Setting Mean and Volatility in a GARCH Price Simulation

Summary

The document asks how to simulate a large sequence of EUR/USD prices with a GARCH model, while targeting a specified level and standard deviation. It frames the task as an implementation question: the author wants to understand how to build the simulation from scratch in Python or R, even though ready-made libraries exist.

No model equations, parameter-selection procedure, code, simulated output, or validation method are provided. The text therefore identifies a modeling problem rather than presenting a worked solution. It also leaves open how the target price mean and standard deviation should map to GARCH returns and conditional volatility, and whether the simulated series represents prices or returns. Those choices must be addressed before a useful simulation can be specified.

Key ideas

• The question concerns simulating a long EUR/USD series with a GARCH model.
• The requested series is intended to match specified mean and standard deviation targets.
• The author wants to implement the simulation from scratch in Python or R.
• The document provides no GARCH specification, parameterization, or worked results.

Tags

# How to perofrm a simple GARCH simulation example?


# How to perofrm a simple GARCH simulation example?












How is it possible to simulate one million of tick data for, say EUR-USD price, using a GARCH model?

For example, how do I simulate $X_i$ for $i = 1 \dots 1000000$, with

- $\text{mean}(X)=X_0 \approx 1.1042$

- $\text{stddev}(X) \approx 0.10$

Even if it's possible with ready to use libraries, I'd like to be able to write it from scratch (Python or R).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.