Welcome to the Option Pricing repository! This project delves into numerical methods for financial mathematics, with a strong emphasis on option pricing. Our primary focus is on implementation and numerical analysis, covering key methods and models such as stochastic differential equations, the Black-Scholes model, and the multilevel Monte Carlo method.
This repository includes a collection of Jupyter notebooks that introduce and explore various methods in option pricing:
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Brownian Motion and Euler-Maruyama
Understand the foundations of the Wiener process, geometric Brownian motion, and the Euler-Maruyama method for solving stochastic differential equations. -
Strong and Weak Convergence
Validate the strong and weak convergence orders for both the Euler-Maruyama and Milstein methods. -
Monte Carlo European Option Pricing
Apply Monte Carlo methods to price European options and explore the primary sources of error in the process. -
Multilevel Monte Carlo Method
An in-depth look at the Multilevel Monte Carlo method, replicating results from Michael B. Giles' paper on path simulation. -
European Basket Call Option with MLMC
Price a European basket call option using the Multilevel Monte Carlo method, leveraging historical data from major tech companies. -
European Capped Symmetric Power Call
Explore pricing techniques for a European capped symmetric power call, utilizing appropriate discretization and finite difference methods.
These notebooks are designed to be practical and accessible, providing insights into both theoretical concepts and their real-world applications. Whether you're a student, researcher, or finance professional, this repository will serve as a valuable resource in your study of option pricing.