Michigan State University
Department of Mathematics
Math 458 Fall 13 Section 1
QUIZ 4 - SDE and pricing
Name (Print): Solutions
1. Consider the SDE
dXt = tXt dt + dWt
X0 = 0.
(1)
Solve for Xt .
Answer:
t2
Using integrating factor e 2 , we compute
t2
t2
d
Michigan State University
Department of Mathematics
Math 458 Fall 13 Section 1
QUIZ 3 - Ito Calculus!
Name (Print): Solutions
1. Consider the SDE
dXt = Xt dt + Xt dWt .
(1)
For Zt = ln Xt , write out the form of dZt in terms of dt and dWt .
Answer:
There
Table 1: Grades
Q# Grade
1
2
3
4
Michigan State University
Department of Mathematics
MATH 458 Fall 2013
Exam 1
Name (Print):
Name (Sign):
Basic Information:
V C (S, t) = er(T t) E [(ST K )+ | St = S ]
= Se(T t) N (d1 ) Ker(T t) N (d2 )
V P (S, t) = er(T t
Michigan State University
Department of Mathematics
MATH 458 Fall 2013
Exam 1 - Practice (Solutions)
Name (Print):
Name (Sign):
Basic Information:
V C (S, t) = er(T t) E [(ST K )+ | St = S ]
= Se(T t) N (d1 ) Ker(T t) N (d2 )
V P (S, t) = er(T t) E [(K ST
Michigan State University
Department of Mathematics
Math 458 Fall 13 Section 1
QUIZ 2
Name (Print):
Name (Sign):
Please feel free to collaborate and consult any source. You have 15 minutes
to complete this quiz. All students that wish to be considered for
Michigan State University
Department of Mathematics
Math 458 Fall 13 Section 1
QUIZ 1 Solutions
Name (Print):
Name (Sign):
Please feel free to collaborate and consult any source. You have 15 minutes
to complete this quiz. All students that wish to be cons
Michigan State University
Department of Mathematics
Math 458 Fall 13 Section 1
HW 1 Solutions
1. For a lognormally distributed asset share St with observed average
growth rate , prove
E[St ] = S0 e()t
P[St > K ] = N
ln S0 + ( 0.5 2 )t
K
.
t
(1)
Proof
1
R