A mathematical proof of the soundness of the Fibonacci retracement rule in technical analysis of asset prices

This project covers the idea of the Fibonacci retracement rule and its mathematical proof. Firstly, a thorough analysis of stochastic processes, in particular, diffusion processes such as the Brownian motion, the CEV model or Bessel processes, will be done. Then it follows with a study of Technical Analysis and the Fibonacci and golden numbers, introducing the concept of the Fibonacci retracement rule. Finally, a detailed proof of the soundness of the rule will be given. At the end, we encounter codes for simulating diffusion process and real financial stocks applying the Fibonacci retracement rule