Blog Posts

Symplectic geometry, originating in classical mechanics, is a branch of differential geometry concerned with symplectic manifolds (a way of representing and visualizing non-linear data). A symplectic manifold is a smooth manifold equipped with a closed, non-degenerate 2-form, known as a symplectic form. This field has found applications in various areas, including finance, particularly in the […]

Differential topology is a field of mathematics concerned with the study of differentiable functions and differentiable manifolds. It has several key concepts that can be theoretically and practically applied to finance and markets, mostly in the form of advanced visual data interpretation.   Key Takeaways – Differential Topology in Finance, Markets & Trading Model Flexibility […]

“Probabilities of probabilities,” often referred to as uncertainty of uncertain events or stochastic uncertainty, is a fascinating concept in finance and markets. Trading and investing is fundamentally an exercise of applied probability, and we have probability distributions to represent this process. However, the probabilities themselves are often unknown. It recognizes the multi-dimensional and nested layers […]

Information geometry applies the concepts and methods of differential geometry to problems in probability theory and statistics, which are important in finance. It explores the geometric structure of statistical models and studies how these structures influence inference and decision-making processes. The key concept in information geometry is the notion of a statistical manifold, which is […]

Probability distributions are one of the most fundamental concepts in finance, markets, and trading. They provide a fundamental framework for understanding, modeling, and managing the unknowns and risks inherent in these domains. Trading isn’t so much about “predicting the future” (i.e., trying to ascertain a deterministic line of how things will transpire) as it is […]

Currency risk premium refers to the additional return a trader or investor demands for holding a currency that may depreciate against their home currency. This concept is important in international finance and investing. The risk premium is influenced by various factors:   Key Takeaways – Currency Risk Premia Currency risk premia reflect the potential return […]

Affine Term Structure Models (ATSMs) are a class of models used in finance to describe the evolution of interest rates or the term structure of interest rates. These models are characterized by the fact that the yield of a bond at any given time can be expressed as an affine (i.e., linear) function of factors […]

Fast Fourier Transform (FFT) pricing is a computational technique in financial quantitative analysis. It’s used primarily for the pricing of options and other financial derivatives. FFT transforms complex pricing models into a more manageable form to perform efficient calculations and analysis.   Key Takeaways – Fast Fourier Transform Pricing Computation Efficiency Fast Fourier Transform (FFT) […]

Rough volatility models emerged from empirical observations that the volatility of financial markets does not behave smoothly. Instead, it displays “roughness,” and needed better quantitative models to represent it accurately.   Key Takeaways – Rough Volatility & Bergomi Model Non-Smooth Volatility – Rough volatility models, including the Bergomi model, capture the observed rough, non-smooth nature […]

There are many games that share similarities to trading. In fact, some of them you can also make money from. Here we’ll take a look at the games most similar to trading.   Key Takeaways – Games Most Similar to Trading We look at the games most similar to trading. These game concepts, when applied […]