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

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

2007-03-19

arxiv.org/abs/math/0703538v12

Mathematics

Optimization and Control

Scientific paper

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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