Regressing Implied Volatility on Realized Volatility: Model Choices and Caveats

Summary

The document proposes studying whether one-month at-the-money European option implied volatility responds more than proportionally to changes in realized volatility. Its initial approach is a linear regression of implied volatility on realized volatility, with the slope interpreted as a measure of sensitivity and a value above one treated as possible overreaction. The author reports that augmented Dickey-Fuller tests found both series stationary at the stated significance level, motivating regression in levels rather than a cointegration analysis.

Realized volatility is defined from five-minute log returns over the trading day, while implied volatility is averaged from options with roughly one-month maturity. The document raises questions about whether the regression interpretation is valid, whether the intercept can represent option pricing costs, and whether residuals should be orthogonal. It contains no fitted coefficients or empirical results. The proposed interpretation therefore remains a hypothesis: mismatched measurement windows, option-market effects, dependence over time, and other model assumptions would need consideration before concluding that the slope measures overreaction.

Key ideas

• The proposed model regresses one-month at-the-money implied volatility on realized volatility.
• The author interprets a slope above one as potential overreaction, but provides no fitted estimate.
• Both series are reported as stationary under the stated augmented Dickey-Fuller test.
• The intercept's interpretation as hedging or pricing costs is acknowledged as uncertain.
• The volatility measures use different sampling and maturity conventions that affect interpretation.

Tags

# Modelling the relationship between the Implied and the Realized Volatility


# Modelling the relationship between the Implied and the Realized Volatility












I am trying to statistically model the relationship between implied volatility of European ATM options (expiring in 1 month) and the realized volatility of the underlying.

I am interested in the question if the implied volatility overreacts to the changes in realized volatility and by how much on average.

My first intuition was to see if these timeseries (IV and RV) are cointegrated. However, I find that both these timeseries are stationary (ADF test) at 5% significance. Therefore, I am thinking to fit a simple linear model:

$$ IV_t = \alpha + \beta RV_t + \epsilon$$

- $\alpha$ would be representative of cost of pricing the option such as hedging costs etc (I agree this is a dicey assumption).

- $\beta > 1$ would measure the degree of overreaction to changes in RV.

- $\epsilon$ are expected to be orthogonal.

- $RV$ is the annualized standard deviation of 5-minute log returns (over all the 78 5-minute intervals in a 6.5-hour trading day.

- $IV$ is the average implied volatility of ATM European options expiring the second Friday of the next month (maturity is somewhere between 28-31 days).

My question is:

- Are my intuitions pointing me to right direction?

- Is the model specification correct?

- Is there anything else I need to be careful about?

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