Cow Shaped Cow


Milk production at a farm was low, so the farmer asked his brother, a physicist, for help. The physicist built some models and did a few calculations and finally told his brother that he had a solution, but it would only work if the cows were spherical and in a vacuum.

The Cow Shaped Cow project was born out of frustration with the textbook derivations of the standard models used in quantitative finance. They are either wrong (e.g. Iain J. Clark), hand-wavey (e.g. John C. Hull, Peter Austing, Wilmott), missing (e.g. Brigo-Mercurio) or vacuous (e.g. Open Gamma Quantitative Research). Moreover, they usually present the simplest case (i.e. the Spherical Cow), ignoring real world considerations like term structures and smiles.

The project aims to provide clear, concise and complete derivations of the standard models that are used in quantitative finance, with all of the algebra for the general case explicitly worked out. Stepping through the algebra is important for two reasons:

  1. Algebra builds character
  2. It provides a clear intepretation and intuition of the terms used in models

The second point is important for anyone who wants to extend the models, or use them in non-standard ways. The project is a work in progress, and this page will be updated as more derivations are published. As a bit of notation, Black-Scholes refers to any model with one stochastic variable, and not just the classical constant parameter model.

Available papers are:

  1. Introduction to Stochastic Calculus
  2. Basic Stochastic Equations
  3. Deriving the Black-Scholes Equation
  4. Deriving the Black-Scholes Formula for a Call Option
  5. Black Scholes Greeks
  6. Solving the Black-Scholes Equation using Finite Differences
  7. Local Volatility in Practice