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arXiv · 2112.08291

A fast Monte Carlo scheme for additive processes and option pricing

Michele Azzone·Roberto Baviera
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Abstract

In this paper, we present a very fast Monte Carlo scheme for additive processes: the computational time is of the same order of magnitude of standard algorithms for Brownian motions. We analyze in detail numerical error sources and propose a technique that reduces the two major sources of error. We also compare our results with a benchmark method: the jump simulation with Gaussian approximation. We show an application to additive normal tempered stable processes, a class of additive processes that calibrates ``exactly" the implied volatility surface.Numerical results are relevant. This fast algorithm is also an accurate tool for pricing path-dependent discretely-monitoring options with errors of one bp or below.

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Michele Azzone, Roberto Baviera. 2021-12-15. A fast Monte Carlo scheme for additive processes and option pricing. https://doi.org/10.1007/s10287-023-00463-1

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