Simulating Price Movement for Monte Carlo Methods
From Brownian Motion to Stochastic Volatility Jump Diffusion
There are a lot of instances where you want to be able to generate a lot of price paths for some asset. Getting statistics like CVAR, pricing derivatives, portfolio optimization and more.
Prices have a ton of interesting effects like clustering volatility, the volatility effect, momentum and more.
It is therefore not an easy task to accurately capture the properties of the asset well.
It’s a huge area of research that has even won nobel prizes.
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Table of Contents
Geometric Brownian Motion
Itô Calculus
Stochastic Volatility Models
Euler–Maruyama method
Getting Asset Statistics
Pricing Derivatives
Final Remarks