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

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Review of Various solution Approaches<br />

Analytical Approximations:<br />

Zhu (2006a) also derived a very eleg<strong>an</strong>t <strong>an</strong>alytical<br />

approximation formula for the optimal exercise price of<br />

<strong>Americ<strong>an</strong></strong> options, Us<strong>in</strong>g the Laplace tr<strong>an</strong>sform approach.<br />

S f (τ) =<br />

γ<br />

1 + γ + e−a2 τ<br />

∫ ∞<br />

e −τρ<br />

π 0 a 2 + ρ e−f 1(ρ) s<strong>in</strong> [f 2 (ρ)] dρ, (3)<br />

IWIF-II www.sw<strong>in</strong>gtum.com/<strong>in</strong>stitute/IWIF PPT 20/68<br />

Song-P<strong>in</strong>g Zhu, SMAS, April 26, 2007 0-19

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