Free Stuff

**Volopta**
I created this site to share derivatives pricing code in C++, Matlab, VBA, and other languages. Feel free
to visit the site and download all the code you need, but kindly adhere to the terms of use of the site.
You may of course submit your own code to share with others,
but please limit your contribution to derivatives pricing only because I want to keep the site specialized.

http://www.Volopta.com/

**Mathematical Finance notes
**Sometimes papers and books on mathematical finance leave out many steps in the derivation of formulas and concepts,
or sometimes these derivations are unclear. I created a bunch of notes in PDF format that, in my humble opinion, explain
concepts in a clear and rigorous fashion. Please e-mail me with your comments, suggestions, or if you find typos in any
of these notes.

Stay tuned, plenty of stuff to come!

Brief derivation of the Heston model

Four derivations of the Black-Scholes PDE

Four derivations of the Black-Scholes formula

Probability of Exercise in Black-Scholes

The Three Methods of Pricing Derivatives

Heuristic derivation of Ito's Lemma

The Feynman-Kac Theorem

The T-forward measure

Derivation of Euler and Milstein Discretization

Derivation of Dupire's local volatility

Derivation of the Fokker-Planck equation

Derivation of a variance swap

Carr-Madan decomposition of the payoff function

The SABR Model

Relationship between butterfly spreads and the risk neutral density

Using the risk neutral density to check for arbitrage in implied volatility