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MELLIN TRANSFORM METHOD FOR THE VALUATION OF AMERICAN POWER PUT OPTION

An p (Sn t ; t) = 1 2 i Z c+i1 c􀀀i1 K!+1 !(! + 1) e 1 2n2 2(!2+ 1!􀀀 2)(T􀀀t)(Sn t )􀀀!d! + rK 2 i Z c+i1 c􀀀i1 Z T t (Sn t )􀀀! ( Sn y )! ! e 1 2n2 2(!2+ 1 !􀀀 2)(y􀀀t)dyd! 􀀀 q 2 i Z c+i1 c􀀀i1 Z T t (Sn t )􀀀! ( Sn y )!+1 ! + 1 e 1 2n2 2(!2+ 1 !􀀀 2)(y􀀀t)dyd!

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Format: Thesis
Published: 2017-05
Subjects:
American power put option,
Geometric Brownian motion
Ito's lemma
Non-homogeneous Black-Scholes-Merton-like equation
Value-matching condition
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Summary:An p (Sn t ; t) = 1 2 i Z c+i1 c􀀀i1 K!+1 !(! + 1) e 1 2n2 2(!2+ 1!􀀀 2)(T􀀀t)(Sn t )􀀀!d! + rK 2 i Z c+i1 c􀀀i1 Z T t (Sn t )􀀀! ( Sn y )! ! e 1 2n2 2(!2+ 1 !􀀀 2)(y􀀀t)dyd! 􀀀 q 2 i Z c+i1 c􀀀i1 Z T t (Sn t )􀀀! ( Sn y )!+1 ! + 1 e 1 2n2 2(!2+ 1 !􀀀 2)(y􀀀t)dyd!

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