Navigating the Waves of Quant Finance: Continuous Time Models with Python

In the vast ocean of quantitative finance, understanding and implementing continuous time models stands as a beacon for navigating the complex waters of financial markets. These models, particularly stochastic differential equations (SDEs), are the backbone of modern financial theory, powering everything from option pricing to risk management. This tutorial embarks on an exploratory journey into the realm of continuous time models in quantitative finance, leveraging the power of Python to bring these abstract concepts to life. So, buckle up as we dive deep into the world of stochastic calculus, implement SDEs and calibrate them using real financial data.

Photo by Shubham Dhage on Unsplash

Setting the Stage with Python

Before we set sail, let’s ensure our vessel is equipped with all the necessary tools. We’ll be using Python, a language renowned for its simplicity and power in numerical and financial analysis. Our journey will be facilitated by libraries such as numpy, pandas, matplotlib, scipy and yfinance for data retrieval. Let's start by installing and importing these libraries.

pip install numpy pandas matplotlib scipy yfinance

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import scipy.optimize as optimize
import yfinance as yf