II. Mathematical Tools and Principles · 06. November 2023
Chaos theory is a field of study in mathematics that deals with systems that appear to be disordered, but are actually following deterministic rules that are highly sensitive to initial conditions. This sensitivity causes the system to appear random and unpredictable. One of the simplest mathematical models to demonstrate chaos is the logistic map. This is a recurrence relation which is used to model population growth and is given by: x(n+1) = r * x(n) * (1 - x(n)) Here, x(n) is the proportion...
IV. Advanced Concepts and Theories · 06. November 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
IV. Advanced Concepts and Theories · 01. November 2023
The Kalman filter refines estimates of financial states like stock prices from noisy data, crucial for asset tracking and trend analysis. It uses initial guesses and uncertainty measures, adjusting predictions with observed data over time. Kalman Gain balances predictions with actual trends for optimal estimation.
IV. Advanced Concepts and Theories · 21. October 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.
IV. Advanced Concepts and Theories · 07. October 2023
Explore the term 'almost surely' in stochastic calculus, a concept denoting events that are virtually certain, accounting for inherent randomness. It ensures mathematical consistency in modeling complex, unpredictable systems. Key in theorems and models, it navigates the fine line between certainty and infinite possibilities.
IV. Advanced Concepts and Theories · 16. September 2023
Learn to optimize pairs trading using copulas & grasp entropy in portfolio diversification. Our guide demystifies complex concepts with simple analogies, making finance easy for all. Dive into the mix of color ball analogy for entropy & understand risk & predictability in portfolios. Stay ahead with insights crafted for clarity & precision. #Copula #PairsTrading #Entropy #PortfolioDiversification #FinanceExplained
IV. Advanced Concepts and Theories · 18. February 2023
The d1 term in BS formula in layman’s terms… #BlackScholes #OptionPricing #Volatility #RiskFreeRate #StrikePrice#FinancialMathematics #QuantitativeFinance #Derivatives#d1Formula #FinancialModeling
IV. Advanced Concepts and Theories · 11. February 2023
Unlock the Black-Scholes PDE with our easy step-by-step guide! Perfect for new quants or those needing a refresher. Dive into options pricing effortlessly! 🌟📈 Check the link to begin! #QuantitativeFinance #OptionsPricing