On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps

2007/03/19 by Erhan Bayraktar, Bayraktar, Erhan
Economics, Econometrics and Finance · Mathematics · #60J75 #62L15 #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #math.OC #msc:60J75 #msc:62L15 #q-fin.PR

paper · pdf · doi:10.48550/arxiv.math/0703538

arxiv created 2009/01/21 · arxiv updated 2009/12/01

Abstract

We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is C² except at the stopping boundary and that it is C¹ everywhere (i.e. the smooth pasting condition always holds).

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