Blog Posts

In this overview, we look at a comprehensive range of terms and definitions for understanding the pricing of derivatives in finance. We cover various processes, concepts, and models.   Key Takeaways – Derivatives Pricing Derivative pricing involves models like Brownian motion and risk-neutral valuation to predict price movements and valuations, considering market risk and arbitrage […]

Here we look at some terms and definitions that form a broad, and reasonably complete, topical outline of mathematical tools in finance.   Key Takeaways – Mathematical Tools in Finance This overview highlights key mathematical tools in finance. Also included are optimization techniques, the Monte Carlo Method for numerical solutions, Real Analysis, and PDEs relevant […]

Theoretical finance forms the backbone of our understanding of how markets operate. It integrates mathematical models and economic theory to predict, explain, and understand the behaviors of financial markets. It includes a range of topics including asset pricing, risk management, market microstructure, and corporate finance.   Key Takeaways – Theoretical Finance Foundation of Market Understanding: […]

Creating a curriculum for someone to learn from scratch and become proficient enough to write institutional-level financial algorithms as a quant or programmer will take time. But it’s fully possible for those who commit, like any career. Below is a structured four-year curriculum (plus Masters and PhD level curriculums) that could equip someone with the […]

Portfolio optimization is a key component of quantitative finance, involving the selection of the best portfolio (asset allocation/distribution), out of a set of all possible portfolios, that offers the highest expected return for a given level of risk. It’s heavily used in trading, investment management, and financial analytics. Portfolio optimization is a well-explored domain across […]

Selecting the right program in quantitative finance involves considering factors such as faculty expertise, research opportunities, industry connections, and geographic location. Prospective students should look for programs that align with their career goals and offer strong placement records in relevant finance positions. It’s advisable to review course offerings, talk to alumni, and consider the mathematical […]

Exter’s Pyramid, developed by John Exter, a central banker and economist, is a model that represents the liquidity of different asset classes. It serves as a visual framework for the hierarchy of assets, typically during times of financial stress. The pyramid ranks assets from the most to the least liquid, reflecting their safety and risk […]

Mathematical modeling of options is used heavily in finance. Both American and European options are types of financial derivatives, but they differ in their exercise rights, which leads to differences in their mathematical modeling. Let’s look into these differences:   Key Takeaways – American Options vs. European Options (Mathematical Modeling) American options can be exercised […]

The Feynman-Kac formula is a result in the theory of stochastic processes and partial differential equations (PDEs). It provides a link between parabolic partial differential equations and stochastic differential equations (SDEs). Essentially, the Feynman-Kac formula expresses the solution to certain PDEs in terms of expectations of functionals of stochastic processes. While originally for math and […]

In quantitative finance, professionals often categorize models and methodologies into two main buckets: Q World and P World. These classifications represent two distinct approaches to quant modeling. They each have their own unique set of assumptions, objectives, and applications.   Q World vs. P World (Quant Modeling) The “Q World,” or “Risk-Neutral World,” uses adjusted […]