Jumps in financial modelling: pitting the Black-Scholes model refinement programme against the Mandelbrot programme

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, overmathematisation 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.

The author

Christian Walter is actuary of the French Institute of Actuaries and holds the Chair «Ethics and Finance” at the Collège d’études mondiales, Fondation Maison des sciences de l’homme. Adjunct Professor at the University of Evry (1999-2002), Sciences Po (2002-2008), and IAE of Paris (2011-2014). Visiting Professor at Columbia University, New York (2008). Member of Research Centre for Contemporary philosophy (Phico) of the University Paris 1 Panthéon-Sorbonne. Member of the Advisory Committee of the legislation and financial regulation (CCLRF) of the Treasury Department of the French Ministry of Finance. His research focuses on financial modeling, history and epistemology of finance theory and ethics of finance. Latest books: The random walk model in Finance, Paris, Economica, 2013; Extreme Financial Risks and Asset Allocation (with Olivier Le Courtois), London, Imperial College Press, 2014.

The text

This text was written in the frame of the Chair Ethics and finance at the Collège d’études mondiales, Fondation Maison des sciences de l’homme...