The refinement programme vs. the Mandelbrot programme

Christian Walter, Jumps in financial modelling: pitting the Black-Scholes model refinement programme against the Mandelbrot programme, FMSH-WP-2015-95, avril 2015.

Updated version published with important modifications: “The Extreme Value Problem in Finance: Comparing the Pragmatic Program with the Mandelbrot Program“, ch. 3 in Fr. Longin (ed.) Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications, Wiley (visit Website), 2016.

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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 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.

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Christian Walter

Actuaire agrégé, chercheur en philosophie et sciences sociales, spécialiste des représentations du hasard en finance et dans les modèles de… Lire la suite

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