Testing Whether Monte Carlo Breaks Coincide with Underestimated Volatility
Summary
The document asks how to test whether observations outside a Monte Carlo model’s 95% interval occur more often when the model’s input volatility is low. Volatility is recalibrated periodically, and a plotted example shows empirical prices crossing the simulated interval more often than the nominal rate would suggest. The proposed approaches are regression or a chi-squared test, but the document does not resolve which test or variable setup is appropriate.
The central research question is whether low model volatility is associated with interval breaches. A useful analysis would need to define each observation’s break status and align it with the volatility estimate used to generate its interval. The post gives no underlying data, statistical results, or discussion of dependence over time, calibration uncertainty, or repeated observations, so it is a question rather than a demonstrated method.
Key ideas
- The question concerns whether Monte Carlo interval breaches are associated with low input volatility.
- A break is defined as an empirical price outside the simulated 95% interval.
- Volatility estimates are recalibrated every three months in the example.
- The document raises regression and chi-squared testing but does not select or apply a test.
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Full text
# Determining the Relationship Between Monte Carlo Breaks and Model Volatility # Determining the Relationship Between Monte Carlo Breaks and Model Volatility I'm looking for a statistical test to understand the relationship (if any) between the model volatilities of a stochastic process, and the occurrence of 'break', defined as the instance when an empirical price breaks past a 95% confidence interval, created by Monte-Carlo. Please see the graph below. - Blue graph is the empircal price series (left-axis) - Yellow graph is the 97.5 percentile of the Monte-Carlo distribution (left-axis) - Green graph is the 2.5 percentile of the Monte-Carlo distribution (left-axis) - Orange dots are instances when empirical price > 97.5 percentile; a break (left-axis) - Green dots are instances when empirical price < 2.5 percentile; a break (left-axis) - Red graph is the model volatilities feeding into the Monte-Calro simulation; volatilities are calibrated every 3 months (right-axis) In an ideal state, the Monte-Carlo simulation perfectly contains the number of breaks to 5% of the number of observations (hence the 95% confidence interval). In this instance, there are more. I want to know if the breaks occur at times where the model volatility is too low. As such, I want to determine the relationship between low model volatilities and incidences of breaks. The first thought is to perform an OLS regression. I'm having trouble selecting the correct regressor and regressand. Once this has been selected appropriately, I'll perform hypothesis testing on a coefficient. Edit: Or a Chi-Sqaured Test? Thank you
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