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A fast Monte Carlo scheme for additive processes and option pricing

Author

Listed:
  • Michele Azzone

    (Politecnico di Milano)

  • Roberto Baviera

    (Politecnico di Milano)

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 simulating 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 basis point or below.

Suggested Citation

  • Michele Azzone & Roberto Baviera, 2023. "A fast Monte Carlo scheme for additive processes and option pricing," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    • Handle: RePEc:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00463-1
    DOI: 10.1007/s10287-023-00463-1
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Additive process; Simulation; Fast Fourier transform; Lewis formula;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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