Simulating the Heston Model with Python | Stochastic Volatility Modelling

The Heston model is a useful model for simulating stochastic volatility and its effect on the potential paths an asset can take over the life of an option. It's popular because of:
- easy closed-form solution for European option pricing
- no risk of negative variances
- incorporation of leverage effect
This allows for more effective modeling than the Black-Scholes formula allows due to its restrictive assumption of constant volatility.

One of the nice things about the Heston model for European option prices is that there is a closed-form solution once you have the characteristic function. So, discretisation of the SDE is not required for valuing a European option, however if you would like to value other option types with complex features using the Heston model than you can use the following code.

Written Tutorial on Medium: https://medium.com/@pythonforquants/simulating-the-heston-model-in-python-226b25a759e4

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Specific Tutorial Link: https://github.com/TheQuantPy/youtube-tutorials/blob/8e64e19629cee840928b51baf4660e5c777e87e7/2022/001%20Jan-Mar/2022-03-18%20Simulating%20the%20Heston%20Model%20with%20Python%20_%20Stochastic%20Volatility%20Modelling.ipynb

Great resource for explanation here in how to complete the Euler Discretization:
- Euler and Milstein Discretization by Fabrice Douglas Rouah https://frouah.com/finance%20notes/Euler%20and%20Milstein%20Discretization.pdf

00:00 Intro
00:53 Heston Model Dynamics
02:15 Monte Carlo Simulation and SDE Discretization
05:03 Heston Model Simulation in Python
10:00 Visualising the asset price density and volatility smile

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