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

Erhan Bayraktar
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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 $C^2$ except at the stopping boundary and that it is $C^1$ everywhere (i.e. the smooth pasting condition always holds).

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Erhan Bayraktar. 2009-01-21. On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps. https://arxiv.org/abs/math/0703538

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