Trading stock volatility with the Ornstein-Uhlenbeck process
Understanding and modelling volatility accurately is of utmost importance in financial mathematics. The emergence of volatility clustering in financial markets can make estimating volatility very difficult.
Here we explain how to use a stochastic model called Ornstein-Uhlenbeck process to model volatility. We explain the mathematics of using a method called Maximum Likelihood Estimation (MLE) to estimate the parameters of the Ornstein-Uhlenbeck process based on S&P500 historical/realised volatility.
We also explain how to derive the dynamics of the stochastic process using Ito Calculus, this is required for deriving the Probability Density Function (PDF) of the Ornstein-Uhlenbeck process used in the MLE method.
Finally, we simulate the volatility using the continuous-time stochastic process at a particular time step with no approximations, and also create sample paths using Euler method to discretize the stochastic differential equation (SDE).
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00:00 Intro
01:43 Volatility Clustering
04:20 Using MLE for estimating model parameters
11:00 Determining distribution of Ornstein-Uhlenbeck process
14:51 Using MLE for Ornstein-Uhlenbeck Volatility Model
18:36 Simulating Volatility Model in Python
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