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Roy’s Safety-First Criterion, formulated by A.D. Roy in 1952, is a risk management approach in portfolio selection. This criterion focuses on minimizing the probability of portfolio returns falling below a threshold level, known as the disaster level. It’s particularly relevant for investors who prioritize capital preservation over high returns.   Theoretical Framework Roy’s criterion is […]

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets. Developed by John L. Kelly Jr. in 1956, it has found application in gambling, trading, investing, and risk management. The criterion aims to maximize the logarithm of wealth. This offers a strategic edge in scenarios where the […]

Correlation and covariance are statistical measures in asset allocation. They provide information on how different financial assets move in relation to each other. Covariance measures the directional relationship between the returns of two assets. When the covariance is positive, asset returns move together; if negative, they move inversely. Correlation, meanwhile, standardizes this relationship, expressing it […]

Particle Filters or Sequential Monte Carlo Methods – a Bayesian inference technique and machine learning algorithm – is increasingly relevant in quantitative finance and high-frequency trading (HFT). This method employs a set of random samples, or “particles,” to approximate the posterior distribution of a stochastic process. In the context of HFT, particle filtering can help […]

Extreme Value Theory (EVT) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It focuses on understanding the behavior of the tails of distributions, which is important in finance and risk management.   Key Takeaways – Extreme Value Theory (EVT) Risk Assessment EVT assesses the risks of rare, […]

The Beneish M-Score is a statistical model that is used to detect whether a company has manipulated its earnings. The model was created by professor Messod Beneish in June 1999 after publishing a paper called The Detection of Earnings Manipulation. The logic behind the Beneish M-Score is that a combination of aggressive revenue recognition practices, […]

Monte Carlo simulations are a tool in finance for modeling and understanding the behavior of financial systems under various scenarios. These simulations use randomness to solve problems that might be deterministic in principle. Python, with its rich library ecosystem, offers an efficient platform for conducting Monte Carlo simulations. Here’s a guide on how to implement […]

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 […]

Partial differential equations (PDEs) serve as the foundation for pricing complex derivatives and assessing risk. These equations enable the translation of financial theories and movements of market variables into mathematical language.   Key Takeaways – Partial Differential Equations in Finance PDEs, such as the Black-Scholes equation, are used for option pricing. Enables traders to calculate […]

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 […]