Pricing American Options - an Important Fundamental Research in ...
Pricing American Options - an Important Fundamental Research in ...
Pricing American Options - an Important Fundamental Research in ...
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An Exact Solution <strong>in</strong> Series Exp<strong>an</strong>sion Form<br />
Let’s now construct two new unknown functions ¯V (x, τ, p) <strong>an</strong>d<br />
¯S f (τ, p) that satisfy the follow<strong>in</strong>g differential system,<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
(1 − p)L[ ¯V (x, τ, p) − ¯V 0 (x, τ)] = −p{A[ ¯V (x, t, p), ¯S f (τ, p)]},<br />
¯V (x, 0, p) = (1 − p) ¯V 0 (x, 0),<br />
¯V (0, τ, p) + ¯S f (τ, p) = 1,<br />
∂ ¯V<br />
[<br />
∂x (0, τ, p) + ¯S f (τ, p) = (1 − p) 1 + ∂ ¯V ]<br />
0<br />
∂x (0, τ) − ¯V 0 (0, τ) ,<br />
lim ¯V (x, τ, p) = 0,<br />
x→∞<br />
IWIF-II www.sw<strong>in</strong>gtum.com/<strong>in</strong>stitute/IWIF PPT 37/68<br />
Song-P<strong>in</strong>g Zhu, SMAS, April 26, 2007 0-36
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