On the Penalisation Error for American Options in a Jump Model

Details On the Penalisation Error for American Options in a Jump Model On the Penalisation Error for American Options in a Jump Model

2010-08-04

arxiv.org/abs/1008.0836v1

Economy

Quantitative Finance

Pricing of Securities

15 Pages, 3 Figures

Scientific paper

We consider the pricing of American options in a model where the underlying asset is assumed to follow a jump diffusion process. The option value can be expressed as the solution to a variational inequality containing an integro-differential operator. A certain nonlinear equation, the so-called penalised equation, can be used to approximate the variational inequality. We study the approximation and provide a bound for the penalisation error. Our bound holds for twice weakly differentiable payoff functions as well as for a wider class of functions including American call and put options.

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