Calibrating the Gaussian model

Financial Analytics in Google Sheets

David Ardia

Professor in Quantitative Methods for Finance

Calibration

  • Ad-hoc calibration:
    • Set the location $m$ of the Gaussian model to the average return
    • Set the dispersion $s$ of the Gaussian model to the volatility of returns

Financial Analytics in Google Sheets

Comparing two histograms

Financial Analytics in Google Sheets

Comparing two histograms

Financial Analytics in Google Sheets

Comparing two histograms

Financial Analytics in Google Sheets

Use of the Gaussian model

  • We can use the calibrated Gaussian model to extrapolate and forecast:

    • Extrapolate the full distribution of returns
    • Compute probabilities of positive or negative returns
    • Compute the 5% value-at-risk
Financial Analytics in Google Sheets

Gaussian value-at-risk

5% value-at-risk with the Gaussian model

Financial Analytics in Google Sheets

Gaussian value-at-risk

Financial Analytics in Google Sheets

Gaussian value-at-risk

Financial Analytics in Google Sheets

Let's practice!

Financial Analytics in Google Sheets

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