By geometric randomization of the option maturity, we transform the usual n-steps backward recursion that arises in option pricing into a set of n independent integral equations. In order to solve these equations,
we consider different quadrature procedures that transform each integral equation into a linear system; moreover, we solve the linear
systems with iterative algorithms and we study the benefits of suitable
preconditioning techniques. We show the relevance of our procedure,
pricing options (such as plain vanilla, lookback, single and double barrier
options) when the underlying evolves according to different exponential L´evy processes.
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