Blog Posts

Large Deviation Theory (LDT) is a branch of probability theory that studies the asymptotic behavior of remote tails of sequences of probability distributions. It’s useful in quantifying the probabilities of rare events in systems with many degrees of freedom, such as financial markets and trading activities. In finance, these “rare events” can include extreme market […]

Measure theory is a branch of mathematics that studies ways of generalizing the notion of integration, length, area, and volume. It’s used in probability theory, and by extension, it is fundamentally important in the fields of finance and trading, which is essentially an applied probability exercise. In these areas, measure theory underpins the mathematical models […]

Complex geometry – particularly fractal geometry and other advanced mathematical concepts – have unique applications in finance, markets, and trading. These applications help model the patterns and structures in financial data in ways that aren’t normally possible (i.e., integrating the use of complex numbers) to understand market behaviors, predict trends, and manage risks more effectively. […]

Execution risks in trading are a critical concern for both individual traders and institutional investors. These risks can significantly affect the profitability and efficiency of trades, and are one of the least talked about factors in trading. Here we’ll discuss key aspects of execution risks, including: Best Execution Implementation Shortfall (Slippage) Trading Curb Market Impact […]

We look at the differences between Exposure at Default (EAD), Probability of Default (PD), and Loss Given Default (LGD).   Key Takeaways – EAD vs. PD vs. LGD Exposure at Default (EAD) quantifies the total value at risk when a borrower defaults. It focuses on the outstanding exposure, including committed but undrawn funds. Probability of […]

Credit Valuation Adjustment (CVA) is a financial metric that quantifies the risk of counterparty default in the valuation of over-the-counter derivatives. It represents the difference between the risk-free portfolio value and the true portfolio value considering the possibility of a counterparty’s default. X-Value Adjustment (XVA) is a collective term representing various adjustments made to the […]

A neural network is a type of machine learning algorithm modeled after the structure and function of the human brain. It is composed of interconnected nodes, called artificial neurons, that process information and make predictions or decisions. Neural networks are trained using a dataset, where the network adjusts the strengths of the connections between neurons, […]

Differential geometry is a field of mathematics dealing with smooth shapes and the properties of surfaces and curves. It has applications in financial markets and trading, mostly in risk management, portfolio optimization, and options pricing models. Its value in these areas stems from its ability to model and analyze complex, multi-dimensional and non-linear relationships (while […]

Topology is a branch of mathematics focusing on the properties of space that are preserved under continuous transformations. Like many forms of math, it’s increasingly finding applications in finance and markets. This application comes from the ability of topological methods to analyze shapes and structures within data, which is relevant in understanding market dynamics and […]

Designing an algorithm for predicting exchange rates involves a series of steps that integrates knowledge in finance, economics, math, programming, and machine learning.   Key Takeaways – How to Design an Algorithm for Predicting Exchange Rates Incorporate Relevant Variables: Include key macroeconomic indicators like interest rates, inflation, GDP, and political stability, as they all influence […]