Math 623 (IOE 623), Winter 2008: Final exam
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use a calculator but not its memory function.
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explanations concise (as time is limited) but clear. State explicitly any additional assumptions you make.
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(1) Suppose I wish to compute the value of a
European Butterfly Spread
option on a stock. The option pays
Φ(
S
) if exercised when the stock price is
S
, where
Φ(
S
) =
0
if
S
≤
40
S

40
if 40
≤
S
≤
50
60

S
if 50
≤
S
≤
60
0
if
S
≥
60
.
The current value of the stock is 48 and it expires 6 months from today.
Its volatility (in units of
years

1
/
2
is 0
.
34.
Assume that the continuous rate of interest over the lifetime of the option is 3
.
75
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
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 Fall '08
 CONLON
 Math, Numerical Analysis, Variance, Mathematical finance, Monte Carlo method

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