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Math 623, F 2011: Homework 2
For full credit, your solutions must be clearly presented and all code included.
(1) Consider the situation described in problem (2) of homework I. In this problem we shall use the
Euler method from there (modiﬁed appropriately), to ﬁnd the value of an American put option.
Suppose
K
is the strike price of the option.
(a) Write down the boundary and terminal data corresponding to (c) of problem 2 in homework
I, which one needs to ﬁnd the value of the American option.
(b) Write down the explicit ﬁnite diﬀerence algorithm (modiﬁed from the one in (d) of problem
2 in homework I) which you will use to numerically compute the value of the option.
(c) Now take
K
= 20
, σ
= 0
.
32
, T
= 0
.
5 in (b) . Implement the scheme with Δ
x
= (
b

a
)
/
2
5
and for the value
α
= 8. For a given value of
r
, plot the graphs of the computed value of
the American option, and the value (using the MATLAB function
blsprice
for example) of
the corresponding European put option against stock price on the same axis. Compare the
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 Fall '08
 CONLON
 Math

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