Stochastic Models and Processes · 14. novembre 2023
In risk-neutral valuation, predicting the next step in a random walk, even with real probabilities of 0.55 up and 0.45 down, is not straightforward. The expected direction—up, down, or indeterminate—depends on additional factors like the risk-free rate and the magnitude of movements.
06. novembre 2023
Benoit Mandelbrot revolutionized finance with his fractal geometry insights, revealing that market prices are rough and self-similar across time scales, not smooth as traditional models suggest. His work, inspired by Hurst's Nile studies, shows markets exhibit 'wild randomness' with frequent large swings. Mandelbrot's methods, using the Hurst exponent, offer a new model for capturing the actual volatility and trends in financial markets. #Mandelbrot #Fractals #Finance #MarketVolatility
Mathematical Principles and Quantitative Finance · 21. octobre 2023
Quantitative finance faces a paradox: static financial models like GBM vs. dynamic market changes. Traditional models, with fixed parameters, struggle against market unpredictability influenced by global events. Emerging AI and machine learning technologies promise more adaptive models, aligning with market fluidity and redefining finance.