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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:

  1. Are my intuitions pointing me to right direction?
  2. Is the model specification correct?
  3. Is there anything else I need to be careful about?
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  • $\begingroup$ Are the periods of IV and RV contemporaneous? ($IV_{t,t+1}$ and $RV_{t,t+1}$) Or are they just at the same point in time? ($IV_{t,t+1}$ and $RV_{t-1,t}$) $\endgroup$
    – KaiSqDist
    Commented Oct 13 at 18:15
  • $\begingroup$ For each trading day $RV$ is annualised standard deviation sampled every 5 minutes. $IV$ is the average $IV$ of all ATM options quoted on that trading day. So in a way they represent what happened on that particular trading day. $\endgroup$
    – DrStrangeLove
    Commented Oct 13 at 20:07
  • $\begingroup$ So $RV$ is the standard deviation of 5-minute returns for the whole day? What is the maturity of the ATM options? There seems to be a mismatch in your regression. $\endgroup$
    – KaiSqDist
    Commented Oct 14 at 7:10
  • $\begingroup$ $$ RV = \sqrt{6.5 \times 12 \times 252} \times \sigma_{5m} $$ - $ \sigma_{5m} $ is the standard deviation of 5-minute log returns (over all the 78 5-minute intervals in a 6.5-hour trading day) which is multiplied by the square root of 12 five-minute intervals every hour, then by 6.5 hours every trading day, then by 252 to annualize the standard deviation. - $IV$ is the average Black Scholes implied volatility of ATM European options expiring the second Friday of the next month (maturity is somewhere between 28-31 days). At the end of the trading day, you can observe both these variables. $\endgroup$
    – DrStrangeLove
    Commented Oct 14 at 17:58
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    $\begingroup$ @DrStrangeLove I would like to reopen this question, but I need you to clarify it a little bit: (1) just keep one question instead of 3, (2) include in the question the clarifications you provided in remarks. $\endgroup$
    – lehalle
    Commented Oct 15 at 6:40

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