Mathematical Principles and Quantitative Finance · 06. décembre 2024
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Doob's inequality provides a key insight into controlling the probability of extreme events in submartingale processes. By analyzing the event where Xt exceeds a threshold C, the inequality bounds the probability P(A) using the expected maximum positive value of the process. This is achieved by introducing a modified process Yt, which mimics Xt until C is reached and then remains fixed.
Quant Interview Questions · 14. novembre 2023
In the context of stochastic calculus, considering the term 'dX' known as a Wiener process, what does the relationship 'dX^2 equals dt' when 'dt' tends toward 0 signify? A) A summation of squared values B) The convergence of a sequence C) The limit of a function D) The behavior of a Wiener process Unveil the hidden connection with your choice! __________ The correct answer is: D) The behavior of a Wiener process Explanation: In the context of stochastic calculus and the Wiener process, dX^2 =...
Stochastic Models and Processes · 12. novembre 2023
The Hull-White model is a versatile framework for modeling short-term interest rates and credit risk. It captures the stochastic behavior of rates or hazard rates, ensuring flexibility and accuracy in pricing derivatives like bonds and Credit Default Swaps (CDS). By modeling hazard rates, the model calculates survival and default probabilities, enabling dynamic risk assessment.
Mathematical Principles and Quantitative Finance · 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