This preview shows pages 1–3. Sign up to view the full content.
Math 623 (IOE 623), Fall 2007: Final exam
Name:
Student ID:
This is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam. You may also
use a calculator but not its memory function.
Please write all your solutions in this exam booklet (front and back of the page if necessary). Keep your
explanations concise (as time is limited) but clear. State explicitly any additional assumptions you make.
Time is counted in years, prices in USD, and all interest rates are continuously compounded unless otherwise
stated.
You are obliged to comply with the Honor Code of the College of Engineering. After you have completed the
examination, please sign the Honor Pledge below. A test where the signed honor pledge does not appear may not
be graded.
I have neither given nor received aid, nor have I used unauthorized resources, on this examination
.
Signed:
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document(1) Suppose I wish to compute the value of a European
put
option on a stock. The option has strike price
23 and it expires 4 months from today. The current value of the stock is 24. Its volatility (in units
of years

1
/
2
is 0
.
29. Assume that the continuous rate of interest over the lifetime of the option is 4
.
34
percent. The value of the option is to be obtained by numerically solving a terminalboundary value
problem for a PDE. The PDE is the BlackScholes PDE transformed by the change of variable
S
=
e
x
,
where
S
is the stock price.
(a) Write down the PDE for the value of the option as a function of the variables
x
and
t
, where the
units of
t
are in years.
(b) The PDE is to be numerically solved in the region
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '08
 CONLON
 Math

Click to edit the document details