Solutions Manual to
AN INTRODUCTION TO MATHEMATICAL
FINANCE: OPTIONS AND OTHER TOPICS
Sheldon M. Ross
1
1.1 (a) 1 p0 p1 p2 p3 = 0.05 (b) p0 + p1 + p2 = 0.80
1.2 P cfw_C R = P cfw_C + P cfw_R P cfw_C R = 0.4 + 0.3 0.2 = 0.5
1.3 (a)
8 7
14 13
=
56
182
(b)
6

Example 9.1 Consider the case of a security whose price is $100, while
the risk-free interest rate is 4% per annum, the annual volatility of the stock
price is 23%, the strike price is set at $105, and the expiry date is 3 months.
Under these conditions t

Calculus 1
HW Assignment #7
Fall, 2012-13
8. (b) Use the Mean Value Theorem to prove the inequality |sin a sin b| 6 |a b| for all a
and b.
Hint:
For any value of a and b (suppose that a < b), by applying MVT, there exists a value of c in
(a,b) such that:

HW Assignment #9
Calculus 1
December 2012
Due on Wednesday, December 19, 2012 at the beginning of class
1. Evaluate the integral formula
R
R
R
R
2
a. x sin xdx, b. (2x + 9) ex dx,
c. x3 ln xdx, d. (lnxx)
dx.
2
(Hint for a c: Use the Integration by Parts.

HW Assignment #8
Calculus 1
December 2012
This homework assignment will not be collected or graded.
1. Using the lHospitals rule to find the limits
2x
x)
sin 4x
, (c) lim tan
,
(a) lim e x31 , (b) lim ln(ln
x
5x
x0
x
x0
ex 1x 12 x2
.
x3
x0
(d) lim
2. For

Homework Assignment #3
Calculus 1
Semester I, 2012-13
HW#3 will not be collected or graded.
1. For the function g whose graph is given, state the value of each quantity, if it exists. If it
does not exist, explain why.
(a) lim g(t),
(b) lim+ g(t),
(c) lim

Calculus 1
HW Assignment #7
November 2012
Due on Wednesday, November 28, 2012 at the beginning of class
1. A ball is thrown vertically upward with a initial velocity 80 ft/s (feet/second), then its height
after t seconds is
s = 80t 16t2 .
(a) At what time

Homework Assignment #5
Calculus 1
Semester I, 2012
1. Prove that
sin x
tan x
ex 1
ln (x + 1)
(a) lim
= 1, (b) lim
= 1, (c) lim
= 1, (d) lim
= 1.
x0 x
x0
x0
x0
x
x
x
Hint: Using the definition of derivative.
Solution
(a) See the lecture note (slide 44).
(b

Homework Assignment #4
Calculus 1
Semester I, 2012
Due date: Wednesday, October 17, 2012 at the beginning of class.
1. For the function g whose graph is given, state the value of each quantity, if it exists. If it
does not exist, explain why.
(a) lim R (x