From First Principles

Introduction In the previous post, we introduced the Feynman-Kac equation by starting with a space of functions and equipping it with the Markov semigroup.

In the previous few posts, we have been building up a small stochastic-calculus library on top of SageMath in Python.

Introduction In the previous blogs we taught SageMath how to represent stochastic differential equations (as a data class), apply Ito’s lemma (as part of our Ito package), derive infinitesimal generators, and connect those generators to the Kolmogorov equ…

Introduction In the previous blog we introduced the Kolmogorov Forward and Backward equations and showed how they arise from the infinitesimal generator of a SDE.

In the previous blog posts we have built an Ito Layer over SageMath in Python, implemented the Lamperti transform, and an infinitesimal generator.

Introduction In the previous two posts in this series we derived the Black–Scholes PDE using SageMath and implemented the Lamperti transform symbolically.

Introduction In the previous blog post we showed how an Ito calculus layer sitting on top of SageMath can produce the Black-Scholes PDE symbolically.

Introduction In the previous post I shared my journey of getting SageMath installed in Windows and writing my first unit tests.

If you try to pip install sagemath, you will not get SageMath, you will only get confusion.

Introduction Building on the work we did in the previous post, I spent today building a normal SABR volatility surface for BTC options, with the end-goal of pricing inverse options on Deribit (which will be in the next post).

Introduction When pricing Constant Maturity Swap (CMS) products, one of the biggest sources of error is not the interest-rate curve, it’s the swaption volatility surface, and in particular its smile.

Introduction Prerequisites Setup Your Derebit Account Setup Your PostgreSQL Server Create a New PostgreSQL Database Setup Python Environment Clone GitHub Repo Database Schema Fetching Derebit Data Calculating the Black-Scholes Price Inverse Options Conclu…