Blog Posts

In the context of finance, the term “high-dimensional” refers to the characteristic of problems or models that involve a large number of variables or factors. Financial markets are complex systems influenced by many elements and variables influencing them. Many things are dependent on lots of other things. Moreover, we have known unknowns (things we know […]

Malliavin calculus, named after the mathematician Paul Malliavin, represents an advanced branch of mathematical finance that extends the traditional scope of stochastic analysis. This calculus introduces a framework for assessing the smoothness of functionals of stochastic processes. This is particularly beneficial in the context of differentiation of random variables. Its applications in finance are used […]

The Hamilton-Jacobi-Bellman (HJB) equation is used in dynamic programming and control theory. It’s heavily used in the context of optimal control and decision-making under uncertainty. This equation provides a framework for solving continuous-time, stochastic control problems by establishing a necessary condition for optimality. In simple terms, the HJB equation is a mathematical formula used to […]

Gradient-based methods are a category of optimization techniques used in quantitative finance. They use the concept of a gradient, which is a vector indicating the direction of the steepest ascent of a function. These methods are particularly effective in scenarios involving continuous and differentiable objective functions.   Key Takeaways – Gradient-Based Methods in Quantitative Finance […]

In quantitative finance, heuristic and metaheuristic algorithms help in solving complex problems where traditional optimization methods may not be efficient or might fail to provide satisfactory solutions. These methods are especially useful in scenarios involving large-scale portfolio optimization, algorithmic trading strategies, and objectives characterized by complexity, non-linearity, and multimodality. They’re often borrowed from events we […]

The Zillow Zestimate and other Automated Valuation Models (AVMs) like it are designed to provide an estimate of a property’s market value using algorithmic modeling. These models typically rely on a combination of publicly available data, historical transaction data, and various computational techniques. They involve statistical analysis (like regressions) and often basic machine learning algorithms. […]

Non-parametric models in finance are valuable for their flexibility and adaptability to various types of financial data. They’re particularly useful in scenarios where the underlying data doesn’t conform to standard distributional assumptions (e.g., normal distribution). We’ll cover many examples of non-parametric mathematical models in finance.   Key Takeaways – Non-Parametric Models in Finance & Trading […]

There are many options pricing models with complex mathematical foundations and variables that go into determining what an option is worth. But in terms of the big-picture intuitive understanding of an option’s value is, it really boils down to two main factors: the probability that an option will be in the money (ITM) by expiration […]

Banks in the US use a clever method called synthetic risk transfers to handle the challenges of tough banking rules and the effects of higher interest rates. This involves selling specialized financial products to investment funds. This lets the banks protect themselves from some of the risks associated with the loans they give out. It’s […]

Hedge funds rely on data analytics and advanced storage solutions to manage vast amounts of real-time and historical data, ensuring both performance and security. Algorithmic trading systems central to many types of hedge funds (i.e., systematic in nature) require continuous refinement for executing trades and integrating with risk management systems for real-time portfolio monitoring. Robust […]