Blog Posts

Correlation and covariance are statistical measures in asset allocation. They provide information on how different financial assets move in relation to each other. Covariance measures the directional relationship between the returns of two assets. When the covariance is positive, asset returns move together; if negative, they move inversely. Correlation, meanwhile, standardizes this relationship, expressing it […]

Particle Filters or Sequential Monte Carlo Methods – a Bayesian inference technique and machine learning algorithm – is increasingly relevant in quantitative finance and high-frequency trading (HFT). This method employs a set of random samples, or “particles,” to approximate the posterior distribution of a stochastic process. In the context of HFT, particle filtering can help […]

The Cramer-Rao Lower Bound (CRLB) is a fundamental concept in statistical estimation theory. It provides a lower bound on the variance of unbiased estimators of a parameter in a statistical model (i.e., there’s always going to be some amount of unavoidable unpredictability in a model). The significance of the CRLB lies in its role as […]

Kalman Filters are used for estimating the state of a dynamic system from a series of incomplete and noisy measurements. Originating from control theory and employed in signal processing and finance, Kalman filters enable the efficient and real-time estimation of variables in systems governed by linear equations.   Key Takeaways – Kalman Filters Predicting Market […]

Extreme Value Theory (EVT) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It focuses on understanding the behavior of the tails of distributions, which is important in finance and risk management.   Key Takeaways – Extreme Value Theory (EVT) Risk Assessment EVT assesses the risks of rare, […]

The Beneish M-Score is a statistical model that is used to detect whether a company has manipulated its earnings. The model was created by professor Messod Beneish in June 1999 after publishing a paper called The Detection of Earnings Manipulation. The logic behind the Beneish M-Score is that a combination of aggressive revenue recognition practices, […]

The basic picture of the financial markets and macro-economies is very important to talk about when it comes to understanding what’s likely to transpire. Inflation, and changes in the discounted expectations of where inflation will go, is one of the main two overarching forces dictating how asset prices move (along with growth and its changes […]

Autocorrelation is the degree of similarity between a given time series and a lagged version of itself. In other words, it quantifies how similar a time series – e.g., interest rates, stock prices – is to itself at different points in time. A high autocorrelation means that the time series is highly similar to itself […]

In finance, Master Equations are a set of mathematical tools used to model and understand various financial processes. They mostly involve stochastic elements. These equations are used in quantitative finance for modeling the dynamics of financial markets and instruments.  They form the backbone of many advanced financial models, including those used for option pricing, risk […]

Spline models can be used in finance for modeling and interpolating financial data, which often exhibits non-linear patterns. These models are frequently applied in yield curve modeling, option pricing, and risk management.   Splines in Simple Terms A spline is a type of mathematical function used to create smooth curves. Imagine you have a series […]