Volatility forecasting: timeframe

Quant Trading Strategies & Ideas
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Course Name: Options Volatility Trading: Concepts and Strategies, Section No: 21, Unit No: 2, Unit type: Document

Dear Varun,

I was trying to plan a different approach regarding to timeframe of a possible strategy. I´ve always seen volatility forecasting in 1D timeframe. But I´m wondering how to work with lower timeframes i.e. 4H or 1H. Can I use the same formulas of estimators but with data of lower timeframes?And GBM?How can I work with that? Many thanks

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Hello Jorge,

When working with lower timeframes like 4-hour (4H) or 1-hour (1H) intervals, you can employ similar methods for estimating volatility and simulating stock prices; however, it's essential to adjust the parameters accordingly.

  1. Both the Parkinson's and Garman-Klass volatility estimators can adapt to 4H or 1H intervals as their formulas are based on open, close, high, and low prices. Remember that the parameter N represents the number of periods based on the new timeframe.
  2. Regarding GARCH(1,1), you can still use the model but consider re-estimating parameters using the new timeframe data, as higher-frequency data may yield different parameter values compared to daily data.
  3. For Geometric Brownian Motion (GBM), the same formula applies, but you must adjust parameters such as price volatility (σ), risk-free interest rate (μ), and time to expiration (t) appropriately to reflect the characteristics of the new timeframe.
I hope this clarifies things. Feel free to ask if you have any more questions on this topic.
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Many thanks for your response Varun,



Can you give me a practical example regarding GBM formula implementation, i.e. 4H timeframe or 1H timeframe? 



Best

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Hello jorge, let's take an example of 1h-timeframe. 



When simulating a Geometric Brownian Motion (GBM) path for a 1-hour timeframe, you can adjust several key parameters to observe their impact on the simulated stock price trajectory. These parameters include:

  1. Volatility (sigma): This reflects the standard deviation of the stock's return. Adjusting volatility allows you to model different levels of price fluctuations within each hourly step.
  2. Initial Stock Price (S0): This is the starting value of the stock price at time zero. Changing the initial stock price will influence the entire trajectory, shifting it up or down.
  3. N(Number of steps in the path): The total number of steps determines the overall duration of the simulation. For a 1-hour timeframe, you might consider adjusting the number of steps to cover a specific period, such as a month or a year. 
  4. Time Step (dt): This parameter defines the length of each time interval. For a 1-hour timeframe, the time step (dt) is set to 1/24 to represent hourly intervals. You can modify this to simulate stock price movements at a different frequency, such as 30 minutes or 15 minutes.
Hope this is clear.