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

An Exact Solution in Series Expansion Form
The normalized PDE system becomes
⎧
⎪⎨
⎪⎩
− ∂V
∂τ + S2 ∂2 V ∂V
+ γS − γV = 0,
∂S2 ∂S
V (S f (τ), τ) = 1 − S f (τ),
∂V
∂S (S f (τ), τ) = −1,
lim V (S, τ) = 0,
S→∞
V (S, 0) = max{1 − S, 0},
in which γ ≡ 2r can be viewed as an interest rate relative to the
σ2 volatility of the asset price.
IWIF-II www.swingtum.com/institute/IWIF PPT 33/68
Song-Ping Zhu, SMAS, April 26, 2007 0-32