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Simulating Price Movement for Monte Carlo Methods

Simulating Price Movement for Monte Carlo Methods

From Brownian Motion to Stochastic Volatility Jump Diffusion

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Vertox
Mar 12, 2024
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Simulating Price Movement for Monte Carlo Methods
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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

  1. Geometric Brownian Motion

  2. Itô Calculus

  3. Stochastic Volatility Models

  4. Euler–Maruyama method

  5. Getting Asset Statistics

  6. Pricing Derivatives

  7. Final Remarks


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