KindiakMath

Finance

Here are my write-ups on the theory of quantitative finance and some non-trivial exercises therein. Given that we have developed a rich amount of linear algebra, multivariable calculus, and probability before, why not monetise it? These posts illustrate the mathematics required to appreciate the many strategies in profiting from the markets.

Much of the material for the first two sections are taken from the Quantopian lecture series, and the material for the latter two sections are taken from J Michael Steele’s treatise on stochastic calculus. We also remark that the theorems stated are given “explanations” that I hope illuminate why the theorem holds, instead of complete rigorous proofs of said theorems—Steele’s writing presents them with astoundingly beautiful completeness.

Theory

Applied Statistics

  1. Returns on Investment
  2. Multiple Linear Regression
  3. Baby Portfolio Theory
  4. Balancing Leverage and Risk

Mathematical Trading

  1. Quantifying Arbitrage
  2. Worst-Case Average Risk
  3. The Conditions of Trading Pairs
  4. Autoregressive Vocabulary
  5. Options and Derivatives

Stochastic Processes

  1. Gambler’s Ruin on Steroids
  2. Martingale Magic
  3. Brownian Motion Math

Itô Calculus

  1. Outlining the Itô Integral
  2. Establishing Itô’s Lemma
  3. Stochastic Differential Equations
  4. The Black-Scholes Solution