Due January 29, 2015 (in class or e-mailed to salt@yorku.ca)
1. Suppose that interest rates are constant, and that the interest rate with monthly
compounding is 2%;
(a) What
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
(
York University
MATH 5370 3.00MW Financial Mathematics for Teachers
Assignment 2 Solutions
Due February 12, 2015 (in class or e-mailed to salt@yorku.ca)
Do one or the other of the following problems (for bonus marks, do both). You
should write up your ans
York University
MATH 5370 3.00MW Financial Mathematics for Teachers
Assignment 1 - Solutions
Due January 29, 2015 (in class or e-mailed to salt@yorku.ca)
1. Suppose that interest rates are constant, and that the interest rate with monthly
compounding is 2
York University
MATH 5370 3.00MW Financial Mathematics for Teachers
Assignment 3, part 1 Solutions
Problems 1 and 2 are due April 2. Problem 3 is now due April 9. You should
write your solutions down and submit them to me on paper or by e-mail, but I
also
York University
MATH 5370 3.00MW Financial Mathematics for Teachers
Assignment 2 (modied)
Due February 12, 2015 (in class or e-mailed to salt@yorku.ca)
Do one or the other of the following problems (for bonus marks, do both). You
should write up your answ
Qami
W
1 &t§6&%x°§ QMK QM? M £33
QKmewkfzi-v » . iv
7 y? a F b E i
N aw msg r/dg 2% avéfxrwmk
Nhggmw 'kaiiCJ'ié/ié {3% mi aag have kW mi; 3&3
a": %m\g £33 Ca\Cm§a\+{v% "Pgkaldli
E++Vms~> m3 w Cm amwmm :ng
4 E i
R a 3
W is NA giwékipxéig
Binomialpricing:Europeancall(nodividends)
T
S0
r
sigma
K
periods
dt
u
d
R
p
s
del
v
d1
d2
BSMprice
Binomialprice
2
12
4%
20%
15
6
0.3333333333
1.1224009024
0.8909472523
1.0134226186
0.5291572038
Weuseu=e^(sigmasqrt(dt),d=1/u
s
del
v
s
del
v
s
del
v
0.3646
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
M 0k+(/\ 537 c? U
Nag km? aduso aux:
aha/3 a 3 ' and 61qu QM um
W9 QUQ" mam +\r\ 9 " QEAW
' Pxvwwkc-Q {1A CMWCVJMW) C COL Mm+k
ch ) err W1 [1&0 . 392.)
Cm\S{§+S (931t SWWFQ me?ouv\ok inkAPS!
OWL 45W mffhcooliws. Ver daig.
WeH (Keats [IA A
ri
lifexpectancy=function(age, m, b, hor, reps)
cfw_ # Monte Carlo simulator, to find life expectancy
# typical call: lifexpectancy(age=30, m=90, b=12, hor=120, reps=1000000 )
# If this file is saved as a file meanlifetime.R then selecting it as the source
York University
MATH 5370 3.00MW Financial Mathematics for Teachers
Assignment 4
Due April 9. For the last problem, send me your simulation by e-mail.
t
1. Find Xt = 0 Bt dBt , where Bt is a Brownian motion.
2
[Hint: by denition, dXt = Bt dBt . Try settin