derivatives

A cheat sheet and reference guide for undergraduate mathematics courses

Short documents about key topics in finance

This manuscript provides another approach to get derivative of odd-power, that is approach based on partial derivatives of polynomial function

Differentiation is process of finding the derivative, or rate of change, of a function. Derivative itself is defined by the limit of function's change divided by the function's argument change as change tends to zero. In particular, for polynomials the function's change is calculated via Binomial expansion.

Worked portfolio of 115+ mathematical finance exercises: forwards, options, no-arbitrage bounds, binomial pricing, a from-scratch Black-Scholes derivation, volatility estimation, and linear programming. LaTeX + a Python companion.

Prices a real SPY option three ways (Black-Scholes, Monte Carlo, CRR binomial tree), cross-checks them against each other, computes Greeks closed-form vs. finite-difference, and compares the methods on speed and use case.

A set of study notes for MATH 314 - Calculus and Linear Algebra for Analytics and Business

Dense three-column LaTeX formula reference: time series, volatility models, factor models, high-frequency econometrics and derivatives.

The power rule for derivatives, typically proven through the limit definition of derivative in conjunction with the Binomial theorem. In this manuscript we present an alternative approach to proving the power rule, by utilizing a certain polynomial identity, such that expresses the function's growth.

Simulates day-by-day delta-hedging of a real SPY call option and measures how the realized hedging error diverges from Black-Scholes theory, across thousands of Monte Carlo price paths.

Calculus tutorial extracted from the MATH&PHYS book. Just a few pages for everything you need to know about limits, derivatives, and integrals.

The course covers integration, applications of integration, and series, while also reviewing and expanding upon concept introduced in Calculus 1 such as limits and derivatives.

Delta-matched risk reversal: slope vega, irreducible vanna, and a dollar-reconciling attribution. Companion to Yan (2026).