Blog Posts

Swaptions, options on swaps, are financial instruments that grant the holder the right, but not the obligation, to enter into a swap at a specified rate on a future date. Interest rate swaps are the dominant use case, but they’re also used in other asset classes as well. Pricing swaptions involves complex mathematical models given […]

The Variance Gamma (VG) process is a mathematical model used in financial markets for option pricing and to capture the dynamics of asset returns. It’s noted for its ability to model the skewness and leptokurtosis (fat tails) observed in the distribution of returns – characteristics often inadequately captured by the simpler Black-Scholes model, which assumes […]

Event-driven strategies in financial markets are trading or investment strategies that seek to exploit pricing inefficiencies that may occur before or after a corporate event takes place. These strategies are primarily based on the premise that corporate events can lead to stocks or assets being mispriced and can provide opportunities for traders/investors to earn above-average […]

Variational Bayesian methods, within the context of probability theory in finance and markets, offer a framework for dealing with uncertainty and making predictions. These methods belong to the family of Bayesian inference techniques, which update the probabilities of hypotheses as more evidence becomes available. Variational Bayesian methods specifically use optimization techniques to approximate complex posterior […]

Network theory and percolation models offer a lens through which we can understand various phenomena in finance and trading. These concepts, derived from mathematics and physics, provide quantitative frameworks for the interconnectedness and vulnerabilities within financial markets. Below, we look into the key concepts, applications, and how traders can leverage network theory and percolation in […]

Random Matrix Theory (RMT) is a statistical framework used to analyze the properties of matrices with random elements. In finance and trading, RMT is useful for analyzing the structure of correlations among assets in large portfolios, which can help with understanding why assets move the way they do, risk management, and portfolio optimization.   Key […]

Heavy-tailed distributions (or fat-tailed distributions) are used in financial modeling as these probability distributions better capture the behavior of financial data. The occurrence of extreme events such as market drops or booms are more common than would be predicted by normal (Gaussian) distributions. These distributions have “heavy tails” – i.e., a higher likelihood of extreme […]

Fractals and scale invariance are two interrelated concepts in mathematics and physics that also have applications in finance, markets, and trading. These concepts provide a framework for understanding the behavior observed in financial markets and for developing trading strategies that can adapt to the nature of market data.   Key Takeaways – Fractals in Finance, […]

Poisson Processes are a fundamental concept in stochastic processes, which are widely used in finance, markets, and trading to model random events that occur independently of each other within a fixed period of time. These events are characterized by some level of unpredictability (and sometimes rarity), such as defaults on loans, arrivals of orders in […]

Renewal theory is a branch of probability theory that deals with the times at which events recur. It’s based on the study of stochastic processes and has found applications across various fields, including finance, economics, and trading. In the context of finance and trading, renewal theory can offer frameworks for decision-making under uncertainty, especially in […]