Pricing American Options - an Important Fundamental Research in ...

The Solution for the Option Price
∫ τ
+
0
⎧
⎨
⎩
[
e (γ+1)2 η ∫
4
√ e 1 2 (γ−1)x
π
e (γ−1)√ τ−η ξ−ξ 2 dξ
∫ ∞
x
2 √ τ−η
x
2 √ τ−η
−
x
2 √ τ−η
[
e 1 2 (γ−1)x f n (2 √ τ − η ξ + x, η)
f n (2 √ τ − η ξ + x, η)
+
]
+e − 1 2 (γ−1)x f n (2 √ ]
τ − η ξ − x, η) e (γ−1)√ τ−η ξ−ξ 2 dξ
−(γ + 1) √ τ − ηe − 1 (γ+1)2
(γ−1)x+ τ
2 4
· e 2γ√ τ−η ξ erfc(ξ + (γ+1)
2
∫ ∞
x
2 √ τ−η
√ τ − η)dξ
}
dη
f n (2 √ τ − η ξ − x, η)
}
,
IWIF-II www.swingtum.com/institute/IWIF PPT 51/68
Song-Ping Zhu, SMAS, April 26, 2007 0-50