VIII. 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 =...

I. Stochastic Models and Processes · 21. octobre 2023

Fractional Brownian Motion (fBm) enriches classical Brownian motion by introducing the Hurst parameter (H), making it vital for modeling varying volatility in finance, physics, and beyond. With H dictating path roughness, fBm handles predictions in systems with long-range dependencies, aiding in asset volatility modeling and risk management. It's pivotal for understanding market behaviors and complex dynamics in diverse scientific fields.

I. Stochastic Models and Processes · 12. octobre 2023

The Poisson process is integral to quant finance, modeling rare yet crucial events with its rate parameter λ, which sets the average event rate. The process calculates the probability of 'k' events in time 't', enhancing stock and option pricing models by accounting for sudden market jumps alongside regular movements. It's a mathematical bridge between predictable trends and unexpected occurrences, making it indispensable for comprehensive financial predictions.

I. Stochastic Models and Processes · 06. octobre 2023

Explore the intricate dance between Brownian Motion & Quadratic Variation. Dive into a world of constant, unpredictable motion and learn how Quadratic Variation quantifies its complexity. Unravel its role in Geometric Brownian Motion & stock price prediction. #Finance #Volatility

I. Stochastic Models and Processes · 02. octobre 2023

Gaussian Process Regression demystified: a statistical tool predicting outcomes by learning patterns from data. Imagine a wise elder foreseeing future events based on past experiences, ensuring precision. Ideal for forecasting trends! #DataScience #Statistics #Prediction

I. Stochastic Models and Processes · 29. juillet 2023

Explore the world of financial volatility with quadratic variation—a tool capturing asset "bumpiness". In finance, much like assessing a hiking trail's roughness, we gauge stock price fluctuations. With roots in Brownian motion, this metric offers insights into market behaviors, aiding predictions in high-frequency trading and refining the Black-Scholes model. Dive deep into market terrain with this crucial quantitative tool. #BrownianMotion #QuadraticVariation #QuantitativeFinance.

I. Stochastic Models and Processes · 27. mai 2023

By using a Lévy process-based model like Variance Gamma, you can better capture the stock's jump behavior, which is essential for pricing options accurately in situations where such jumps are common.

I. Stochastic Models and Processes · 06. mai 2023

Navigating the stock market is like playing a game where your pieces can shift between categories like "Tech" and "Energy." But, there's a twist! When stocks move into the "Consumer Goods" category, they tend to stay there, much like landing in a cozy inn in a board game where you're inclined to settle. This behavior is explained by the "absorbing Markov chain," a model highlighting the probability of such transitions. It's a useful tool to predict where stocks might settle in the long run.

I. Stochastic Models and Processes · 04. février 2023

Brownian motion, a term often mentioned in the worlds of physics, mathematics, and finance, can be a puzzling concept to grasp. A seemingly random path that a particle traces in a liquid or gas medium, Brownian motion is often likened to the unpredictable movement of pollen particles in water. At its core, this stochastic process is governed by specific mathematical rules, one of the most intriguing being that its variance is directly proportional to time. Before delving into its variance-time...