The Misbehavior of Markets
Mandelbrot, Benoit; Hudson, Richard L.
Read: 2024-05-01 • Rating: 6/10
This book was pretty much Mandelbrot applying fractal geometry to SDEs which was interesting for me in particular as I took a course in SDEs while I read this. The main idea of the book was that modelling the market as a Brownian Motion is overly simplistic and does not accurately model the long tailed nature of the market, making models built on this assumption vulnerable to the volatile nature of markets. Mandelbrot goes on to provide examples of fractals being manifesting in real-world rock formation, tides, etc. to give some intuition on their applications. He finishes the book by explaining in more detail how fractals are applied specifically in financial markets and how using this model we can make better assumptions.
Finance is no science. Everyone uses their own models, and a lot of the time they’re very speculative and are built on very grossly oversimplified assumptions of how markets behave. Mandelbrot asserts that his model does something others don’t, which is that it restates the initial assumptions of how markets behave. The main differences exists in how standard Brownian motion is independent and normally distributed. Mandelbrot’s model states that actually financial markets demonstrate some long-term dependence as well as varying distributions which have longer tails than Gaussian ones. He introduces the concept of the Hurst exponent, H and alpha, ⍺ where the former describes the long-term dependence and the latter describes the fatness of the tails. This more generalized form allows us more flexibility when modelling markets as say a FOREX market may be different than a commodities market.
Overall I found the book to be interesting but I think it’s just a 12-page paper drawn out to be 276 pages in a more high-level novel. For business people, it should be cool to read but for a math student maybe less cool and perhaps I could have just read some scientific literature to get a more low-level understanding of how this idea looks in practice.