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Jumps in financial modelling: pitting the Black-Scholes model refinement programme against the Mandelbrot programme
[La modélisation des discontinuités boursières : le programme de Mandelbrot et le programme pragmatique]

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  • Christian Walter

    () (PHICO - Philosophies contemporaines - UP1 - Université Panthéon-Sorbonne, Le Collège d'études mondiales/FMSH - FMSH - Fondation Maison des sciences de l'homme)

Abstract

This paper gives an overview of the financial modelling of discontinuities in the behaviour of stock market prices. I adopt an epistemological perspective to present to the two main competitors for this stake: Mandelbrot's programme and the non-stable Lévy processes based approach. I explain this contest using the De Bruin's notions of refinement programme, over-mathematisation and model-tinkering: I argue that the non-stable Lévy based approach of discontinuities can be viewed as a " Black-Scholes model refinement programme " (BSMRP) in the De Bruin's sense, launched against the radical view of Mandelbrot. I use Sato's classification to contrast the two competitors. Next I present the two strands of research from an historical perspective between 1960 and 2000. Mandelbrot's initial model based on alpha-stable motions initiated huge controversies in the finance field and failed to fully describe the observed behaviour of returns due to the stronger fractal hypothesis. The mixed jump-diffusion non fractal processes began in the 1970s, followed after two decades by infinite activity processes in the 1990s. At the end, the time-change representation of the 2000s seems to unify the two competitors.

Suggested Citation

  • Christian Walter, 2015. "Jumps in financial modelling: pitting the Black-Scholes model refinement programme against the Mandelbrot programme
    [La modélisation des discontinuités boursières : le programme de Mandelbrot et le
    ," Working Papers halshs-01146581, HAL.
  • Handle: RePEc:hal:wpaper:halshs-01146581
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01146581
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    References listed on IDEAS

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    1. Guilhem Fabre, 2013. "The Lion's Share. What's behind China's economic slowdown," Working Papers halshs-00874077, HAL.
    2. Pierre Salama, 2014. "Les classes moyennes peuvent-elles dynamiser la croissance du PIB dans les économies émergentes latino-américaines et asiatiques ?," Revue Tiers-Monde, Armand Colin, vol. 0(3), pages 141-157.
    3. Pierre Salama, 2014. "Les classes moyennes peuvent-elles dynamiser la croissance du PIB dans les économies émergentes ?," CEPN Working Papers halshs-00952752, HAL.
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    5. Pierre Salama, 2014. "Les classes moyennes peuvent-elles dynamiser la croissance du PIB dans les économies émergentes ?," Working Papers halshs-00952752, HAL.
    6. Sudip Chaudhuri, 2015. "Premature Deindustrialization in India and Re thinking the Role of Government
      [La désindustrialisation précoce en Inde : pour un nouveau rôle du gouvernement]
      ," Working Papers halshs-01143795, HAL.
    7. Guilhem Fabre, 2015. "The Lions's Share, Act 2. What's Behind China's Anti-Corruption Campaign?
      [La part du lion, acte 2 : Les dessous de la campagne anti-corruption en Chine]
      ," Working Papers halshs-01143800, HAL.
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    Keywords

    financial modelling; Mandelbrot; refinement program; finance; epistemology; overmathematisation;

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