Linear Congruential Generators in Python

Vasicek Model Simulation with Python

Ornstein-Uhlenbeck Simulation with Python

Brownian Motion Simulation with Python

Derivatives Pricing III: Models driven by Lévy processes

Derivatives Pricing II: Volatility Is Rough

Derivatives Pricing I: Pricing under the Black-Scholes model

Introduction to Stochastic Calculus

The Markov and Martingale Properties

Brownian Motion and the Wiener Process

Stochastic Differential Equations

Geometric Brownian Motion

Ito's Lemma

Deriving the Black-Scholes Equation

Derivative Approximation via Finite Difference Methods

Solving the Diffusion Equation Explicitly

Crank-Nicholson Implicit Scheme

Tridiagonal Matrix Solver via Thomas Algorithm

Options Pricing in Python

European Vanilla Call-Put Option Pricing with Python

Introduction to Option Pricing with Binomial Trees

Hedging the sale of a Call Option with a Two-State Tree

Risk Neutral Pricing of a Call Option with a Two-State Tree

Replication Pricing of a Call Option with a One-Step Binomial Tree

Multinomial Trees and Incomplete Markets

Pricing a Call Option with Two Time-Step Binomial Trees

Pricing a Call Option with Multi-Step Binomial Trees

Derivative Pricing with a Normal Model via a Multi-Step Binomial Tree

Risk Neutral Pricing of a Call Option with Binomial Trees with Non-Zero Interest Rates

Calculating the Greeks with Finite Difference and Monte Carlo Methods in C++